Center for Quantum Devices > Research > Publications > Mark Rudner
Publications by Mark Spencer Rudner
 2019

Topology and Broken Symmetry in Floquet Systems 
Abstract
 Floquet systems are governed by periodic, timedependent, 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 behaviorsome 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 singleparticle systems, the existence and classification of exotic Floquet drives in interacting systems, and the attendant notion of manybody Floquet phases and arguments for their stability to heating.
Fenner Harper, Rahul Roy, Mark S. Rudner, S. L. Sondhi 1905.01317v1 [pdf]

Nagaoka ferromagnetism observed in a quantum dot plaquette 
Abstract
 The analytical tractability of Nagaoka ferromagnetism makes it a convenient model to explore the capabilities of quantum simulators of collective electron interactions. However, the small groundtoexcited state energy compared to electron interactions, as well as the difficulty of measuring magnetization in few particle devices, have made the Nagaoka model experimentally unattainable. Here we present experimental signatures of the ferromagnetic ground state, predicted for 3 electrons in a 4 site square plaquette, engineered using electrostatically defined quantum dots. We test the robustness of the Nagaoka condition under different scenarios of lattice topology, device homogeneity and magnetic flux through the plaquette. This longsought demonstration of Nagaoka ferromagnetism establishes quantum dot systems as prime candidates for quantum simulators of magnetic phenomena driven by electronelectron interactions.

Floquet metal to insulator phase transitions in semiconductor nanowires 
Abstract
 We study steadystates of semiconductor nanowires subjected to strong resonant timeperiodic drives. The steadystates arise from the balance between electronphonon scattering, electronhole recombination via photoemission, and Auger scattering processes. We show that tuning the strength of the driving field drives a transition between an electronhole metal (EHM) phase and a Floquet insulator (FI) phase. We study the critical point controlling this transition. The EHMtoFI transition can be observed by monitoring the presence of peaks in the densitydensity 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 nonequilibrium phases of matter by periodic driving.
Iliya Esin, Mark S. Rudner, Netanel H. Lindner 1904.07856v1 [pdf]

Parton construction of particleholeconjugate ReadRezayi parafermion
fractional quantum Hall states and beyond 
Abstract
 The ReadRezayi (RR) parafermion states form an exotic series of nonAbelian fractional quantum Hall (FQH) states at filling $\nu = k/(k+2)$. Computationally, these wave functions 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 particleholeconjugate RR (`antiRR') 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 nontrivial dualities with respect to previously known descriptions. This construction allows wave functions in antiRR 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 1902.04173v1 [pdf]

Exponentially long lifetime of universal quasisteady states in
topological Floquet pumps 
Abstract
 Topological phenomena in periodically driven, isolated quantum many body systems are difficult to obtain due to the generic tendency of such systems to heat up towards a maximum entropy state in the long time limit. Here we investigate a mechanism to transiently stabilize topological phenomena over a longtime window, for systems driven at low frequencies. This mechanism provides a route for obtaining longlived prethermal states with anomalous topological properties, unattainable in equilibrium. We consider the dynamics of interacting particles in a slowly driven lattice with two (or more) bands separated by a bandgap. In the case where the bandgap of the Hamiltonian at any specific time is large we obtain an analytical bound for the rate of change in the number of particles populating these bands. The bound is exponentially small in the ratio between the instantaneous bandgap and the maximum between the driving frequency, interaction strength, and the bandwidth. Within the prethermal time window, this leads to the existence of a quasisteady state which is characterized by maximum entropy subject to the constraint of fixed number of particles in each band. By initializing the system with a majority of particles in one of the bands, the topological properties of the bands can be measured. For example, this mechanism can be used to obtain quasisteady states in slowly driven one dimensional systems which carry universal currents, or quasisteady states of driveinduced Weyl points in 3dimensional systems.
Tobias Gulden, Erez Berg, Mark S. Rudner, Netanel H. Lindner 1901.08385v1 [pdf]

Stability of Anomalous Floquet Insulators 
Abstract
 We demonstrate the existence of a twodimensional anomalous Floquet insulator (AFI) phase: an interacting (periodicallydriven) nonequilibrium topological phase of matter with no counterpart in equilibrium. The AFI is characterized by a manybody 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 manybody 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 nonuniform 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 1712.02789v3 [pdf]

