Center for Quantum Devices > Research > Publications > Ferdinand Kuemmeth
Publications by Ferdinand Kuemmeth
 2018

VoltageControlled Superconducting Quantum Bus 
Abstract
 We demonstrate the ability of an epitaxial semiconductorsuperconductor nanowire to serve as a fieldeffect switch to tune a superconducting cavity. Two superconducting gatemon qubits are coupled to the cavity, which acts as a quantum bus. Using a gate voltage to control the superconducting switch yields up to a factor of 8 change in qubitqubit coupling between the on and off states without detrimental effect on qubit coherence. Highbandwidth operation of the coupling switch on nanosecond timescales degrades qubit coherence.
L. Casparis, N. J. Pearson, A. Kringhøj, T. W. Larsen, F. Kuemmeth, J. Nygård, P. Krogstrup, K. D. Petersson, C. M. Marcus 1802.01327v1 [pdf]

VoltageControlled Superconducting Quantum Bus 
Abstract
 2017

Superconducting Gatemon Qubit based on a Proximitized TwoDimensional
Electron Gas 
Abstract
 The coherent tunnelling of Cooper pairs across Josephson junctions (JJs) generates a nonlinear inductance that is used extensively in quantum information processors based on superconducting circuits, from setting qubit transition frequencies and interqubit coupling strengths, to the gain of parametric amplifiers for quantumlimited readout. The inductance is either set by tailoring the metaloxide dimensions of single JJs, or magnetically tuned by parallelizing multiple JJs in superconducting quantum interference devices (SQUIDs) with local currentbiased flux lines. JJs based on superconductorsemiconductor hybrids represent a tantalizing allelectric alternative. The gatemon is a recently developed transmon variant which employs locally gated nanowire (NW) superconductorsemiconductor JJs for qubit control. Here, we go beyond proofofconcept and demonstrate that semiconducting channels etched from a waferscale twodimensional electron gas (2DEG) are a suitable platform for building a scalable gatemonbased quantum computer. We show 2DEG gatemons meet the requirements by performing voltagecontrolled single qubit rotations and twoqubit swap operations. We measure qubit coherence times up to ~2 us, limited by dielectric loss in the 2DEG host substrate.

Spin of a Multielectron Quantum Dot and Its Interaction with a Neighboring Electron 
Abstract
 We investigate the spin of a multielectron GaAs quantum dot in a sequence of nine charge occupancies, by exchange coupling the multielectron dot to a neighboring twoelectron double quantum dot. For all nine occupancies, we make use of a leakage spectroscopy technique to reconstruct the spectrum of spin states in the vicinity of the interdot charge transition between a single and a multielectron quantum dot. In the same regime we also perform timeresolved measurements of coherent exchange oscillations between the single and multielectron quantum dot. With these measurements, we identify distinct characteristics of the multielectron spin state, depending on whether the dot's occupancy is even or odd. For three out of four even occupancies we do not observe any exchange interaction with the single quantum dot, indicating a spin0 ground state. For the one remaining even occupancy, we observe an exchange interaction that we associate with a spin1 multielectron quantum dot ground state. For all five of the odd occupancies, we observe an exchange interaction associated with a spin1/2 ground state. For three of these odd occupancies, we clearly demonstrate that the exchange interaction changes sign in the vicinity of the charge transition. For one of these, the exchange interaction is negative (i.e. tripletpreferring) beyond the interdot charge transition, consistent with the observed spin1 for the next (even) occupancy. Our experimental results are interpreted through the use of a Hubbard model involving two orbitals of the multielectron quantum dot. Allowing for the spin correlation energy (i.e. including a term favoring Hund's rules) and different tunnel coupling to different orbitals, we qualitatively reproduce the measured exchange profiles for all occupancies.
Filip K. Malinowski, Frederico Martins, Thomas B. Smith, Stephen D. Bartlett, Andrew C. Doherty, Peter D. Nissen, Saeed Fallahi, Geoffrey C. Gardner, Michael J. Manfra, Charles M. Marcus, Ferdinand Kuemmeth Journal reference: Phys. Rev. X 8, 011045 (2018) [ 1710.10012v1 ] DOI: 10.1103/PhysRevX.8.011045

