Publications by Mark Spencer Rudner

  • 2020
    • Exponentially long lifetime of universal quasi-steady states in topological Floquet pumps - Abstract
      • We investigate a mechanism to transiently stabilize topological phenomena in long-lived quasi-steady states of isolated quantum many-body systems driven at low frequencies. We obtain an analytical bound for the lifetime of the quasi-steady states which is exponentially large in the inverse driving frequency. Within this lifetime, the quasi-steady state is characterized by maximum entropy subject to the constraint of fixed number of particles in the system's Floquet-Bloch bands. In such a state, all the non-universal properties of these bands are washed out, hence only the topological properties persist.
    • Tobias Gulden, Erez Berg, Mark S. Rudner, Netanel H. Lindner
      1901.08385v3 [pdf]

    • Universal Lindblad equation for open quantum systems - Abstract
      • We develop a novel Markovian master equation in the Lindblad form that enables the efficient study of a wide range of quantum few- and many-body systems coupled to external baths. The validity of the master equation is based entirely on properties of the bath and the system-bath coupling, without any requirements on the level structure within the system itself. The master equation is derived using a Markov approximation that is distinct from that used in earlier approaches. We provide a rigorous bound for the error induced by this Markov approximation; the error is controlled by a dimensionless combination of intrinsic correlation and relaxation timescales of the bath. Our master equation is accurate on the same level of approximation as the Bloch-Redfield equation. In contrast to the Bloch-Redfield approach, our approach ensures preservation of the positivity of the density matrix. As a result, our method is robust, and can be solved efficiently using stochastic evolution of pure states (rather than density matrices). We discuss how our method can be applied to static or driven quantum many-body systems, and illustrate its power through numerical simulation of a spin chain that would be challenging to treat by existing methods.
    • Frederik Nathan, Mark S. Rudner
      2004.01469v1 [pdf]

    • The Floquet Engineer's Handbook - Abstract
      • We provide a pedagogical technical guide to many of the key theoretical tools and ideas that underlie work in the field of Floquet engineering. We hope that this document will serve as a useful resource for new researchers aiming to enter the field, as well as experienced researchers who wish to gain new insight into familiar or possibly unfamiliar methods. This guide was developed out of supplementary material as a companion to our recent review, "Band structure engineering and non-equilibrium dynamics in Floquet topological insulators," arXiv:1909.02008. The primary focus is on analytical techniques relevant for Floquet-Bloch band engineering and related many-body dynamics. We will continue to update this document over time to include additional content, and welcome suggestions for further topics to consider.
    • Mark S. Rudner, Netanel H. Lindner
      2003.08252v1 [pdf]

    • Quantum phase-locking and frequency down-conversion in a driven cavity-qubit system - Abstract
      • We study a periodically driven qubit coupled to a quantized cavity mode. Despite its apparent simplicity, this system supports a rich variety of exotic phenomena, such as topological frequency conversion as recently discovered in [PRX 7, 041008 (2017)]. Here we report on a qualitatively different phenomenon that occurs in this platform, namely the phase-locking of the cavity mode to a rational fraction $r/q$ of the driving frequency $\Omega$. The phase-locking regime is characterized by the emergence of $q$-tuplets of stationary (Floquet) states whose quasienergies are separated by $\Omega/q$, up to exponentially small corrections. The Wigner functions of these states are nearly identical, and exhibit highly-regular and symmetric structure in phase space. Similarly to Floquet time crystals, these phase-locked states underlie discrete time-translation symmetry breaking in the model. We develop two complementary approaches for analyzing and predicting phase locking in the model, and use them to identify the conditions under which it occurs.
    • Frederik Nathan, Gil Refael, Mark S. Rudner, Ivar Martin
      2003.05648v1 [pdf]

    • Nagaoka ferromagnetism observed in a quantum dot plaquette - Abstract
      • Engineered, highly-controllable quantum systems hold promise as simulators of emergent physics beyond the capabilities of classical computers. An important problem in many-body physics is itinerant magnetism, which originates purely from long-range interactions of free electrons and whose existence in real systems has been subject to debate for decades. Here we use a quantum simulator consisting of a four-site square plaquette of quantum dots to demonstrate Nagaoka ferromagnetism. This form of itinerant magnetism has been rigorously studied theoretically but has remained unattainable in experiment. We load the plaquette with three electrons and demonstrate the predicted emergence of spontaneous ferromagnetic correlations through pairwise measurements of spin. We find the ferromagnetic ground state is remarkably robust to engineered disorder in the on-site potentials and can induce a transition to the low-spin state by changing the plaquette topology to an open chain. This demonstration of Nagaoka ferromagnetism highlights that quantum simulators can be used to study physical phenomena that have not yet been observed in any system before. The work also constitutes an important step towards large-scale quantum dot simulators of correlated electron systems.
    • Juan P. Dehollain, Uditendu Mukhopadhyay, Vincent P. Michal, Yao Wang, Bernhard Wunsch, Christian Reichl, Werner Wegscheider, Mark S. Rudner, Eugene Demler, Lieven M. K. Vandersypen
      DOI: 10.1038/s41586-020-2051-0
      1904.05680v3 [pdf]

    • Topological transition of a non-Markovian dissipative quantum walk - Abstract
      • We extend non-Hermitian topological quantum walks on a Su-Schrieffer-Heeger (SSH) lattice [M. S. Rudner and L. Levitov, Phys. Rev. Lett. 102, 065703 (2009)] to the case of non-Markovian evolution. This non-Markovian model is established by coupling each unit cell in the SSH lattice to a reservoir formed by a quasi-continuum of levels. We find a topological transition in this model even in the case of non-Markovian evolution, where the walker may visit the reservoir and return to the SSH lattice at a later time. The existence of a topological transition does, however, depend on the low-frequency properties of the reservoir, characterized by a spectral density $J(\epsilon)\propto |\epsilon|^\alpha$. In particular, we find a robust topological transition for a sub-Ohmic ($\alpha<1$) ($\alpha a and but for no ohmic reservoir, super-ohmic topological transition>1$) reservoir. This behavior is directly related to the well-known localization transition for the spin-boson model. We confirm the presence of non-Markovian dynamics by explicitly evaluating a measure of Markovianity for this model.
    • A. Ricottone, M. S. Rudner, W. A. Coish
      2003.00350v1 [pdf]

  • 2019
    • Current-Induced Gap Opening in Interacting Topological Insulator Surfaces - Abstract
      • Two-dimensional topological insulators (TIs) host gapless helical edge states that are predicted to support a quantized two-terminal conductance. Quantization is protected by time-reversal symmetry, which forbids elastic backscattering. Paradoxically, the current-carrying state itself breaks the time-reversal symmetry that protects it. Here we show that the combination of electron-electron interactions and momentum-dependent spin polarization in helical edge states gives rise to feedback through which an applied current opens a gap in the edge state dispersion, thereby breaking the protection against elastic backscattering. Current-induced gap opening is manifested via a nonlinear contribution to the system's $I-V$ characteristic, which persists down to zero temperature. We discuss prospects for realizations in recently discovered large bulk band gap TIs, and an analogous current-induced gap opening mechanism for the surface states of three-dimensional TIs.
    • Ajit C. Balram, Karsten Flensberg, Jens Paaske, Mark S. Rudner
      Journal reference: Phys. Rev. Lett. 123, 246803 (2019) [ 1901.08067v2 ]
      DOI: 10.1103/PhysRevLett.123.246803

    • Quantized large-bias current in the anomalous Floquet-Anderson insulator - Abstract
      • We study two-terminal transport through two-dimensional periodically driven systems in which all bulk Floquet eigenstates are localized by disorder. We focus on the Anomalous Floquet-Anderson Insulator (AFAI) phase, a topologically-nontrivial phase within this class, which hosts topologically protected chiral edge modes coexisting with its fully localized bulk. We show that the unique properties of the AFAI yield remarkable far-from-equilibrium transport signatures: for a large bias between leads, a quantized amount of charge is transported through the system each driving period. Upon increasing the bias, the chiral Floquet edge mode connecting source to drain becomes fully occupied and the current rapidly approaches its quantized value.
    • Arijit Kundu, Mark Rudner, Erez Berg, Netanel H. Lindner
      Journal reference: Phys. Rev. B 101, 041403 (2020) [ 1708.05023v2 ]
      DOI: 10.1103/PhysRevB.101.041403

    • Ab Initio Exact Diagonalization Simulation of the Nagaoka Transition in Quantum Dots - Abstract
      • Recent progress of quantum simulators provides insight into the fundamental problems of strongly correlated systems. To adequately assess the accuracy of these simulators, the precise modeling of the many-body physics, with accurate model parameters, is crucially important. In this paper, we introduce an \emph{ab intio} exact diagonalization framework to compute the correlated physics of a few electrons in artificial potentials. We apply this approach to a quantum-dot system and study the magnetism of the correlated electrons, obtaining good agreement with recent experimental measurements. Through dot separation, potential detuning and control of single tunneling, we examine the Nagaoka transition and determine the robustness of the ferromagnetic state. While the standard Nagaoka theorem considers only a single-band Hubbard model, in this work we perform extensive $ab$ $intio$ calculations that include realistic multi-orbital conditions in which the level splitting is smaller than the interactions. This simulation complements the experiments and provides insight into the formation of ferromagnetism in correlated systems. More generally, our calculation sets the stage for further theoretical analysis of analog quantum simulators at a quantitative level.
    • Yao Wang, Juan Pablo Dehollain, Fang Liu, Uditendu Mukhopadhyay, Mark S. Rudner, Lieven M. K. Vandersypen, Eugene Demler
      Journal reference: Phys. Rev. B 100, 155133 (2019) [ 1907.01658v3 ]
      DOI: 10.1103/PhysRevB.100.155133