Currentinduced gap opening in interacting topological insulator
surfaces 
Abstract
 Twodimensional topological insulators (TIs) host gapless helical edge states that are predicted to support a quantized twoterminal conductance. Quantization is protected by timereversal symmetry, which forbids elastic backscattering. Paradoxically, the currentcarrying state itself breaks the timereversal symmetry that protects it. Here we show that the combination of electronelectron interactions and momentumdependent spinpolarization 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. Currentinduced gap opening is manifested via a nonlinear contribution to the system's $IV$ characteristic, which persists down to zero temperature. We discuss prospects for realizations in recently discovered large bulk band gap TIs, and an analogous currentinduced gap opening mechanism for the surface states of threedimensional TIs.
Ajit C. Balram, Karsten Flensberg, Jens Paaske, Mark S. Rudner 1901.08067v1 [pdf]

Topology and Broken Symmetry in Floquet Systems 
Abstract
 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 onedimensional 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 nonequilibrium 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 antiPfaffian phase 
Abstract
 In this work we propose a parton state as a candidate state to describe the fractional quantum Hall effect in the halffilled 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 antiPfaffian state. This state has a good overlap with the antiPfaffian 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 antiPfaffian 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 particleholesymmetric Pfaffian (PHPfaffian) state. We find that the proposed candidate wave function for the PHPfaffian state is particlehole symmetric to a high degree but it does not appear to arise as the ground state of any simple Hamiltonian with twobody 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: selfinduced Berry flux and spontaneous nonequilibrium
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 timereversal 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 selfinduced Bloch band Berry flux. The selfinduced Berry flux supports and is sustained by a circulating plasmonic motion, which may arise even for a linearly polarized driving field. This nonequilibrium 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 plasmonmediated spontaneous nonequilibrium magnetization in presentday devices.
Mark S. Rudner, Justin C. W. Song 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 nontrivial nonequilibrium steady state is therefore of crucial importance. In this work, we study the dynamics of an interacting onedimensional periodicallydriven electronic system coupled to a phonon heat bath. Using the FloquetBoltzmann 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, CharlesEdouard 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 radiofrequency 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

Fractional Quantum Hall Effect at $ν=2+6/13$: The Parton Paradigm for
the Second Landau Level 
Abstract
 2017

ManyBody Dynamics and Gap Opening in Interacting Periodically Driven Systems 
Abstract
 We study the transient dynamics in a twodimensional 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 noninteracting 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 FloquetBloch 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 electronphonon 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 twoterminal transport and describe the regimes where edgestate transport can be observed. Our results show that signatures of the nontrivial topology persist in the nonequilibrium 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 twodimensional periodically driven systems in which all bulk Floquet eigenstates are localized by disorder. We show that this micromotion gives rise to a quantized timeaveraged 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 timeaveraged 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

Quantized largebias current in the anomalous FloquetAnderson insulator 
Abstract
 We study twoterminal transport through twodimensional periodically driven systems in which all bulk Floquet eigenstates are localized by disorder. We focus on the Anomalous FloquetAnderson Insulator (AFAI) phase, a topologicallynontrivial 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 farfromequilibrium 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 1708.05023v1 [pdf]

Spectrum of the Nuclear Environment for GaAs Spin Qubits 
Abstract
 Using a singlettriplet 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 electronmediated 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 fewpulse regime ($\lesssim \! 16$ $\pi$pulses), where transverse Overhauser fluctuations dominate dephasing, to the manypulse 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 socalled 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 threedimensional 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 gatedefined quantum dots provide a promising platform for quantum computation. In particular, spinbased 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 gatedefined 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, 1620 (2017) [ 1601.06677v3 ] DOI: 10.1038/nnano.2016.170

ManyBody Dynamics and Gap Opening in Interacting Periodically Driven Systems 
Abstract
 2016