Negative Spin Exchange in a Multielectron Quantum Dot 
Abstract
 By operating a oneelectron quantum dot (fabricated between a multielectron dot and a oneelectron reference dot) as a spectroscopic probe, we study the spin properties of a gatecontrolled multielectron GaAs quantum dot at the transition between odd and even occupation number. We observe that the multielectron groundstate transitions from spin1/2like to singletlike to tripletlike as we increase the detuning towards the next higher charge state. The sign reversal in the inferred exchange energy persists at zero magnetic field, and the exchange strength is tunable by gate voltages and inplane magnetic fields. Complementing spin leakage spectroscopy data, the inspection of coherent multielectron spin exchange oscillations provides further evidence for the sign reversal and, inferentially, for the importance of nontrivial multielectron spin exchange correlations.
Frederico Martins, Filip K. Malinowski, Peter D. Nissen, Saeed Fallahi, Geoffrey C. Gardner, Michael J. Manfra, Charles M. Marcus, Ferdinand Kuemmeth Journal reference: Phys. Rev. Lett. 119, 227701 (2017) [ 1706.01007v1 ] DOI: 10.1103/PhysRevLett.119.227701

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

Symmetric operation of the resonant exchange qubit 
Abstract
 We operate a resonant exchange qubit in a highly symmetric tripledot configuration using IQmodulated RF pulses. At the resulting threedimensional sweet spot the qubit splitting is an order of magnitude less sensitive to all relevant control voltages, compared to the conventional operating point, but we observe no significant improvement in the quality of Rabi oscillations. For weak driving this is consistent with Overhauser field fluctuations modulating the qubit splitting. For strong driving we infer that effective voltage noise modulates the coupling strength between RF drive and the qubit, thereby quickening Rabi decay. Application of CPMG dynamical decoupling sequences consisting of up to n = 32 {\pi} pulses significantly prolongs qubit coherence, leading to marginally longer dephasing times in the symmetric configuration. This is consistent with dynamical decoupling from low frequency noise, but quantitatively cannot be explained by effective gate voltage noise and Overhauser field fluctuations alone. Our results inform recent strategies for the utilization of partial sweet spots in the operation and longdistance coupling of tripledot qubits.
Filip K. Malinowski, Frederico Martins, Peter D. Nissen, Saeed Fallahi, Geoffrey C. Gardner, Michael J. Manfra, Charles M. Marcus, Ferdinand Kuemmeth Journal reference: Phys. Rev. B 96, 045443 (2017) [ 1704.01298v1 ] DOI: 10.1103/PhysRevB.96.045443

Anharmonicity of a superconducting qubit with a fewmode Josephson junction 
Abstract
 Coherent operation of gatevoltagecontrolled hybrid transmon qubits (gatemons) based on semiconductor nanowires was recently demonstrated. Here we experimentally investigate the anharmonicity in epitaxial InAsAl Josephson junctions, a key parameter for their use as a qubit. Anharmonicity is found to be reduced by roughly a factor of two compared to conventional metallic junctions, and dependent on gate voltage. Experimental results are consistent with a theoretical model, indicating that Josephson coupling is mediated by a small number of highly transmitting modes in the semiconductor junction.
A. Kringhøj, L. Casparis, M. Hell, T. W. Larsen, F. Kuemmeth, M. Leijnse, K. Flensberg, P. Krogstrup, J. Nygård, K. D. Petersson, C. M. Marcus Journal reference: Phys. Rev. B 97, 060508 (2018) [ 1703.05643v1 ] DOI: 10.1103/PhysRevB.97.060508

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

Superconducting Gatemon Qubit based on a Proximitized TwoDimensional
Electron Gas 
Abstract
 2016