    • Charge and spin textures of Ising quantum Hall ferromagnet domain walls - Abstract
      • We investigate the charge and spin structures associated with arbitrary smooth polarization textures in Ising (integer) quantum Hall ferromagnets. We consider the case where the two polarizations (denoted "pseudospin" up and down) correspond to states with opposite physical spin and different Landau level indices, $n\uparrow$ and $m\downarrow$. We derive analytic expressions for the charge and spin densities, as functions of the underlying pseudospin texture, and use these results to investigate different types of linear domain walls, both analytically and numerically. We find that any smooth domain wall between two oppositely polarized domains carries a universal quantized charge dipole density proportional to the difference of Landau level indices, $n-m$. Additionally, non-uniformities in the domain wall may give rise to excess net charge localized at the domain wall. Interestingly, the physical spin density associated with the domain wall generally exhibits a much more complex multipolar structure than that of the pseudospin texture. These results should for example help to elucidate the mechanisms underlying nuclear electric resonance and nuclear polarization oscillations in Ising quantum Hall systems.
    • Jeroen Danon, Ajit C. Balram, Samuel Sánchez, Mark S. Rudner
      Journal reference: Phys. Rev. B 100, 235406 (2019) [ 1909.13249v1 ]
      DOI: 10.1103/PhysRevB.100.235406

    • Floquet topological insulators: from band structure engineering to novel non-equilibrium quantum phenomena - Abstract
      • We review methods for using time-periodic fields (e.g., laser or microwave fields) to induce non-equilibrium topological phenomena in quantum many-body systems. We discuss how such fields can be used to change the topological properties of the single particle spectrum, and key experimental demonstrations in solid state, cold atomic, and photonic systems. The single particle Floquet band structure provides a stage on which the system's dynamics play out; the crucial question is then how to obtain robust topological behaviour in the many-particle setting. In the regime of mesoscopic transport, we discuss manifestations of topological edge states induced in the Floquet spectrum. Outside the context of mesoscopic transport, the main challenge of inducing stable topological phases in many-body Floquet systems is their tendency to absorb energy from the drive and thereby to heat up. We discuss three routes to overcoming this challenge: long-lived transient dynamics and prethermalization, disorder-induced many-body localization, and engineered couplings to external baths. We discuss the types of phenomena that can be explored in each of these regimes, and their experimental realizations.
    • Mark S. Rudner, Netanel H. Lindner
      1909.02008v1 [pdf]

    • Hierarchy of many-body invariants and quantized magnetization in anomalous Floquet insulators - Abstract
      • The anomalous Floquet insulator (AFI) is an intrinsically nonequilibrium topological phase that arises in disordered, periodically driven systems. In the noninteracting case, the nontrivial topology of the AFI gives rise to a quantized current at the edge, and a quantized magnetization in the bulk. Recent work indicates that the AFI is compatible with many-body localization, and is thus stable in the presence of interactions. Here we study the bulk topological properties of the AFI in the interacting case. Compared with the non-interacting case, interactions lead to an enrichment of the topological phase diagram: we find that the AFI is characterized by a family of bulk topological invariants, which are encoded in the time-averaged magnetization density operator of the system. A nontrivial value of the $\ell$-th invariant signifies a quantized contribution to the magnetization density in filled regions arising from correlated $\ell$-particle circulating orbits. The non-interacting ''anomalous Floquet-Anderson insulator'' (AFAI) is characterized by a nonzero value of the first invariant, with all higher invariants equal to zero. We discuss novel strongly correlated anomalous phases, with nonzero values of higher invariants, that are topologically distinct from the AFAI.
    • Frederik Nathan, Dmitry A. Abanin, Netanel H. Lindner, Erez Berg, Mark S. Rudner
      1907.12228v1 [pdf]

    • Parton construction of particle-hole-conjugate Read-Rezayi parafermion fractional quantum Hall states and beyond - Abstract
      • The Read-Rezayi (RR) parafermion states form a series of exotic non-Abelian fractional quantum Hall (FQH) states at filling $\nu = k/(k+2)$. Computationally, the wave functions of these states are prohibitively expensive to generate for large systems. We introduce a series of parton states, denoted "$\bar{2}^{k}1^{k+1}$," and show that they lie in the same universality classes as the particle-hole-conjugate RR ("anti-RR") states. Our analytical results imply that a $(U(1)_{k+1} \times U(2k)_{-1})/(SU(k)_{-2} \times U(1)_{-1})$ coset conformal field theory describes the edge excitations of the $\bar{2}^{k}1^{k+1}$ state, suggesting non-trivial dualities with respect to previously known descriptions. The parton construction allows wave functions in anti-RR phases to be generated for hundreds of particles. We further propose the parton sequence "$\bar{n}\bar{2}^{2}1^{4}$," with $n=1,2,3$, to describe the FQH states observed at $\nu=2+1/2,~2+2/5$ and $2+3/8$.
    • Ajit C. Balram, Maissam Barkeshli, Mark S. Rudner
      Journal reference: Phys. Rev. B 99, 241108 (2019) [ 1902.04173v2 ]
      DOI: 10.1103/PhysRevB.99.241108

    • Topology and Broken Symmetry in Floquet Systems - Abstract
      • Floquet systems are governed by periodic, time-dependent, Hamiltonians. Prima facie they should absorb energy from the external drives involved in modulating their couplings and heat up to infinite temperature. However this unhappy state of affairs can be avoided in many ways. Instead, as has become clear from much recent work, they can exhibit a variety of nontrivial behavior---some of it impossible in undriven systems. In this review we describe the main ideas and themes of this work: novel Floquet drives which exhibit nontrivial topology in single-particle systems, the existence and classification of exotic Floquet drives in interacting systems, and the attendant notion of many-body Floquet phases and arguments for their stability to heating.
    • Fenner Harper, Rahul Roy, Mark S. Rudner, S. L. Sondhi
      1905.01317v2 [pdf]

    • Anomalous Floquet insulators - Abstract
      • We demonstrate the existence of a two-dimensional anomalous Floquet insulator (AFI) phase: an interacting (periodically-driven) non-equilibrium topological phase of matter with no counterpart in equilibrium. The AFI is characterized by a many-body localized bulk, exhibiting nontrivial micromotion within a driving period, and delocalized (thermalizing) chiral states at its boundaries. For a geometry without edges, we argue analytically that the bulk may be many-body localized in the presence of interactions, deriving conditions where stability is expected. We investigate the interplay between the thermalizing edge and the localized bulk via numerical simulations of an AFI in a geometry with edges. We find that non-uniform particle density profiles remain stable in the bulk up to the longest timescales that we can access, while the propagating edge states persist and thermalize, despite being coupled to the bulk. These findings open the possibility of observing quantized edge transport in interacting systems at high temperature. The analytical approach introduced in this paper can be used to study the stability of other anomalous Floquet phases.
    • Frederik Nathan, Dmitry Abanin, Erez Berg, Netanel H. Lindner, Mark S. Rudner
      Journal reference: Phys. Rev. B 99, 195133 (2019) [ 1712.02789v4 ]
      DOI: 10.1103/PhysRevB.99.195133

    • Floquet metal to insulator phase transitions in semiconductor nanowires - Abstract
      • We study steady-states of semiconductor nanowires subjected to strong resonant time-periodic drives. The steady-states arise from the balance between electron-phonon scattering, electron-hole recombination via photo-emission, and Auger scattering processes. We show that tuning the strength of the driving field drives a transition between an electron-hole metal (EHM) phase and a Floquet insulator (FI) phase. We study the critical point controlling this transition. The EHM-to-FI transition can be observed by monitoring the presence of peaks in the density-density response function which are associated with the Fermi momentum of the EHM phase, and are absent in the FI phase. Our results may help guide future studies towards inducing novel non-equilibrium phases of matter by periodic driving.
    • Iliya Esin, Mark S. Rudner, Netanel H. Lindner
      1904.07856v1 [pdf]

  • 2018
    • Fractional Quantum Hall Effect at $ν=2+6/13$: The Parton Paradigm for the Second Landau Level - Abstract
      • The unexpected appearance of a fractional quantum Hall effect (FQHE) plateau at $\nu=2+6/13$~ [Kumar \emph{et al.}, Phys. Rev. Lett. {\bf 105}, 246808 (2010)] offers a clue into the physical mechanism of the FQHE in the second Landau level (SLL). Here we propose a "$\bar{3}\bar{2}111$" parton wave function, which is topologically distinct from the 6/13 state in the lowest Landau level. We demonstrate the $\bar{3}\bar{2}111$ state to be a good candidate for the $\nu=2+6/13$ FQHE, and make predictions for experimentally measurable properties that can reveal the nature of this state. Furthermore, we propose that the "$\bar{n}\bar{2}111$" family of parton states naturally describes many observed SLL FQHE plateaus.
    • Ajit C. Balram, Sutirtha Mukherjee, Kwon Park, Maissam Barkeshli, Mark S. Rudner, J. K. Jain
      Journal reference: Phys. Rev. Lett. 121, 186601 (2018) [ 1807.02997v2 ]
      DOI: 10.1103/PhysRevLett.121.186601

    • Topological transport in the steady state of a quantum particle with dissipation - Abstract
      • We study topological transport in the steady state of a quantum particle hopping on a one-dimensional lattice in the presence of dissipation. The model exhibits a rich phase structure, with the average particle velocity in the steady state playing the role of a non-equilibrium order parameter. Within each phase the average velocity is proportional to a topological winding number and to the inverse of the average time between quantum jumps. While the average velocity depends smoothly on system parameters within each phase, nonanalytic behavior arises at phase transition points. We show that certain types of spatial boundaries between regions where different phases are realized host a number of topological bound states which is equal to the difference between the winding numbers characterizing the phases on the two sides of the boundary. These topological bound states are attractors for the dynamics; in cases where the winding number changes by more than one when crossing the boundary, the subspace of topological bound states forms a dark, decoherence free subspace for the dissipative system. Finally we discuss how the dynamics we describe can be realized in a simple cavity or circuit QED setup, where the topological boundary mode emerges as a robust coherent state of the light field.
    • Michael J. Kastoryano, Mark S. Rudner
      Journal reference: Phys. Rev. B 99, 125118 (2019) [ 1808.06963v1 ]
      DOI: 10.1103/PhysRevB.99.125118