Direct Probe of Topological Invariants Using Bloch Oscillating Quantum Walks 
Abstract
 The topology of a singleparticle 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 timedependent, Blochoscillating quantum walk enables the direct measurement of topological invariants. We consider two classes of onedimensional 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 FerromagnetSuperconductor Heterostructures 
Abstract
 We investigate the formation of a new type of composite topological excitation  the skyrmionvortex pair (SVP)  in hybrid systems consisting of coupled ferromagnetic and superconducting layers. Spinorbit 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 skyrmionvortex 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 nonHermitian quantum
transport 
Abstract
 NonHermitian quantum systems can exhibit unique observables characterizing topologically protected transport in the presence of decay. The topological protection arises from winding numbers associated with nondecaying dark states, which are decoupled from the environment and thus immune to dissipation. Here we develop a classification of topological dynamical phases for onedimensional quantum systems with periodicallyarranged 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 darkstate submanifolds in the Hamiltonian parameter space. Changes in the winding numbers at topological transitions are manifested in nonanalytic 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 twodimensional metallic systems including gapped Dirac materials. As we show, in these materials the interplay between Berry curvature and electronelectron 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 opticallypumped 2D Dirac materials. Realization of CBPs will offer a new paradigm for magnetic fieldfree, subwavelength optical nonreciprocity, in the mid IRTHz range, with tunable splittings as large as tens of THz, as well as sensitive alloptical diagnostics of topological bands.
Justin C. W. Song, Mark S. Rudner Journal reference: Proceedings of the National Academy of Sciences (PNAS) 113(17): 46584663 (2016) [ 1506.04743v2 ] DOI: 10.1073/pnas.1519086113

Universal Chiral Quasisteady States in Periodically Driven ManyBody Systems 
Abstract
 We investigate manybody dynamics in a onedimensional interacting periodically driven system, based on a partiallyfilled 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 manybody dynamics separately conserves the occupations of the two chiral bands. Within this intermediate time regime we predict that the system reaches a chiral quasisteady 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 twodimensional 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 nonlocal 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 sofar unexplained oscillatory electronictransport 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 nonMarkovian noise in singlettriplet 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 singlettriplet 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

Direct Probe of Topological Invariants Using Bloch Oscillating Quantum Walks 
Abstract
 2015

Nonlocal damping of helimagnets in onedimensional interacting electron systems 
Abstract
 We investigate the magnetization relaxation of a onedimensional helimagnetic system coupled to interacting itinerant electrons. The relaxation is assumed to result from the emission of plasmons, the elementary excitations of the onedimensional 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 electronelectron 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 FloquetBloch bands of periodicallydriven systems feature a richer topological structure than their nondriven counterparts. The additional structure in the driven case arises from the periodicity of quasienergy, the energylike quantity that defines the spectrum of a periodicallydriven system. Here we develop a new paradigm for the topological classification of FloquetBloch bands, based on the timedependent spectrum of the driven system's evolution operator throughout one driving period. Specifically, we show that this spectrum may host topologicallyprotected 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 FloquetBloch bands and yielding new insight into the topological features that distinguish driven and nondriven systems.
Frederik Nathan, Mark S. Rudner Journal reference: New J. Phys. 17, 125014 (2015) [ 1506.07647v1 ] DOI: 10.1088/13672630/17/12/125014

Anomalous FloquetAnderson 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 quasienergy 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 topologicallyprotected nonequilibrium transport phenomenon: quantized nonadiabatic 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 disorderdriven 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

SpinLattice Order in OneDimensional Conductors: Beyond the RKKY Effect 
Abstract
 We investigate magnetic order in a lattice of classical spins coupled to an isotropic gas of onedimensional (1d) conduction electrons via local exchange interactions. The frequently discussed RudermanKittelKasuyaYosida (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 spinlattice state to drive a onedimensional 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 FloquetBloch 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 nonequilibrium states that result, however, are challenging to describe and control. We study the steady states of a periodically driven onedimensional electronic system, including the effects of radiative recombination, electronphonon interactions, and the coupling to an external fermionic reservoir. Using a kinetic equation for the populations of the Floquet eigenstates, we show that the steadystate 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 photonassisted 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, CharlesEdouard Bardyn, Netanel H. Lindner, Mark S. Rudner, Gil Refael Journal reference: Phys. Rev. X 5, 041050 (2015) [pdf] DOI: 10.1103/PhysRevX.5.041050

Nonlocal damping of helimagnets in onedimensional interacting electron systems 
Abstract
 2014

Observation of a Topological Transition in the Bulk of a NonHermitian 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 nonhermiticy 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 ThreeLevel Systems 
Abstract
 We study multiphoton resonances in a stronglydriven threelevel quantum system, where one level is periodically swept through a pair of levels with constant energy separation $E$. Near the multiphoton 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 multilevel 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 stronglydriven 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 realtime chargesensing 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 fewelectron 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 fewlevel 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 fewlevel 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]