Transport Signatures of Quasiparticle Poisoning in a Majorana Island 
Abstract
 We investigate effects of quasiparticle poisoning in a Majorana island with strong tunnel coupling to normalmetal leads. In addition to the main Coulomb blockade diamonds, "shadow" diamonds appear, shifted by 1e in gate voltage, consistent with transport through an excited (poisoned) state of the island. Comparison to a simple model yields an estimate of parity lifetime for the strongly coupled island (~ 1 {\mu}s) and sets a bound for a weakly coupled island (> 10 {\mu}s). Fluctuations in the gatevoltage spacing of Coulomb peaks at high field, reflecting Majorana hybridization, are enhanced by the reduced lever arm at strong coupling. In energy units, fluctuations are consistent with previous measurements.
S. M. Albrecht, E. B. Hansen, A. P. Higginbotham, F. Kuemmeth, T. S. Jespersen, J. Nygård, P. Krogstrup, J. Danon, K. Flensberg, C. M. Marcus Journal reference: Phys. Rev. Lett. 118, 137701 (2017) [ 1612.05748v1 ] DOI: 10.1103/PhysRevLett.118.137701

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

Exponential protection of zero modes in Majorana islands 
Abstract
 Majorana zero modes are quasiparticle excitations in condensed matter systems that have been proposed as building blocks of faulttolerant quantum computers [1]. They are expected to exhibit nonAbelian particle statistics, in contrast to the usual statistics of fermions and bosons, enabling quantum operations to be performed by braiding isolated modes around one another. Quantum braiding operations are topologically protected insofar as these modes are pinned near zero energy, and the pinning is predicted to be exponential as the modes become spatially separated. Following theoretical proposals, several experiments have identified signatures of Majorana modes in proximitized nanowires and atomic chains, with small modesplitting potentially explained by hybridization of Majoranas. Here, we use Coulombblockade spectroscopy in an InAs nanowire segment with epitaxial aluminum, which forms a proximityinduced superconducting Coulomb island (a Majorana island) that is isolated from normalmetal leads by tunnel barriers, to measure the splitting of nearzeroenergy Majorana modes. We observe exponential suppression of energy splitting with increasing wire length. For short devices of a few hundred nanometers, subgap state energies oscillate as the magnetic field is varied, as is expected for hybridized Majorana modes. Splitting decreases by a factor of about ten for each half micrometer of increased wire length. For devices longer than about one micrometer, transport in strong magnetic fields occurs through a zeroenergy state that is energetically isolated from a continuum, yielding uniformly spaced Coulombblockade conductance peaks, consistent with teleportation via Majorana modes. Our results help explain the trivialtotopological transition in finite systems and to quantify the scaling of topological protection with endmode separation.
S. M. Albrecht, A. P. Higginbotham, M. Madsen, F. Kuemmeth, T. S. Jespersen, J. Nygård, P. Krogstrup, C. M. Marcus Journal reference: Nature 531, 206 (2016) [pdf] DOI: 10.1038/nature17162

Noise Suppression Using Symmetric Exchange Gates in Spin Qubits 
Abstract
 We demonstrate a substantial improvement in the spinexchange gate using symmetric control instead of conventional detuning in GaAs spin qubits, up to a factorofsix increase in the quality factor of the gate. For symmetric operation, nanosecond voltage pulses are applied to the barrier that controls the interdot potential between quantum dots, modulating the exchange interaction while maintaining symmetry between the dots. Excellent agreement is found with a model that separately includes electrical and nuclear noise sources for both detuning and symmetric gating schemes. Unlike exchange control via detuning, the decoherence of symmetric exchange rotations is dominated by rotationaxis fluctuations due to nuclear field noise rather than direct exchange noise.
Frederico Martins, Filip K. Malinowski, Peter D. Nissen, Edwin Barnes, Saeed Fallahi, Geoffrey C. Gardner, Michael J. Manfra, Charles M. Marcus, Ferdinand Kuemmeth Journal reference: Phys. Rev. Lett. 116, 116801 (2016) [pdf] DOI: 10.1103/PhysRevLett.116.116801

Transport Signatures of Quasiparticle Poisoning in a Majorana Island 
Abstract
 2015