    • Parton construction of a wave function in the anti-Pfaffian phase - Abstract
      • In this work we propose a parton state as a candidate state to describe the fractional quantum Hall effect in the half-filled second Landau level. The wave function for this parton state is $\mathcal{P}_{\rm LLL} \Phi_{1}^3[\Phi_{2}^{*}]^{2}\sim\Psi^{2}_{2/3}/\Phi_{1}$ and in the spherical geometry it occurs at the same flux as the anti-Pfaffian state. This state has a good overlap with the anti-Pfaffian state and with the ground state obtained by exact diagonalization, using the second Landau level Coulomb interaction pseudopotentials for an ordinary semiconductor such as GaAs. By calculating the entanglement spectrum we show that this state lies in the same phase as the anti-Pfaffian state. A major advantage of this parton state is that its wave function can be evaluated for large systems, which makes it amenable to variational calculations. In the appendix of this work we have numerically assessed the validity of another candidate state at filling factor $\nu=5/2$, namely the particle-hole-symmetric Pfaffian (PH-Pfaffian) state. We find that the proposed candidate wave function for the PH-Pfaffian state is particle-hole symmetric to a high degree but it does not appear to arise as the ground state of any simple Hamiltonian with two-body interactions.
    • Ajit C. Balram, Maissam Barkeshli, Mark S. Rudner
      Journal reference: Phys. Rev. B 98, 035127 (2018) [ 1803.10427v2 ]
      DOI: 10.1103/PhysRevB.98.035127

    • Berryogenesis: self-induced Berry flux and spontaneous non-equilibrium magnetism - Abstract
      • Spontaneous symmetry breaking is central to the description of interacting phases of matter. Here we reveal a new mechanism through which a driven interacting system subject to a time-reversal symmetric driving field can spontaneously magnetize. We show that the strong internal ac fields of a metal driven close to its plasmon resonance may enable Berryogenesis: the spontaneous generation of a self-induced Bloch band Berry flux. The self-induced Berry flux supports and is sustained by a circulating plasmonic motion, which may arise even for a linearly polarized driving field. This non-equilibrium phase transition occurs above a critical driving amplitude, and may be of either continuous or discontinuous type. Berryogenesis relies on feedback due to interband coherences induced by internal fields, and may readily occur in a wide variety of multiband systems. We anticipate that graphene devices, in particular, provide a natural platform to achieve Berryogenesis and plasmon-mediated spontaneous non-equilibrium magnetization in present-day devices.
    • Mark S. Rudner, Justin C. W. Song
      DOI: 10.1038/s41567-019-0578-5
      1807.01708v1 [pdf]

    • Steady states of interacting Floquet insulators - Abstract
      • Floquet engineering offers tantalizing opportunities for controlling the dynamics of quantum many body systems and realizing new nonequilibrium phases of matter. However, this approach faces a major challenge: generic interacting Floquet systems absorb energy from the drive, leading to uncontrolled heating which washes away the sought after behavior. How to achieve and control a non-trivial nonequilibrium steady state is therefore of crucial importance. In this work, we study the dynamics of an interacting one-dimensional periodically-driven electronic system coupled to a phonon heat bath. Using the Floquet-Boltzmann equation (FBE) we show that the electronic populations of the Floquet eigenstates can be controlled by the dissipation. We find the regime in which the steady state features an insulatorlike filling of the Floquet bands, with a low density of additional excitations. Furthermore, we develop a simple rate equation model for the steady state excitation density that captures the behavior obtained from the numerical solution of the FBE over a wide range of parameters.
    • Karthik I. Seetharam, Charles-Edouard Bardyn, Netanel H. Lindner, Mark S. Rudner, Gil Refael
      Journal reference: Phys. Rev. B 99, 014307 (2019) [ 1806.10620v1 ]
      DOI: 10.1103/PhysRevB.99.014307

    • Topological phase transition measured in a dissipative metamaterial - Abstract
      • We construct a metamaterial from radio-frequency harmonic oscillators, and find two topologically distinct phases resulting from dissipation engineered into the system. These phases are distinguished by a quantized value of bulk energy transport. The impulse response of our circuit is measured and used to reconstruct the band structure and winding number of circuit eigenfunctions around a dark mode. Our results demonstrate that dissipation can lead to topological transport in a much wider class of physical systems than considered before.
    • Eric I. Rosenthal, Nicole K. Ehrlich, Mark S. Rudner, Andrew P. Higginbotham, K. W. Lehnert
      Journal reference: Phys. Rev. B 97, 220301 (2018) [ 1802.02243v2 ]
      DOI: 10.1103/PhysRevB.97.220301

  • 2017
    • Many-Body Dynamics and Gap Opening in Interacting Periodically Driven Systems - Abstract
      • We study the transient dynamics in a two-dimensional system of interacting Dirac fermions subject to a quenched drive with circularly polarized light. In the absence of interactions, the drive opens a gap at the Dirac point in the quasienergy spectrum, inducing nontrivial band topology. Here we investigate the dynamics of this gap opening process in the presence of interactions, as captured by the generalized spectral function and correlators probed by photoemission experiments. Through a mechanism akin to that known for equilibrium systems, interactions renormalize and enhance the induced gap over its value for the non-interacting system. We additionally study the heating that naturally accompanies driving in the interacting system, and discuss the regimes where dynamical gap emergence and enhancement can be probed before heating becomes significant.
    • Ervand Kandelaki, Mark S. Rudner
      Journal reference: Phys. Rev. Lett. 121, 036801 (2018) [ 1709.04448v2 ]
      DOI: 10.1103/PhysRevLett.121.036801

    • Quantized transport and steady states of Floquet topological insulators - Abstract
      • We study the open system dynamics and steady states of two dimensional Floquet topological insulators: systems in which a topological Floquet-Bloch spectrum is induced by an external periodic drive. We solve for the bulk and edge state carrier distributions, taking into account energy and momentum relaxation through radiative recombination and electron-phonon interactions, as well as coupling to an external lead. We show that the resulting steady state resembles a topological insulator in the Floquet basis. The particle distribution in the Floquet edge modes exhibits a sharp feature akin to the Fermi level in equilibrium systems, while the bulk hosts a small density of excitations. We discuss two-terminal transport and describe the regimes where edge-state transport can be observed. Our results show that signatures of the non-trivial topology persist in the non-equilibrium steady state.
    • Iliya Esin, Mark S. Rudner, Gil Refael, Netanel H. Lindner
      Journal reference: Phys. Rev. B 97, 245401 (2018) [ 1710.09404v1 ]
      DOI: 10.1103/PhysRevB.97.245401

    • Quantized Magnetization Density in Periodically Driven Systems - Abstract
      • We study micromotion in two-dimensional periodically driven systems in which all bulk Floquet eigenstates are localized by disorder. We show that this micromotion gives rise to a quantized time-averaged magnetization density when the system is filled with fermions. Furthermore we find that a quantized current flows around the boundary of any filled region of finite extent. The quantization has a topological origin: we relate the time-averaged magnetization density to the winding number characterizing the new phase identified in Phys. Rev. X 6, 021013 (2016). We thus establish that the winding number invariant can be accessed directly in bulk measurements, and propose an experimental protocol to do so using interferometry in cold atom based realizations.
    • Frederik Nathan, Mark S. Rudner, Netanel H. Lindner, Erez Berg, Gil Refael
      Journal reference: Phys. Rev. Lett. 119, 186801 (2017) [ 1610.03590v3 ]
      DOI: 10.1103/PhysRevLett.119.186801

    • Spectrum of the Nuclear Environment for GaAs Spin Qubits - Abstract
      • Using a singlet-triplet spin qubit as a sensitive spectrometer of the GaAs nuclear spin bath, we demonstrate that the spectrum of Overhauser noise agrees with a classical spin diffusion model over six orders of magnitude in frequency, from 1 mHz to 1 kHz, is flat below 10 mHz, and falls as $1/f^2$ for frequency $f \! \gtrsim \! 1$ Hz. Increasing the applied magnetic field from 0.1 T to 0.75 T suppresses electron-mediated spin diffusion, which decreases spectral content in the $1/f^2$ region and lowers the saturation frequency, each by an order of magnitude, consistent with a numerical model. Spectral content at megahertz frequencies is accessed using dynamical decoupling, which shows a crossover from the few-pulse regime ($\lesssim \! 16$ $\pi$-pulses), where transverse Overhauser fluctuations dominate dephasing, to the many-pulse regime ($\gtrsim \! 32$ $\pi$-pulses), where longitudinal Overhauser fluctuations with a $1/f$ spectrum dominate.
    • Filip K. Malinowski, Frederico Martins, Łukasz Cywiński, Mark S. Rudner, Peter D. Nissen, Saeed Fallahi, Geoffrey C. Gardner, Michael J. Manfra, Charles M. Marcus, Ferdinand Kuemmeth
      Journal reference: Phys. Rev. Lett. 118, 177702 (2017) [ 1701.01855v2 ]
      DOI: 10.1103/PhysRevLett.118.177702

    • Fermi arc plasmons in Weyl semimetals - Abstract
      • In the recently discovered Weyl semimetals, the Fermi surface may feature disjoint, open segments -- the so-called Fermi arcs -- associated with topological states bound to exposed crystal surfaces. Here we show that the collective dynamics of electrons near such surfaces sharply departs from that of a conventional three-dimensional metal. In magnetic systems with broken time reversal symmetry, the resulting Fermi arc plasmons (FAPs) are chiral, with dispersion relations featuring open, hyperbolic constant frequency contours. As a result, a large range of surface plasmon wave vectors can be supported at a given frequency, with corresponding group velocity vectors directed along a few specific collimated directions. Fermi arc plasmons can be probed using near field photonics techniques, which may be used to launch highly directional, focused surface plasmon beams. The unusual characteristics of FAPs arise from the interplay of bulk and surface Fermi arc carrier dynamics, and give a window into the unusual Fermiology of Weyl semimetals.
    • Justin C. W. Song, Mark S. Rudner
      Journal reference: Phys. Rev. B 96, 205443 (2017) [ 1702.00022v1 ]
      DOI: 10.1103/PhysRevB.96.205443