Observation of a Topological Transition in the Bulk of a NonHermitian System 
Abstract
 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 spinorbit interaction, in various schemes of periodically repeated sweeps through the ST+ avoided crossing. By treating the problem semiclassically, 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 nontrivial dependence on those control parameter. We find that even for small spinorbit term, the dynamical polarization dominates the DNP in presence of a long waiting period near the ST+ 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 bulkedge correspondence for
periodicallydriven two dimensional systems 
Abstract
 Recently, several authors have investigated topological phenomena in periodicallydriven systems of noninteracting 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]

The theory of coherent dynamic nuclear polarization in quantum dots 
Abstract
 2012

SelfSustaining Dynamical Nuclear Polarization Oscillations in Quantum Dots 
Abstract
 Early experiments on spinblockaded double quantum dots revealed surprising robust, largeamplitude current oscillations in the presence of a static (dc) sourcedrain 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 selfsustained oscillations. Our mechanism relies on a nuclearspin analog of the tunneling magnetoresistance phenomenon (spindependent 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

SpinOrbitInduced Strong Coupling of a Single Spin to a Nanomechanical Resonator 
Abstract
 We theoretically investigate the deflectioninduced coupling of an electron spin to vibrational motion due to spinorbit 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 JaynesCummings model of quantum electrodynamics in the strongcoupling regime. A quantized flexural mode of the suspended tube plays the role of the optical mode and we identify two distinct twolevel subspaces, at small and large magnetic field, which can be used as qubits in this setup. The strong intrinsic spinmechanical 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 spinorbit coupled twodimensional electron gas 
Abstract
 We argue that the ground state of a twodimensional electron gas with Rashba spinorbit coupling realizes one of several possible liquid crystalline or Wigner crystalline phases in the lowdensity limit, even for shortrange repulsive electronelectron interactions (which decay with distance with a power larger than 2). Depending on specifics of the interactions, preferred groundstates 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 pointgroup 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 nonmagnetic nematic phase which preserves timereversal symmetry.
Erez Berg, Mark S. Rudner, Steven A. Kivelson Journal reference: Phys. Rev. B 85, 035116 (2012) [pdf] DOI: 10.1103/PhysRevB.85.035116

SelfSustaining Dynamical Nuclear Polarization Oscillations in Quantum Dots 
Abstract
 2011

Singlettriplet splitting in double quantum dots due to spin orbit and
hyperfine interactions 
Abstract
 We analyze the lowenergy spectrum of a twoelectron 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 twolevel Hamiltonian in the vicinity of an avoided crossing between singlet and triplet levels, which are coupled by the spinorbit 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 spinorbit 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 electronelectron interactions in graphene are expected to result in multipleexcitation 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 hotcarriermediated 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 hotcarrierdominated transport and carrier multiplication.
Justin C. W. Song, Mark S. Rudner, Charles M. Marcus, Leonid S. Levitov Journal reference: Nano Lett., 11 (11), pp 46884692 (2011) [pdf] DOI: 10.1021/nl202318u

GateActivated 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 pn junction is formed, allowing onoff control of photodetection. Photocurrents generated near pn junctions do not require biasing and can be realized using submicron gates. Locally modulated photoresponse enables a new range of applications for graphenebased 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 twoelectron spin qubit coupled to a coherently evolving nuclear spin bath 
Abstract
 We study electron spin decoherence in a twoelectron double quantum dot due to the hyperfine interaction, under spinecho conditions as studied in recent experiments. We develop a semiclassical model for the interaction between the electron and nuclear spins, in which the timedependent Overhauser fields induced by the nuclear spins are treated as classical vector variables. Comparison of the model with experimentallyobtained 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 spinblockaded 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

ChiralityAssisted 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 pnp 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 twoterminal conductance as transmission resonances with nonLorentzian, singular peak shapes. The response of these phenomena to a weak magnetic field or electricfieldinduced 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 nonabelian 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 longstanding 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 AspuruGuzik, 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 soughtafter 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 manybody systems can be used as a tool to reduce fluctuations below the standard quantum limit. For spins, or spinlike systems, such a reduction of fluctuations can be realized with socalled squeezed states. Here we present a scheme for achieving coherent spin squeezing of nuclear spin states in fewelectron 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 nuclearpolarizationdependence of the electron spin resonance (ESR) to provide a nonlinearity which generates a nontrivial, areapreserving, "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