Gatemon Benchmarking and TwoQubit Operations 
Abstract
 Recent experiments have demonstrated superconducting transmon qubits with semiconductor nanowire Josephson junctions. These hybrid gatemon qubits utilize field effect tunability characteristic for semiconductors to allow complete qubit control using gate voltages, potentially a technological advantage over conventional fluxcontrolled transmons. Here, we present experiments with a twoqubit gatemon circuit. We characterize qubit coherence and stability and use randomized benchmarking to demonstrate singlequbit gate errors below 0.7% for all gates, including voltagecontrolled $Z$ rotations. We show coherent capacitive coupling between two gatemons and coherent swap operations. Finally, we perform a twoqubit controlledphase gate with an estimated fidelity of 91%, demonstrating the potential of gatemon qubits for building scalable quantum processors.
L. Casparis, T. W. Larsen, M. S. Olsen, F. Kuemmeth, P. Krogstrup, J. Nygård, K. D. Petersson, C. M. Marcus Journal reference: Phys. Rev. Lett. 116, 150505 (2016) [ 1512.09195v1 ] DOI: 10.1103/PhysRevLett.116.150505

Quantum transport in carbon nanotubes 
Abstract
 Carbon nanotubes are a versatile material in which many aspects of condensed matter physics come together. Recent discoveries, enabled by sophisticated fabrication, have uncovered new phenomena that completely change our understanding of transport in these devices, especially the role of the spin and valley degrees of freedom. This review describes the modern understanding of transport through nanotube devices. Unlike conventional semiconductors, electrons in nanotubes have two angular momentum quantum numbers, arising from spin and from valley freedom. We focus on the interplay between the two. In single quantum dots defined in short lengths of nanotube, the energy levels associated with each degree of freedom, and the spinorbit coupling between them, are revealed by Coulomb blockade spectroscopy. In double quantum dots, the combination of quantum numbers modifies the selection rules of Pauli blockade. This can be exploited to read out spin and valley qubits, and to measure the decay of these states through coupling to nuclear spins and phonons. A second unique property of carbon nanotubes is that the combination of valley freedom and electronelectron interactions in one dimension strongly modifies their transport behaviour. Interaction between electrons inside and outside a quantum dot is manifested in SU(4) Kondo behavior and level renormalization. Interaction within a dot leads to Wigner molecules and more complex correlated states. This review takes an experimental perspective informed by recent advances in theory. As well as the wellunderstood overall picture, we also state clearly open questions for the field. These advances position nanotubes as a leading system for the study of spin and valley physics in one dimension where electronic disorder and hyperfine interaction can both be reduced to a very low level.
E. A. Laird, F. Kuemmeth, G. Steele, K. GroveRasmussen, J. Nygård, K. Flensberg, L. P. Kouwenhoven Journal reference: Rev. Mod. Phys. 87, 703 (2015) [pdf] DOI: 10.1103/RevModPhys.87.703

SemiconductorNanowireBased Superconducting Qubit 
Abstract
 We introduce a hybrid qubit based on a semiconductor nanowire with an epitaxially grown superconductor layer. Josephson energy of the transmonlike device ("gatemon") is controlled by an electrostatic gate that depletes carriers in a semiconducting weak link region. Strong coupling to an onchip microwave cavity and coherent qubit control via gate voltage pulses is demonstrated, yielding reasonably long relaxation times (0.8 {\mu}s) and dephasing times (1 {\mu}s), exceeding gate operation times by two orders of magnitude, in these firstgeneration devices. Because qubit control relies on voltages rather than fluxes, dissipation in resistive control lines is reduced, screening reduces crosstalk, and the absence of flux control allows operation in a magnetic field, relevant for topological quantum information.
T. W. Larsen, K. D. Petersson, F. Kuemmeth, T. S. Jespersen, P. Krogstrup, J. Nygard, C. M. Marcus Journal reference: Phys. Rev. Lett. 115, 127001 (2015) [pdf] DOI: 10.1103/PhysRevLett.115.127001