    • Notch filtering the nuclear environment of a spin qubit - Abstract
      • Electron spins in gate-defined quantum dots provide a promising platform for quantum computation. In particular, spin-based quantum computing in gallium arsenide takes advantage of the high quality of semiconducting materials, reliability in fabricating arrays of quantum dots, and accurate qubit operations. However, the effective magnetic noise arising from the hyperfine interaction with uncontrolled nuclear spins in the host lattice constitutes a major source of decoherence. Low frequency nuclear noise, responsible for fast (10 ns) inhomogeneous dephasing, can be removed by echo techniques. High frequency nuclear noise, recently studied via echo revivals, occurs in narrow frequency bands related to differences in Larmor precession of the three isotopes $\mathbf{^{69}Ga}$, $\mathbf{^{71}Ga}$, and $\mathbf{^{75}As}$. Here we show that both low and high frequency nuclear noise can be filtered by appropriate dynamical decoupling sequences, resulting in a substantial enhancement of spin qubit coherence times. Using nuclear notch filtering, we demonstrate a spin coherence time ($\mathbf{T_{2}}$) of 0.87 ms, five orders of magnitude longer than typical exchange gate times, and exceeding the longest coherence times reported to date in Si/SiGe gate-defined quantum dots.
    • F. K. Malinowski, F. Martins, P. D. Nissen, E. Barnes, Ł. Cywiński, M. S. Rudner, S. Fallahi, G. C. Gardner, M. J. Manfra, C. M. Marcus, F. Kuemmeth
      Journal reference: Nat. Nanotechnol. 12, 16-20 (2017) [ 1601.06677v3 ]
      DOI: 10.1038/nnano.2016.170

  • 2016
    • Direct Probe of Topological Invariants Using Bloch Oscillating Quantum Walks - Abstract
      • The topology of a single-particle band structure plays a fundamental role in understanding a multitude of physical phenomena. Motivated by the connection between quantum walks and such topological band structures, we demonstrate that a simple time-dependent, Bloch-oscillating quantum walk enables the direct measurement of topological invariants. We consider two classes of one-dimensional quantum walks and connect the global phase imprinted on the walker with its refocusing behavior. By disentangling the dynamical and geometric contributions to this phase we describe a general strategy to measure the topological invariant in these quantum walks. As an example, we propose an experimental protocol in a circuit QED architecture where a superconducting transmon qubit plays the role of the coin, while the quantum walk takes place in the phase space of a cavity.
    • Vinay V. Ramasesh, Emmanuel Flurin, Mark S. Rudner, Irfan Siddiqi, Norman Y. Yao
      Journal reference: Phys. Rev. Lett. 118, 130501 (2017) [ 1609.09504v1 ]
      DOI: 10.1103/PhysRevLett.118.130501

    • Composite Topological Excitations in Ferromagnet-Superconductor Heterostructures - Abstract
      • We investigate the formation of a new type of composite topological excitation -- the skyrmion-vortex pair (SVP) -- in hybrid systems consisting of coupled ferromagnetic and superconducting layers. Spin-orbit interaction in the superconductor mediates a magnetoelectric coupling between the vortex and the skyrmion, with a sign (attractive or repulsive) that depends on the topological indices of the constituents. We determine the conditions under which a bound SVP is formed, and characterize the range and depth of the effective binding potential through analytical estimates and numerical simulations. Furthermore, we develop a semiclassical description of the coupled skyrmion-vortex dynamics and discuss how SVPs can be controlled by applied spin currents.
    • Kjetil M. D. Hals, Michael Schecter, Mark S. Rudner
      Journal reference: Phys. Rev. Lett. 117, 017001 (2016) [ 1603.07550v2 ]
      DOI: 10.1103/PhysRevLett.117.017001

    • Survival, decay, and topological protection in non-Hermitian quantum transport - Abstract
      • Non-Hermitian quantum systems can exhibit unique observables characterizing topologically protected transport in the presence of decay. The topological protection arises from winding numbers associated with non-decaying dark states, which are decoupled from the environment and thus immune to dissipation. Here we develop a classification of topological dynamical phases for one-dimensional quantum systems with periodically-arranged absorbing sites. This is done using the framework of Bloch theory to describe the dark states and associated topological invariants. The observables, such as the average particle displacement over its life span, feature quantized contributions that are governed by the winding numbers of cycles around dark-state submanifolds in the Hamiltonian parameter space. Changes in the winding numbers at topological transitions are manifested in non-analytic behavior of the observables. We discuss the conditions under which nontrivial topological phases may be found, and provide examples that demonstrate how additional constraints or symmetries can lead to rich topological phase diagrams.
    • Mark S. Rudner, Michael Levin, Leonid S. Levitov
      1605.07652v1 [pdf]

    • Chiral plasmons without magnetic field - Abstract
      • Plasmons, the collective oscillations of interacting electrons, possess emergent properties that dramatically alter the optical response of metals. We predict the existence of a new class of plasmons -- chiral Berry plasmons (CBPs) -- for a wide range of two-dimensional metallic systems including gapped Dirac materials. As we show, in these materials the interplay between Berry curvature and electron-electron interactions yields chiral plasmonic modes at zero magnetic field. The CBP modes are confined to system boundaries, even in the absence of topological edge states, with chirality manifested in split energy dispersions for oppositely directed plasmon waves. We unveil a rich CBP phenomenology and propose setups for realizing them, including in anomalous Hall metals and optically-pumped 2D Dirac materials. Realization of CBPs will offer a new paradigm for magnetic field-free, sub-wavelength optical non-reciprocity, in the mid IR-THz range, with tunable splittings as large as tens of THz, as well as sensitive all-optical diagnostics of topological bands.
    • Justin C. W. Song, Mark S. Rudner
      Journal reference: Proceedings of the National Academy of Sciences (PNAS) 113(17): 4658-4663 (2016) [ 1506.04743v2 ]
      DOI: 10.1073/pnas.1519086113

    • Universal Chiral Quasisteady States in Periodically Driven Many-Body Systems - Abstract
      • We investigate many-body dynamics in a one-dimensional interacting periodically driven system, based on a partially-filled version of Thouless's topologically quantized adiabatic pump. The corresponding single particle Floquet bands are chiral, with the Floquet spectrum realizing nontrivial cycles around the quasienergy Brillouin zone. For generic filling, with either bosons or fermions, the system is gapless; here the driving cannot be adiabatic and the system is expected to rapidly absorb energy from the driving field. We identify parameter regimes where scattering between Floquet bands of opposite chirality is exponentially suppressed, opening a long time window where the many-body dynamics separately conserves the occupations of the two chiral bands. Within this intermediate time regime we predict that the system reaches a chiral quasi-steady state. This state is universal in the sense that the current it carries is determined solely by the density of particles in each band and the topological winding numbers of the Floquet bands. This remarkable behavior, which holds for both bosons and fermions, may be readily studied experimentally in recently developed cold atom systems.
    • Netanel H. Lindner, Erez Berg, Mark S. Rudner
      Journal reference: Phys. Rev. X 7, 011018 (2017) [ 1603.03053v2 ]
      DOI: 10.1103/PhysRevX.7.011018

    • Nonlocal Polarization Feedback in a Fractional Quantum Hall Ferromagnet - Abstract
      • In a quantum Hall ferromagnet, the spin polarization of the two-dimensional electron system can be dynamically transferred to nuclear spins in its vicinity through the hyperfine interaction. The resulting nuclear field typically acts back locally, modifying the local electronic Zeeman energy. Here we report a non-local effect arising from the interplay between nuclear polarization and the spatial structure of electronic domains in a $\nu=2/3$ fractional quantum Hall state. In our experiments, we use a quantum point contact to locally control and probe the domain structure of different spin configurations emerging at the spin phase transition. Feedback between nuclear and electronic degrees of freedom gives rise to memristive behavior, where electronic transport through the quantum point contact depends on the history of current flow. We propose a model for this effect which suggests a novel route to studying edge states in fractional quantum Hall systems and may account for so-far unexplained oscillatory electronic-transport features observed in previous studies.
    • Szymon Hennel, Beat A. Braem, Stephan Baer, Lars Tiemann, Pirouz Sohi, Dominik Wehrli, Andrea Hofmann, Christian Reichl, Werner Wegscheider, Clemens Rössler, Thomas Ihn, Klaus Ensslin, Mark S. Rudner, Bernd Rosenow
      Journal reference: Phys. Rev. Lett. 116, 136804 (2016) [ 1511.03593v2 ]
      DOI: 10.1103/PhysRevLett.116.136804

    • Filter function formalism beyond pure dephasing and non-Markovian noise in singlet-triplet qubits - Abstract
      • The filter function formalism quantitatively describes the dephasing of a qubit by a bath that causes Gaussian fluctuations in the qubit energies with an arbitrary noise power spectrum. Here, we extend this formalism to account for more general types of noise that couple to the qubit through terms that do not commute with the qubit's bare Hamiltonian. Our approach applies to any power spectrum that generates slow noise fluctuations in the qubit's evolution. We demonstrate our formalism in the case of singlet-triplet qubits subject to both quasistatic nuclear noise and $1/\omega^\alpha$ charge noise and find good agreement with recent experimental findings. This comparison shows the efficacy of our approach in describing real systems and additionally highlights the challenges with distinguishing different types of noise in free induction decay experiments.
    • Edwin Barnes, Mark S. Rudner, Frederico Martins, Filip K. Malinowski, Charles M. Marcus, Ferdinand Kuemmeth
      Journal reference: Phys. Rev. B 93, 121407 (2016) [pdf]
      DOI: 10.1103/PhysRevB.93.121407