Singlettriplet splitting in double quantum dots due to spin orbit and
hyperfine interactions 
Abstract
 2010

Detection of spin injection into a double quantum dot: Violation of
magneticfieldinversion symmetry of nuclear polarization instabilities 
Abstract
 In mesoscopic systems with spinorbit coupling, spininjection 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 spinblockaded double quantum dot is dramatically manifested in the breaking of magnetic fieldinversion 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 spinbased 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 wellknown phenomenon of quantized adiabatic pumping. Systems whose Floquet operators belong to the trivial class simulate the dynamics generated by timeindependent 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 twodimensional 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

Phasesensitive probes of nuclear polarization in spinblockaded transport 
Abstract
 Spinblockaded quantum dots provide a unique setting for studying nuclearspin dynamics in a nanoscale system. Despite recent experimental progress, observing phasesensitive 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 spinflip mechanism such as the spinorbital interaction. Interference between the two spinflip processes, resulting from longlived coherence of the nuclearspin bath, modulates the electronspinflip rate, making it sensitive to the transverse component of nuclear polarization. In a system repeatedly swept through a singlettriplet avoided crossing, nuclear precession is manifested in oscillations and sign reversal of the nuclearspin pumping rate as a function of the waiting time between sweeps. This constitutes a purely electrical method for the detection of coherent nuclearspin 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

SelfPolarization and Dynamical Cooling of Nuclear Spins in Double Quantum Dots 
Abstract
 Spontaneous nuclear polarization is predicted in double quantum dots in the spinblocked electron transport regime. The polarization results from an instability of the zeropolarization 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) [ condmat/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 nonHermitian 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 spinblockaded electron triplet state in the presence of spinorbit and hyperfine interactions. The transition occurs when the strength of spinorbit 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 nondecaying "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 singlepulse 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 semiclassical model for the electron spin dynamics in the presence of a nuclear spin bath. Using a multiplepulse CarrPurcellMeiboomGill 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 spinorbit 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 spinorbit split levels in both the high and lowtemperature 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 Shubnikovde 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 SdHtype 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 nontrivial 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 nontrivial 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

Detection of spin injection into a double quantum dot: Violation of
magneticfieldinversion symmetry of nuclear polarization instabilities 
Abstract
 2008

Pulse imaging and nonadiabatic control of solidstate artificial atoms 
Abstract
 Transitions in an artificial atom, driven nonadiabatically through an energylevel avoided crossing, can be controlled by carefully engineering the driving protocol. We have driven a superconducting persistentcurrent qubit with a largeamplitude, radiofrequency field. By applying a biharmonic 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 quantumrelativistic phenomena in graphene 
Abstract
 Electrons in graphene, behaving as massless relativistic Dirac particles, provide a new perspective on the relation between condensed matter and highenergy 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 pn 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 pn junctions. Finally, we review recent proposal to use FabryPerot resonances in pnp 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 FabryPérot Interference in Graphene Heterojunctions 
Abstract
 We present a theory of quantumcoherent transport through a lateral pnp structure in graphene, which fully accounts for the interference of forward and backward scattering on the pn 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 pn 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 FabryPerot 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 NonHermitian Quantum Walk 
Abstract
 We analyze a quantum walk on a bipartite onedimensional lattice, in which the particle can decay whenever it visits one of the two sublattices. The corresponding nonHermitian tightbinding 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 nondecaying 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 spinblockaded electron transport regime of quantum dots in the presence of competing hyperfine and spinorbital interactions. The predicted transition from pumping to nonpumping 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 LandauZener 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 stronglydriven regime in qubits, quantum dots and other twolevel systems. The twodimensional Fourier transforms of these patterns are found to exhibit a family of onedimensional 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 solidstate artificial atom 
Abstract
 The energylevel 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 energylevel 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

Pulse imaging and nonadiabatic control of solidstate artificial atoms 
Abstract
 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 Overhauserlike detailed balance constraints. This allows polarization in the direction opposite to that expected from the Overhauser effect. Competition of the electricallydriven 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 spinblockade 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 10fold reduction of fluctuations is possible.
M. S. Rudner, L. S. Levitov 0705.2177v1 [pdf]

Electrically Driven Reverse Overhauser Pumping of Nuclear Spins in Quantum Dots 
Abstract