Hard gap in epitaxial semiconductor–superconductor nanowires 
Abstract
 Many present and future applications of superconductivity would benefit from electrostatic control of carrier density and tunneling rates, the hallmark of semiconductor devices. One particularly exciting application is the realization of topological superconductivity as a basis for quantum information processing. Proposals in this direction based on proximity effect in semiconductor nanowires are appealing because the key ingredients are currently in hand. However, previous instances of proximitized semiconductors show significant tunneling conductance below the superconducting gap, suggesting a continuum of subgap statesa situation that nullifies topological protection. Here, we report a hard superconducting gap induced by proximity effect in a semiconductor, using epitaxial AlInAs superconductorsemiconductor nanowires. The hard gap, along with favorable material properties and gatetunability, makes this new hybrid system attractive for a number of applications, as well as fundamental studies of mesoscopic superconductivity.
W. Chang, S. M. Albrecht, T. S. Jespersen, F. Kuemmeth, P. Krogstrup, J. Nygård, C. M. Marcus Journal reference: Nature Nanotechnology 10, 232 (2015) [pdf] DOI: 10.1038/nnano.2014.306

Parity lifetime of bound states in a proximitized semiconductor nanowire 
Abstract
 Quasiparticle excitations can compromise the performance of superconducting devices, causing high frequency dissipation, decoherence in Josephson qubits, and braiding errors in proposed Majoranabased topological quantum computers. Quasiparticle dynamics have been studied in detail in metallic superconductors but remain relatively unexplored in semiconductorsuperconductor structures, which are now being intensely pursued in the context of topological superconductivity. To this end, we introduce a new physical system comprised of a gateconfined semiconductor nanowire with an epitaxially grown superconductor layer, yielding an isolated, proximitized nanowire segment. We identify Andreevlike bound states in the semiconductor via bias spectroscopy, determine the characteristic temperatures and magnetic fields for quasiparticle excitations, and extract a parity lifetime (poisoning time) of the bound state in the semiconductor exceeding 10 ms.
A. P. Higginbotham, S. M. Albrecht, G. Kirsanskas, W. Chang, F. Kuemmeth, P. Krogstrup, T. S. Jespersen, J. Nygard, K. Flensberg, C. M. Marcus Journal reference: Nature Physics 11, 1017 (2015) [pdf] DOI: 10.1038/nphys3461

Gatemon Benchmarking and TwoQubit Operations 
Abstract
 2014

Hole Spin Coherence in a Ge/Si Heterostructure Nanowire 
Abstract
 Relaxation and dephasing of hole spins are measured in a gatedefined Ge/Si nanowire double quantum dot using a fast pulsedgate method and dispersive readout. An inhomogeneous dephasing time $T_2^* \sim 0.18~\mathrm{\mu s}$ exceeds corresponding measurements in IIIV semiconductors by more than an order of magnitude, as expected for predominately nuclearspinfree materials. Dephasing is observed to be exponential in time, indicating the presence of a broadband noise source, rather than Gaussian, previously seen in systems with nuclearspindominated dephasing.
A. P. Higginbotham, T. W. Larsen, J. Yao, H. Yan, C. M. Lieber, C. M. Marcus, F. Kuemmeth Journal reference: Nano Letters 14, 3582 (2014) [pdf] DOI: 10.1021/nl501242b

Antilocalization of Coulomb Blockade in a Ge/Si Nanowire 
Abstract
 The distribution of Coulomb blockade peak heights as a function of magnetic field is investigated experimentally in a GeSi nanowire quantum dot. Strong spinorbit coupling in this holegas system leads to antilocalization of Coulomb blockade peaks, consistent with theory. In particular, the peak height distribution has its maximum away from zero at zero magnetic field, with an average that decreases with increasing field. Magnetoconductance in the openwire regime places a bound on the spinorbit length ($l_{so}$ < 20 nm), consistent with values extracted in the Coulomb blockade regime ($l_{so}$ < 25 nm).
A. P. Higginbotham, F. Kuemmeth, T. W. Larsen, M. Fitzpatrick, J. Yao, H. Yan, C. M. Lieber, C. M. Marcus Journal reference: Phys. Rev. Lett. 112, 216806 (2014) [pdf] DOI: 10.1103/PhysRevLett.112.216806