  • 2015
    • Nonlocal damping of helimagnets in one-dimensional interacting electron systems - Abstract
      • We investigate the magnetization relaxation of a one-dimensional helimagnetic system coupled to interacting itinerant electrons. The relaxation is assumed to result from the emission of plasmons, the elementary excitations of the one-dimensional interacting electron system, caused by slow changes of the magnetization profile. This dissipation mechanism leads to a highly nonlocal form of magnetization damping that is strongly dependent on the electron-electron interaction. Forward scattering processes lead to a spatially constant damping kernel, while backscattering processes produce a spatially oscillating contribution. Due to the nonlocal damping, the thermal fluctuations become spatially correlated over the entire system. We estimate the characteristic magnetization relaxation times for magnetic quantum wires and nuclear helimagnets.
    • Kjetil M. D. Hals, Karsten Flensberg, Mark S. Rudner
      Journal reference: Phys. Rev. B 92, 094403 (2015) [pdf]
      DOI: 10.1103/PhysRevB.92.094403

    • Topological singularities and the general classification of Floquet–Bloch systems - Abstract
      • Recent works have demonstrated that the Floquet-Bloch bands of periodically-driven systems feature a richer topological structure than their non-driven counterparts. The additional structure in the driven case arises from the periodicity of quasienergy, the energy-like quantity that defines the spectrum of a periodically-driven system. Here we develop a new paradigm for the topological classification of Floquet-Bloch bands, based on the time-dependent spectrum of the driven system's evolution operator throughout one driving period. Specifically, we show that this spectrum may host topologically-protected degeneracies at intermediate times, which control the topology of the Floquet bands of the full driving cycle. This approach provides a natural framework for incorporating the role of symmetries, enabling a unified and complete classification of Floquet-Bloch bands and yielding new insight into the topological features that distinguish driven and non-driven systems.
    • Frederik Nathan, Mark S. Rudner
      Journal reference: New J. Phys. 17, 125014 (2015) [ 1506.07647v1 ]
      DOI: 10.1088/1367-2630/17/12/125014

    • Anomalous Floquet-Anderson Insulator as a Nonadiabatic Quantized Charge Pump - Abstract
      • Periodically driven quantum systems provide a novel and versatile platform for realizing topological phenomena. Among these are analogs of topological insulators and superconductors, attainable in static systems; however, some of these phenomena are unique to the periodically driven case. Here, we show that disordered, periodically driven systems admit an "anomalous" two dimensional phase, whose quasi-energy spectrum consists of chiral edge modes that coexist with a fully localized bulk - an impossibility for static Hamiltonians. This unique situation serves as the basis for a new topologically-protected non-equilibrium transport phenomenon: quantized non-adiabatic charge pumping. We identify the bulk topological invariant that characterizes the new phase (which we call the "anomalous Floquet Anderson Insulator", or AFAI). We provide explicit models which constitute a proof of principle for the existence of the new phase. Finally, we present evidence that the disorder-driven transition from the AFAI to a trivial, fully localized phase is in the same universality class as the quantum Hall plateau transition.
    • Paraj Titum, Erez Berg, Mark S. Rudner, Gil Refael, Netanel H. Lindner
      Journal reference: Phys. Rev. X 6, 021013 (2016) [ 1506.00650v1 ]
      DOI: 10.1103/PhysRevX.6.021013

    • Spin-Lattice Order in One-Dimensional Conductors: Beyond the RKKY Effect - Abstract
      • We investigate magnetic order in a lattice of classical spins coupled to an isotropic gas of one-dimensional (1d) conduction electrons via local exchange interactions. The frequently discussed Ruderman-Kittel-Kasuya-Yosida (RKKY) effective exchange model for this system predicts that spiral order is always preferred. Here we consider the problem nonperturbatively, and find that such order vanishes above a critical value of the exchange coupling that depends strongly on the lattice spacing. The critical coupling tends to zero as the lattice spacing becomes commensurate with the Fermi wave vector, signalling the breakdown of the perturbative RKKY picture, and spiral order, even at weak coupling. We provide the exact phase diagram for arbitrary exchange coupling and lattice spacing, and discuss its stability. Our results shed new light on the problem of utilizing a spiral spin-lattice state to drive a one-dimensional superconductor into a topological phase.
    • Michael Schecter, Mark S. Rudner, Karsten Flensberg
      Journal reference: Phys. Rev. Lett. 114, 247205 (2015) [pdf]
      DOI: 10.1103/PhysRevLett.114.247205

    • Controlled Population of Floquet-Bloch States via Coupling to Bose and Fermi Baths - Abstract
      • External driving is emerging as a promising tool for exploring new phases in quantum systems. The intrinsically non-equilibrium states that result, however, are challenging to describe and control. We study the steady states of a periodically driven one-dimensional electronic system, including the effects of radiative recombination, electron-phonon interactions, and the coupling to an external fermionic reservoir. Using a kinetic equation for the populations of the Floquet eigenstates, we show that the steady-state distribution can be controlled using the momentum and energy relaxation pathways provided by the coupling to phonon and Fermi reservoirs. In order to utilize the latter, we propose to couple the system and reservoir via an energy filter which suppresses photon-assisted tunneling. Importantly, coupling to these reservoirs yields a steady state resembling a band insulator in the Floquet basis. The system exhibits incompressible behavior, while hosting a small density of excitations. We discuss transport signatures, and describe the regimes where insulating behavior is obtained. Our results give promise for realizing Floquet topological insulators.
    • Karthik I. Seetharam, Charles-Edouard Bardyn, Netanel H. Lindner, Mark S. Rudner, Gil Refael
      Journal reference: Phys. Rev. X 5, 041050 (2015) [pdf]
      DOI: 10.1103/PhysRevX.5.041050

  • 2014
    • Observation of a Topological Transition in the Bulk of a Non-Hermitian System - Abstract
      • Topological insulators are insulating in the bulk but feature conducting states on their surfaces. Standard methods for probing their topological properties largely involve probing the surface, even though topological invariants are defined via the bulk band structure. Here, we utilize non-hermiticy to experimentally demonstrate a topological transition in an optical system, using bulk behavior only, without recourse to surface properties. This concept is relevant for a wide range of systems beyond optics, where the surface physics is difficult to probe.
    • Julia M. Zeuner, Mikael C. Rechtsman, Yonatan Plotnik, Yaakov Lumer, Mark S. Rudner, Mordechai Segev, Alexander Szameit
      Journal reference: Phys. Rev. Lett. 115, 040402 (2015) [pdf]
      DOI: 10.1103/PhysRevLett.115.040402

    • Multilevel Interference Resonances in Strongly Driven Three-Level Systems - Abstract
      • We study multi-photon resonances in a strongly-driven three-level quantum system, where one level is periodically swept through a pair of levels with constant energy separation $E$. Near the multi-photon resonance condition $n\hbar\omega = E$, where $n$ is an integer, we find qualitatively different behavior for $n$ even or odd. We explain this phenomenon in terms of families of interfering trajectories of the multi-level system. Remarkably, the behavior is insensitive to fluctuations of the energy of the driven level, and survives deep into the strong dephasing regime. The setup can be relevant for a variety of solid state and atomic or molecular systems. In particular, it provides a clear mechanism to explain recent puzzling experimental observations in strongly-driven double quantum dots.
    • Jeroen Danon, Mark S. Rudner
      Journal reference: Phys. Rev. Lett. 113, 247002 (2014) [pdf]
      DOI: 10.1103/PhysRevLett.113.247002

    • Ultranarrow ionization resonances in a quantum dot under broadband excitation - Abstract
      • Semiconductor quantum dots driven by the broadband radiation fields of nearby quantum point contacts provide an exciting new setting for probing dynamics in driven quantum systems at the nanoscale. We report on real-time charge-sensing measurements of the dot occupation, which reveal sharp resonances in the ionization rate as a function of gate voltage and applied magnetic field. Despite the broadband nature of excitation, the resonance widths are much smaller than the scale of thermal broadening. We show that such resonant enhancement of ionization is not accounted for by conventional approaches relying on elastic scattering processes, but can be explained via a mechanism based on a bottleneck process that is relieved near excited state level crossings. The experiment thus reveals a new regime of a strongly driven quantum dynamics in few-electron systems. The theoretical results are in good agreement with observations.
    • Simon Gustavsson, Mark S. Rudner, Leonid S. Levitov, Renaud Leturcq, Matthias Studer, Thomas Ihn, Klaus Ensslin
      Journal reference: Phys. Rev. B 89, 115304 (2014) [pdf]
      DOI: 10.1103/PhysRevB.89.115304

    • Vibration multistability and quantum switching for dispersive coupling - Abstract
      • We investigate a resonantly modulated harmonic mode, dispersively coupled to a nonequilibrium few-level quantum system. We focus on the regime where the relaxation rate of the system greatly exceeds that of the mode, and develop a quantum adiabatic approach for analyzing the dynamics. Semiclassically, the dispersive coupling leads to a mutual tuning of the mode and system into and out of resonance with their modulating fields, leading to multistability. In the important case where the system has two energy levels and is excited near resonance, the compound system can have up to three metastable states. Nonadiabatic quantum fluctuations associated with spontaneous transitions in the few-level system lead to switching between the metastable states. We provide parameter estimates for currently available systems.
    • Z. Maizelis, M. Rudner, M. I. Dykman
      DOI: 10.1103/PhysRevB.89.155439
      1401.4702v1 [pdf]

  • 2013
    • The theory of coherent dynamic nuclear polarization in quantum dots - Abstract
      • We consider the dynamic nuclear spin polarization (DNP) using two electrons in a double quantum dot in presence of external magnetic field and spin-orbit interaction, in various schemes of periodically repeated sweeps through the S-T+ avoided crossing. By treating the problem semi-classically, we find that generally the DNP have two distinct contributions - a geometrical polarization and a dynamic polarization, which have different dependence on the control parameters such as the sweep rates and waiting times in each period. Both terms show non-trivial dependence on those control parameter. We find that even for small spin-orbit term, the dynamical polarization dominates the DNP in presence of a long waiting period near the S-T+ avoided crossing, of the order of the nuclear Larmor precession periods. A detailed numerical analysis of a specific control regime can explain the oscillations observed by Foletti et.~al.~in arXiv:0801.3613.
    • Izhar Neder, Mark S. Rudner, Bertrand I. Halperin
      DOI: 10.1103/PhysRevB.89.085403
      1309.3027v1 [pdf]

    • Anomalous edge states and the bulk-edge correspondence for periodically-driven two dimensional systems - Abstract
      • Recently, several authors have investigated topological phenomena in periodically-driven systems of non-interacting particles. These phenomena are identified through analogies between the Floquet spectra of driven systems and the band structures of static Hamiltonians. Intriguingly, these works have revealed that the topological characterization of driven systems is richer than that of static systems. In particular, in driven systems in two dimensions (2D), robust chiral edge states can appear even though the Chern numbers of all the bulk Floquet bands are zero. Here we elucidate the crucial distinctions between static and driven 2D systems, and construct a new topological invariant that yields the correct edge state structure in the driven case. We provide formulations in both the time and frequency domains, which afford additional insight into the origins of the "anomalous" spectra which arise in driven systems. Possible realizations of these phenomena in solid state and cold atomic systems are discussed.
    • Mark S. Rudner, Netanel H. Lindner, Erez Berg, Michael Levin
      Journal reference: Phys. Rev. X 3, 031005 (2013) [pdf]

  • 2012
    • Self-Sustaining Dynamical Nuclear Polarization Oscillations in Quantum Dots - Abstract
      • Early experiments on spin-blockaded double quantum dots revealed surprising robust, large-amplitude current oscillations in the presence of a static (dc) source-drain bias [see e.g. K. Ono, S. Tarucha, Phys. Rev. Lett. 92, 256803 (2004)]. Experimental evidence strongly indicates that dynamical nuclear polarization plays a central role, but the mechanism has remained a mystery. Here we introduce a minimal albeit realistic model of coupled electron and nuclear spin dynamics which supports robust self-sustained oscillations. Our mechanism relies on a nuclear-spin analog of the tunneling magnetoresistance phenomenon (spin-dependent tunneling rates in the presence of an inhomogeneous Overhauser field) and nuclear spin diffusion, which governs dynamics of the spatial profile of nuclear polarization. The extremely long oscillation periods (up to hundreds of seconds) observed in experiments as well as the differences in phenomenology between vertical and lateral quantum dot structures are naturally explained in the proposed framework.
    • M. S. Rudner, L. S. Levitov
      Journal reference: Phys. Rev. Lett. 110, 086601 (2013) [pdf]
      DOI: 10.1103/PhysRevLett.110.086601

    • Spin-Orbit-Induced Strong Coupling of a Single Spin to a Nanomechanical Resonator - Abstract
      • We theoretically investigate the deflection-induced coupling of an electron spin to vibrational motion due to spin-orbit coupling in suspended carbon nanotube quantum dots. Our estimates indicate that, with current capabilities, a quantum dot with an odd number of electrons can serve as a realization of the Jaynes-Cummings model of quantum electrodynamics in the strong-coupling regime. A quantized flexural mode of the suspended tube plays the role of the optical mode and we identify two distinct two-level subspaces, at small and large magnetic field, which can be used as qubits in this setup. The strong intrinsic spin-mechanical coupling allows for detection, as well as manipulation of the spin qubit, and may yield enhanced performance of nanotubes in sensing applications.
    • András Pályi, P. R. Struck, Mark Rudner, Karsten Flensberg, Guido Burkard
      Journal reference: Phys. Rev. Lett. 108, 206811 (2012) [pdf]
      DOI: 10.1103/PhysRevLett.108.206811

    • Electronic liquid crystalline phases in a spin-orbit coupled two-dimensional electron gas - Abstract
      • We argue that the ground state of a two-dimensional electron gas with Rashba spin-orbit coupling realizes one of several possible liquid crystalline or Wigner crystalline phases in the low-density limit, even for short-range repulsive electron-electron interactions (which decay with distance with a power larger than 2). Depending on specifics of the interactions, preferred ground-states include an anisotropic Wigner crystal with an increasingly anisotropic unit cell as the density decreases, a striped or electron smectic phase, and a ferromagnetic phase which strongly breaks the lattice point-group symmetry, i.e. exhibits nematic order. Melting of the anisotropic Wigner crystal or the smectic phase by thermal or quantum fluctuations can gives rise to a non-magnetic nematic phase which preserves time-reversal symmetry.
    • Erez Berg, Mark S. Rudner, Steven A. Kivelson
      Journal reference: Phys. Rev. B 85, 035116 (2012) [pdf]
      DOI: 10.1103/PhysRevB.85.035116

  • 2011
    • Singlet-triplet splitting in double quantum dots due to spin orbit and hyperfine interactions - Abstract
      • We analyze the low-energy spectrum of a two-electron double quantum dot under a potential bias in the presence of an external magnetic field. We focus on the regime of spin blockade, taking into account the spin orbit interaction and hyperfine coupling of electron and nuclear spins. Starting from a model for two interacting electrons in a double dot, we derive a perturbative, effective two-level Hamiltonian in the vicinity of an avoided crossing between singlet and triplet levels, which are coupled by the spin-orbit and hyperfine interactions. We evaluate the level splitting at the anticrossing, and show that it depends on a variety of parameters including the spin orbit coupling strength, the orientation of the external magnetic field relative to an internal spin-orbit axis, the potential detuning of the dots, and the difference between hyperfine fields in the two dots. We provide a formula for the splitting in terms of the spin orbit length, the hyperfine fields in the two dots, and the double dot parameters such as tunnel coupling and Coulomb energy. This formula should prove useful for extracting spin orbit parameters from transport or charge sensing experiments in such systems. We identify a parameter regime where the spin orbit and hyperfine terms can become of comparable strength, and discuss how this regime might be reached.
    • Dimitrije Stepanenko, Mark Rudner, Bertrand I. Halperin, Daniel Loss
      DOI: 10.1103/PhysRevB.85.075416
      1112.1644v1 [pdf]

    • Hot Carrier Transport and Photocurrent Response in Graphene - Abstract
      • Strong electron-electron interactions in graphene are expected to result in multiple-excitation generation by the absorption of a single photon. We show that the impact of carrier multiplication on photocurrent response is enhanced by very inefficient electron cooling, resulting in an abundance of hot carriers. The hot-carrier-mediated energy transport dominates the photoresponse and manifests itself in quantum efficiencies that can exceed unity, as well as in a characteristic dependence of the photocurrent on gate voltages. The pattern of multiple photocurrent sign changes as a function of gate voltage provides a fingerprint of hot-carrier-dominated transport and carrier multiplication.
    • Justin C. W. Song, Mark S. Rudner, Charles M. Marcus, Leonid S. Levitov
      Journal reference: Nano Lett., 11 (11), pp 4688-4692 (2011) [pdf]
      DOI: 10.1021/nl202318u

    • Gate-Activated Photoresponse in a Graphene p–n Junction - Abstract
      • We study photodetection in graphene near a local electrostatic gate, which enables active control of the potential landscape and carrier polarity. We find that a strong photoresponse only appears when and where a p-n junction is formed, allowing on-off control of photodetection. Photocurrents generated near p-n junctions do not require biasing and can be realized using submicron gates. Locally modulated photoresponse enables a new range of applications for graphene-based photodetectors including, for example, pixilated infrared imaging with control of response on subwavelength dimensions.
    • M. C. Lemme, F. H. L. Koppens, A. L. Falk, M. S. Rudner, H. Park, L. S. Levitov, C. M. Marcus
      Journal reference: Nano Letters 11, 4134 (2011) [pdf]
      DOI: 10.1021/nl2019068

    • Semiclassical model for the dephasing of a two-electron spin qubit coupled to a coherently evolving nuclear spin bath - Abstract
      • We study electron spin decoherence in a two-electron double quantum dot due to the hyperfine interaction, under spin-echo conditions as studied in recent experiments. We develop a semi-classical model for the interaction between the electron and nuclear spins, in which the time-dependent Overhauser fields induced by the nuclear spins are treated as classical vector variables. Comparison of the model with experimentally-obtained echo signals allows us to quantify the contributions of various processes such as coherent Larmor precession and spin diffusion to the nuclear spin evolution.
    • Izhar Neder, Mark S. Rudner, Hendrik Bluhm, Sandra Foletti, Bertrand I. Halperin, Amir Yacoby
      Journal reference: Phys. Rev. B 84, 035441 (2011) [pdf]
      DOI: 10.1103/PhysRevB.84.035441

    • Nuclear spin dynamics in double quantum dots: Fixed points, transients, and intermittency - Abstract
      • Transport through spin-blockaded quantum dots provides a means for electrical control and detection of nuclear spin dynamics in the host material. Although such experiments have become increasingly popular in recent years, interpretation of their results in terms of the underlying nuclear spin dynamics remains challenging. Here we point out a fundamental process in which nuclear spin dynamics can be driven by electron shot noise; fast electric current fluctuations generate much slower nuclear polarization dynamics, which in turn affect electron dynamics via the Overhauser field. The resulting extremely slow intermittent current fluctuations account for a variety of observed phenomena that were not previously understood.
    • M. S. Rudner, F. H. L. Koppens, J. A. Folk, L. M. K. Vandersypen, L. S. Levitov
      Journal reference: Phys. Rev. B 84, 075339 (2011) [pdf]
      DOI: 10.1103/PhysRevB.84.075339

    • Chirality-Assisted Electronic Cloaking of Confined States in Bilayer Graphene - Abstract
      • We show that the strong coupling of pseudospin orientation and charge carrier motion in bilayer graphene has a drastic effect on transport properties of ballistic p-n-p junctions. Electronic states with zero momentum parallel to the barrier are confined under it for one pseudospin orientation, whereas states with the opposite pseudospin tunnel through the junction totally uninfluenced by the presence of confined states. We demonstrate that the junction acts as a cloak for confined states, making them nearly invisible to electrons in the outer regions over a range of incidence angles. This behavior is manifested in the two-terminal conductance as transmission resonances with non-Lorentzian, singular peak shapes. The response of these phenomena to a weak magnetic field or electric-field-induced interlayer gap can serve as an experimental fingerprint of electronic cloaking.
    • Nan Gu, Mark Rudner, Leonid Levitov
      Journal reference: Phys. Rev. Lett. 107, 156603 (2011) [pdf]
      DOI: 10.1103/PhysRevLett.107.156603