Hole Spin Coherence in a Ge/Si Heterostructure Nanowire 
Abstract
 2013

Coherent Operations and Screening in Multielectron Spin Qubits 
Abstract
 The performance of multielectron spin qubits is examined by comparing exchange oscillations in coupled singleelectron and multielectron quantum dots in the same device. Fast (> 1 GHz) exchange oscillations with a quality factor Q > 15 are found for the multielectron case, compared to Q ~ 2 for the singleelectron case, the latter consistent with previous experiments. A model of dephasing that includes voltage and hyperfine noise is developed that is in good agreement with both single and multielectron data, though in both cases additional exchangeindependent dephasing is needed to obtain quantitative agreement across a broad parameter range.
A. P. Higginbotham, F. Kuemmeth, M. P. Hanson, A. C. Gossard, C. M. Marcus Journal reference: Phys. Rev. Lett. 112, 026801 (2014) [pdf] DOI: 10.1103/PhysRevLett.112.026801

Observation and spectroscopy of a twoelectron Wigner molecule in an ultraclean carbon nanotube 
Abstract
 Coulomb interactions can have a decisive effect on the ground state of electronic systems. The simplest system in which interactions can play an interesting role is that of two electrons on a string. In the presence of strong interactions the two electrons are predicted to form a Wigner molecule, separating to the ends of the string due to their mutual repulsion. This spatial structure is believed to be clearly imprinted on the energy spectrum, yet to date a direct measurement of such a spectrum in a controllable onedimensional setting is still missing. Here we use an ultraclean suspended carbon nanotube to realize this system in a tunable potential. Using tunneling spectroscopy we measure the excitation spectra of two interacting carriers, electrons or holes, and identify seven lowenergy states characterized by their spin and isospin quantum numbers. These states fall into two multiplets according to their exchange symmetries. The formation of a stronglyinteracting Wigner molecule is evident from the small energy splitting measured between the two multiplets, that is quenched by an order of magnitude compared to the noninteracting value. Our ability to tune the twoelectron state in space and to study it for both electrons and holes provides an unambiguous demonstration of the fundamental Wigner molecule state.
S. Pecker, F. Kuemmeth, A. Secchi, M. Rontani, D. C. Ralph, P. L. McEuen, S. Ilani Journal reference: Nature Physics 9, 576581 (2013) [pdf] DOI: 10.1038/nphys2692

Coherent Operations and Screening in Multielectron Spin Qubits 
Abstract
 2011

Hole spin relaxation in Ge–Si core–shell nanowire qubits 
Abstract
 Controlling decoherence is the most challenging task in realizing quantum information hardware. Single electron spins in gallium arsenide are a leading candidate among solid state implementations, however strong coupling to nuclear spins in the substrate hinders this approach. To realize spin qubits in a nuclearspinfree system, intensive studies based on groupIV semiconductor are being pursued. In this case, the challenge is primarily control of materials and interfaces, and device nanofabrication. We report important steps toward implementing spin qubits in a predominantly nuclearspinfree system by demonstrating state preparation, pulsed gate control, and chargesensing spin readout of confined hole spins in a onedimensional Ge/Si nanowire. With fast gating, we measure T1 spin relaxation times in coupled quantum dots approaching 1 ms, increasing with lower magnetic field, consistent with a spinorbit mechanism that is usually masked by hyperfine contributions.
Yongjie Hu, Ferdinand Kuemmeth, Charles M. Lieber, Charles M. Marcus Journal reference: Nature Nanotechnology 7, 4750 (2012) [pdf] DOI: 10.1038/nnano.2011.234