    • Observation of topologically protected bound states in photonic quantum walks - Abstract
      • One of the most striking features of quantum mechanics is the appearance of phases of matter with topological origins. These phases result in remarkably robust macroscopic phenomena such as the edge modes in integer quantum Hall systems, the gapless surface states of topological insulators, and elementary excitations with non-abelian statistics in fractional quantum Hall systems and topological superconductors. Many of these states hold promise in the applications to quantum memories and quantum computation. Artificial quantum systems, with their precise controllability, provide a versatile platform for creating and probing a wide variety of topological phases. Here we investigate topological phenomena in one dimension, using photonic quantum walks. The photon evolution simulates the dynamics of topological phases which have been predicted to arise in, for example, polyacetylene. We experimentally confirm the long-standing prediction of topologically protected localized states associated with these phases by directly imaging their wavefunctions. Moreover, we reveal an entirely new topological phenomenon: the existence of a topologically protected pair of bound states which is unique to periodically driven systems. Our experiment demonstrates a powerful new approach for controlling topological properties of quantum systems through periodic driving.
    • Takuya Kitagawa, Matthew A. Broome, Alessandro Fedrizzi, Mark S. Rudner, Erez Berg, Ivan Kassal, Alán Aspuru-Guzik, Eugene Demler, Andrew G. White
      Journal reference: Nature Communications 3, 882, 2012 [pdf]
      DOI: 10.1038/ncomms1872

    • Generating Entanglement and Squeezed States of Nuclear Spins in Quantum Dots - Abstract
      • Entanglement generation and detection are two of the most sought-after goals in the field of quantum control. Besides offering a means to probe some of the most peculiar and fundamental aspects of quantum mechanics, entanglement in many-body systems can be used as a tool to reduce fluctuations below the standard quantum limit. For spins, or spin-like systems, such a reduction of fluctuations can be realized with so-called squeezed states. Here we present a scheme for achieving coherent spin squeezing of nuclear spin states in few-electron quantum dots. This work represents a major shift from earlier studies in quantum dots, which have explored classical "narrowing" of the nuclear polarization distribution through feedback involving stochastic spin flips. In contrast, we use the nuclear-polarization-dependence of the electron spin resonance (ESR) to provide a non-linearity which generates a non-trivial, area-preserving, "twisting" dynamics that squeezes and stretches the nuclear spin Wigner distribution without the need for nuclear spin flips.
    • M. S. Rudner, L. M. K. Vandersypen, V. Vuletic, L. S. Levitov
      Journal reference: Phys. Rev. Lett. 107, 206806 (2011) [pdf]
      DOI: 10.1103/PhysRevLett.107.206806

  • 2010
    • Detection of spin injection into a double quantum dot: Violation of magnetic-field-inversion symmetry of nuclear polarization instabilities - Abstract
      • In mesoscopic systems with spin-orbit coupling, spin-injection into quantum dots at zero magnetic field is expected under a wide range of conditions. However, up to now, a viable approach for experimentally identifying such injection has been lacking. We show that electron spin injection into a spin-blockaded double quantum dot is dramatically manifested in the breaking of magnetic- field-inversion symmetry of nuclear polarization instabilities. Over a wide range of parameters, the asymmetry between positive and negative instability fields is extremely sensitive to the injected electron spin polarization and allows for the detection of even very weak spin injection. This phenomenon may be used to investigate the mechanisms of spin transport, and may hold implications for spin-based information processing.
    • Mark S. Rudner, Emmanuel I. Rashba
      DOI: 10.1103/PhysRevB.83.073406
      1011.2247v1 [pdf]

    • Topological characterization of periodically driven quantum systems - Abstract
      • Topological properties of physical systems can lead to robust behaviors that are insensitive to microscopic details. Such topologically robust phenomena are not limited to static systems but can also appear in driven quantum systems. In this paper, we show that the Floquet operators of periodically driven systems can be divided into topologically distinct (homotopy) classes, and give a simple physical interpretation of this classification in terms of the spectra of Floquet operators. Using this picture, we provide an intuitive understanding of the well-known phenomenon of quantized adiabatic pumping. Systems whose Floquet operators belong to the trivial class simulate the dynamics generated by time-independent Hamiltonians, which can be topologically classified according to the schemes developed for static systems. We demonstrate these principles through an example of a periodically driven two--dimensional hexagonal lattice model which exhibits several topological phases. Remarkably, one of these phases supports chiral edge modes even though the bulk is topologically trivial.
    • Takuya Kitagawa, Erez Berg, Mark Rudner, Eugene Demler
      Journal reference: Phys. Rev. B 82, 235114 (2010) [pdf]
      DOI: 10.1103/PhysRevB.82.235114

    • Phase-sensitive probes of nuclear polarization in spin-blockaded transport - Abstract
      • Spin-blockaded quantum dots provide a unique setting for studying nuclear-spin dynamics in a nanoscale system. Despite recent experimental progress, observing phase-sensitive phenomena in nuclear spin dynamics remains challenging. Here we point out that such a possibility opens up in the regime where hyperfine exchange directly competes with a purely electronic spin-flip mechanism such as the spin-orbital interaction. Interference between the two spin-flip processes, resulting from long-lived coherence of the nuclear-spin bath, modulates the electron-spin-flip rate, making it sensitive to the transverse component of nuclear polarization. In a system repeatedly swept through a singlet-triplet avoided crossing, nuclear precession is manifested in oscillations and sign reversal of the nuclear-spin pumping rate as a function of the waiting time between sweeps. This constitutes a purely electrical method for the detection of coherent nuclear-spin dynamics.
    • M. S. Rudner, I. Neder, L. S. Levitov, B. I. Halperin
      Journal reference: Phys. Rev. B 82, 041311(R) (2010) [pdf]
      DOI: 10.1103/PhysRevB.82.041311

    • Self-Polarization and Dynamical Cooling of Nuclear Spins in Double Quantum Dots - Abstract
      • Spontaneous nuclear polarization is predicted in double quantum dots in the spin-blocked electron transport regime. The polarization results from an instability of the zero-polarization state when singlet and triplet electron energy levels are brought into resonance by the effective hyperfine field of the nuclei on the electrons. The nuclear spins, once polarized, serve as a cold bath for cooling electrons below the lattice (phonon) temperature. We estimate the relevant time scales and discuss the conditions necessary to observe these phenomena.
    • M. S. Rudner, L. S. Levitov
      Journal reference: Physical Review Letters 99, 036602 (2007) [ cond-mat/0609409v2 ]
      DOI: 10.1103/PhysRevLett.99.036602

    • Phase transitions in dissipative quantum transport and mesoscopic nuclear spin pumping - Abstract
      • Topological phase transitions can occur in the dissipative dynamics of a quantum system when the ratio of matrix elements for competing transport channels is varied. Here we establish a relation between such behavior in a class of non-Hermitian quantum walk problems [M. S. Rudner and L. S. Levitov, Phys. Rev. Lett. 102, 065703 (2009)] and nuclear spin pumping in double quantum dots, which is mediated by the decay of a spin-blockaded electron triplet state in the presence of spin-orbit and hyperfine interactions. The transition occurs when the strength of spin-orbit coupling exceeds the strength of the net hyperfine coupling, and results in the complete suppression of nuclear spin pumping. Below the transition point, nuclear pumping is accompanied by a strong reduction in current due to the presence of non-decaying "dark states" in this regime. Due to its topological character, the transition is expected to be robust against dephasing of the electronic degrees of freedom.
    • M. S. Rudner, L. S. Levitov
      Journal reference: Phys. Rev. B 82, 155418 (2010) [pdf]
      DOI: 10.1103/PhysRevB.82.155418

    • Long coherence of electron spins coupled to a nuclear spin bath - Abstract
      • Qubits, the quantum mechanical bits required for quantum computing, must retain their fragile quantum states over long periods of time. In many types of electron spin qubits, the primary source of decoherence is the interaction between the electron spins and nuclear spins of the host lattice. For electrons in gate defined GaAs quantum dots, previous spin echo measurements have revealed coherence times of about 1 $\mu$s at low magnetic fields below 100 mT. Here, we show that coherence in such devices can actually survive to much longer times, and provide a detailed understanding of the measured nuclear spin induced decoherence. At fields above a few hundred millitesla, the coherence time measured using a single-pulse spin echo extends to 30 $\mu$s. At lower magnetic fields, the echo first collapses, but then revives at later times given by the period of the relative Larmor precession of different nuclear species. This behavior was recently predicted, and as we show can be quantitatively accounted for by a semi-classical model for the electron spin dynamics in the presence of a nuclear spin bath. Using a multiple-pulse Carr-Purcell-Meiboom-Gill echo sequence, the decoherence time can be extended to more than 200 $\mu$s, which represents an improvement by two orders of magnitude compared to previous measurements. This demonstration of effective methods to mitigate nuclear spin induced decoherence puts the quantum error correction threshold within reach.
    • Hendrik Bluhm, Sandra Foletti, Izhar Neder, Mark Rudner, Diana Mahalu, Vladimir Umansky, Amir Yacoby
      1005.2995v1 [pdf]

    • Spin relaxation due to deflection coupling in nanotube quantum dots - Abstract
      • We consider relaxation of an electron spin in a nanotube quantum dot due to its coupling to flexural phonon modes, and identify a new spin-orbit mediated coupling between the nanotube deflection and the electron spin. This mechanism dominates other spin relaxation mechanisms in the limit of small energy transfers. Due to the quadratic dispersion law of long wavelength flexons, $\omega \propto q^2$, the density of states $dq/d\omega \propto \omega^{-1/2}$ diverges as $\omega \to 0$. Furthermore, because here the spin couples directly to the nanotube deflection, there is an additional enhancement by a factor of $1/q$ compared to the deformation potential coupling mechanism. We show that the deflection coupling robustly gives rise to a minimum in the magnetic field dependence of the spin lifetime $T_1$ near an avoided crossing between spin-orbit split levels in both the high and low-temperature limits. This provides a mechanism that supports the identification of the observed $T_1$ minimum with an avoided crossing in the single particle spectrum by Churchill et al.[Phys. Rev. Lett. {\bf 102}, 166802 (2009)].
    • Mark S. Rudner, Emmanuel I. Rashba
      Journal reference: Phys. Rev. B 81, 125426 (2010). [pdf]
      DOI: 10.1103/PhysRevB.81.125426

    • Collapse of Landau Levels in Gated Graphene Structures - Abstract
      • We describe a new regime of magnetotransport in two dimensional electron systems in the presence of a narrow potential barrier imposed by external gates. In such systems, the Landau level states, confined to the barrier region in strong magnetic fields, undergo a deconfinement transition as the field is lowered. We present transport measurements showing Shubnikov-de Haas (SdH) oscillations which, in the unipolar regime, abruptly disappear when the strength of the magnetic field is reduced below a certain critical value. This behavior is explained by a semiclassical analysis of the transformation of closed cyclotron orbits into open, deconfined trajectories. Comparison to SdH-type resonances in the local density of states is presented.
    • Nan Gu, Mark Rudner, Andrea Young, Philip Kim, Leonid Levitov
      Journal reference: Phys. Rev. Lett. 106, 066601 (2011) [pdf]
      DOI: 10.1103/PhysRevLett.106.066601

    • Exploring topological phases with quantum walks - Abstract
      • The quantum walk was originally proposed as a quantum mechanical analogue of the classical random walk, and has since become a powerful tool in quantum information science. In this paper, we show that discrete time quantum walks provide a versatile platform for studying topological phases, which are currently the subject of intense theoretical and experimental investigation. In particular, we demonstrate that recent experimental realizations of quantum walks simulate a non-trivial one dimensional topological phase. With simple modifications, the quantum walk can be engineered to realize all of the topological phases which have been classified in one and two dimensions. We further discuss the existence of robust edge modes at phase boundaries, which provide experimental signatures for the non-trivial topological character of the system.
    • Takuya Kitagawa, Mark S. Rudner, Erez Berg, Eugene Demler
      Journal reference: Phys. Rev. A 82, 033429 (2010) [pdf]
      DOI: 10.1103/PhysRevA.82.033429

  • 2008
    • Pulse imaging and nonadiabatic control of solid-state artificial atoms - Abstract
      • Transitions in an artificial atom, driven non-adiabatically through an energy-level avoided crossing, can be controlled by carefully engineering the driving protocol. We have driven a superconducting persistent-current qubit with a large-amplitude, radio-frequency field. By applying a bi-harmonic waveform generated by a digital source, we demonstrate a mapping between the amplitude and phase of the harmonics produced at the source and those received by the device. This allows us to image the actual waveform at the device. This information is used to engineer a desired time dependence, as confirmed by detailed comparison with simulation.
    • Jonas Bylander, Mark S. Rudner, Andrey V. Shytov, Sergio O. Valenzuela, David M. Berns, Karl K. Berggren, Leonid S. Levitov, William D. Oliver
      Journal reference: Phys. Rev. B vol. 80, 220506(R) (2009) [pdf]
      DOI: 10.1103/PhysRevB.80.220506

    • Atomic collapse, Lorentz boosts, Klein scattering, and other quantum-relativistic phenomena in graphene - Abstract
      • Electrons in graphene, behaving as massless relativistic Dirac particles, provide a new perspective on the relation between condensed matter and high-energy physics. We discuss atomic collapse, a novel state of superheavy atoms stripped of their discrete energy levels, which are transformed into resonant states. Charge impurities in graphene provide a convenient condensed matter system in which this effect can be explored. Relativistic dynamics also manifests itself in another system, graphene p-n junctions. We show how the transport problem in the presence of magnetic field can be solved with the help of a Lorentz transformation, and use it to investigate magnetotransport in p-n junctions. Finally, we review recent proposal to use Fabry-Perot resonances in p-n-p structures as a vehicle to investigate Klein scattering, another hallmark phenomenon of relativistic dynamics.
    • Andrei Shytov, Mark Rudner, Nan Gu, Mikhail Katsnelson, Leonid Levitov
      Journal reference: Sol. State Comm. 149, 1087 (2009) [pdf]
      DOI: 10.1016/j.ssc.2009.02.043

    • Klein Backscattering and Fabry-Pérot Interference in Graphene Heterojunctions - Abstract
      • We present a theory of quantum-coherent transport through a lateral p-n-p structure in graphene, which fully accounts for the interference of forward and backward scattering on the p-n interfaces. The backreflection amplitude changes sign at zero incidence angle because of the Klein phenomenon, adding a phase $\pi$ to the interference fringes. The contributions of the two p-n interfaces to the phase of the interference cancel with each other at zero magnetic field, but become imbalanced at a finite field. The resulting half a period shift in the Fabry-Perot fringe pattern, induced by a relatively weak magnetic field, can provide a clear signature of Klein scattering in graphene. This effect is shown to be robust in the presence of spatially inhomogeneous potential of moderate strength.
    • A. V. Shytov, M. S. Rudner, L. S. Levitov
      Journal reference: Phys. Rev. Lett. 101, 156804 (2008) [pdf]
      DOI: 10.1103/PhysRevLett.101.156804

    • Topological Transition in a Non-Hermitian Quantum Walk - Abstract
      • We analyze a quantum walk on a bipartite one-dimensional lattice, in which the particle can decay whenever it visits one of the two sublattices. The corresponding non-Hermitian tight-binding problem with a complex potential for the decaying sites exhibits two different phases, distinguished by a winding number defined in terms of the Bloch eigenstates in the Brillouin zone. We find that the mean displacement of a particle initially localized on one of the non-decaying sites can be expressed in terms of the winding number, and is therefore quantized as an integer, changing from zero to one at the critical point. This problem can serve as a simplified model for nuclear spin pumping in the spin-blockaded electron transport regime of quantum dots in the presence of competing hyperfine and spin-orbital interactions. The predicted transition from pumping to non-pumping is topological in nature, and is hence robust against certain types of noise and decoherence.
    • M. S. Rudner, L. S. Levitov
      DOI: 10.1103/PhysRevLett.102.065703
      0807.2048v1 [pdf]

    • Quantum Phase Tomography of a Strongly Driven Qubit - Abstract
      • The interference between repeated Landau-Zener transitions in a qubit swept through an avoided level crossing results in Stueckelberg oscillations in qubit magnetization. The resulting oscillatory patterns are a hallmark of the coherent strongly-driven regime in qubits, quantum dots and other two-level systems. The two-dimensional Fourier transforms of these patterns are found to exhibit a family of one-dimensional curves in Fourier space, in agreement with recent observations in a superconducting qubit. We interpret these images in terms of time evolution of the quantum phase of qubit state and show that they can be used to probe dephasing mechanisms in the qubit.
    • M. S. Rudner, A. V. Shytov, L. S. Levitov, D. M. Berns, W. D. Oliver, S. O. Valenzuela, T. P. Orlando
      Journal reference: Phys. Rev. Lett. 101, 190502 (2008) [pdf]
      DOI: 10.1103/PhysRevLett.101.190502

    • Amplitude spectroscopy of a solid-state artificial atom - Abstract
      • The energy-level structure of a quantum system plays a fundamental role in determining its behavior and manifests itself in a discrete absorption and emission spectrum. Conventionally, spectra are probed via frequency spectroscopy whereby the frequency \nu of a harmonic driving field is varied to fulfill the conditions \Delta E = h \nu, where the driving field is resonant with the level separation \Delta E (h is Planck's constant). Although this technique has been successfully employed in a variety of physical systems, including natural and artificial atoms and molecules, its application is not universally straightforward, and becomes extremely challenging for frequencies in the range of 10's and 100's of gigahertz. Here we demonstrate an alternative approach, whereby a harmonic driving field sweeps the atom through its energy-level avoided crossings at a fixed frequency, surmounting many of the limitations of the conventional approach. Spectroscopic information is obtained from the amplitude dependence of the system response. The resulting ``spectroscopy diamonds'' contain interference patterns and population inversion that serve as a fingerprint of the atom's spectrum. By analyzing these features, we determine the energy spectrum of a manifold of states with energies from 0.01 to 120 GHz \times h in a superconducting artificial atom, using a driving frequency near 0.1 GHz. This approach provides a means to manipulate and characterize systems over a broad bandwidth, using only a single driving frequency that may be orders of magnitude smaller than the energy scales being probed.
    • David M. Berns, Mark S. Rudner, Sergio O. Valenzuela, Karl K. Berggren, William D. Oliver, Leonid S. Levitov, Terry P. Orlando
      Journal reference: Nature 455, 51 (2008) [pdf]
      DOI: 10.1038/nature07262

  • 2007
    • Electrically Driven Reverse Overhauser Pumping of Nuclear Spins in Quantum Dots - Abstract
      • We propose a new mechanism for polarizing nuclear spins in quantum dots, based on periodic modulation of the hyperfine coupling by electric driving at the electron spin resonance frequency. Dynamical nuclear polarization results from resonant excitation rather than hyperfine relaxation mediated by a thermal bath, and thus is not subject to Overhauser-like detailed balance constraints. This allows polarization in the direction opposite to that expected from the Overhauser effect. Competition of the electrically-driven and bath assisted mechanisms can give rise to spatial modulation and sign reversal of polarization on a scale smaller than the electron confinement radius in the dot. The relation to reverse Overhauser polarization observed in GaAs quantum dots is discussed.
    • M. S. Rudner, L. S. Levitov
      Journal reference: Phys. Rev. Lett. 99, 246602 (2007) [pdf]
      DOI: 10.1103/PhysRevLett.99.246602

    • Resonant Cooling of Nuclear Spins in Quantum Dots - Abstract
      • We propose to use the spin-blockade regime in double quantum dots to reduce nuclear spin polarization fluctuations in analogy with optical Doppler cooling. The Overhauser shift brings electron levels in and out of resonance, creating feedback to suppress fluctuations. Coupling to the disordered nuclear spin background is a major source of noise and dephasing in electron spin measurements in such systems. Estimates indicate that a better than 10-fold reduction of fluctuations is possible.
    • M. S. Rudner, L. S. Levitov
      0705.2177v1 [pdf]