Hole spin relaxation in Ge–Si core–shell nanowire qubits 
Abstract
 2010

Spinorbit effects in carbonnanotube double quantum dots 
Abstract
 We study the energy spectrum of symmetric double quantum dots in narrowgap carbon nanotubes with one and two electrostatically confined electrons in the presence of spinorbit and Coulomb interactions. Compared to GaAs quantum dots, the spectrum exhibits a much richer structure because of the spinorbit interaction that couples the electron's isospin to its real spin through two independent coupling constants. In a single dot, both constants combine to split the spectrum into two Kramers doublets, while the antisymmetric constant solely controls the difference in the tunneling rates of the Kramers doublets between the dots. For the twoelectron regime, the detailed structure of the spinorbit split energy spectrum is investigated as a function of detuning between the quantum dots in a 22dimensional Hilbert space within the framework of a singlelongitudinalmode model. We find a competing effect of the tunneling and Coulomb interaction. The former favors a leftright symmetric twoparticle ground state, while in the regime where the Coulomb interaction dominates over tunneling, a leftright antisymmetric ground state is found. As a result, ground states on both sides of the $(11)$$(02)$ degeneracy point may possess opposite leftright symmetry, and the electron dynamics when tuning the system from one side of the $(11)$$(02)$ degeneracy point to the other is controlled by three selection rules (in spin, isospin, and leftright symmetry). We discuss implications for the spindephasing and Pauli blockade experiments.
S. Weiss, E. I. Rashba, F. Kuemmeth, H. O. H Churchill, K. Flensberg Journal reference: Physical Review B 82, 165427 (2010) [pdf] DOI: 10.1103/PhysRevB.82.165427

Spinorbit effects in carbonnanotube double quantum dots 
Abstract
 2009

Giant spin rotation under quasiparticlephotoelectron conversion: Joint effect of sublattice interference and spinorbit coupling 
Abstract
 Spin and angularresolved photoemission spectroscopy is a basic experimental tool for unveiling spin polarization of electron eigenstates in crystals. We prove, by using spinorbit coupled graphene as a model, that photoconversion of a quasiparticle inside a crystal into a photoelectron can be accompanied with a dramatic change in its spin polarization, up to a total spin flip. This phenomenon is typical of quasiparticles residing away from the Brillouin zone center and described by higher rank spinors, and results in exotic patterns in the angular distribution of photoelectrons.
Ferdinand Kuemmeth, Emmanuel I. Rashba Journal reference: Phys. Rev. B 80, 241409 (2009) [pdf] DOI: 10.1103/PhysRevB.80.241409

Carbon nanotubes for coherent spintronics 
Abstract
 Carbon nanotubes bridge the molecular and crystalline quantum worlds, and their extraordinary electronic, mechanical and optical properties have attracted enormous attention from a broad scientific community. We review the basic principles of fabricating spinelectronic devices based on individual, electricallygated carbon nanotubes, and present experimental efforts to understand their electronic and nuclear spin degrees of freedom, which in the future may enable quantum applications.
F. Kuemmeth, H. O. H. Churchill, P. K. Herring, C. M. Marcus Journal reference: Materials Today 13, 18 (2010) [pdf] DOI: 10.1016/S13697021(10)700304

Giant spin rotation under quasiparticlephotoelectron conversion: Joint effect of sublattice interference and spinorbit coupling 
Abstract
 2008

Measurement of Discrete EnergyLevel Spectra in Individual Chemically Synthesized Gold Nanoparticles 
Abstract
 We form singleelectron transistors from individual chemicallysynthesized gold nanoparticles, 515 nm in diameter, with monolayers of organic molecules serving as tunnel barriers. These devices allow us to measure the discrete electronic energy levels of individual gold nanoparticles that are, by virtue of chemical synthesis, welldefined in their composition, size and shape. We show that the nanoparticles are nonmagnetic and have spectra in good accord with randommatrixtheory predictions taking into account strong spinorbit coupling.
F. Kuemmeth, K. I. Bolotin, S. F. Shi, D. C. Ralph Journal reference: Nano Lett., 8 (12), 45064512 (2008) [pdf] DOI: 10.1021/nl802473n

Electron–nuclear interaction in 13C nanotube double quantum dots 
Abstract
 For coherent electron spins, hyperfine coupling to nuclei in the host material can either be a dominant source of unwanted spin decoherence or, if controlled effectively, a resource allowing storage and retrieval of quantum information. To investigate the effect of a controllable nuclear environment on the evolution of confined electron spins, we have fabricated and measured gatedefined double quantum dots with integrated charge sensors made from singlewalled carbon nanotubes with a variable concentration of 13C (nuclear spin I=1/2) among the majority zeronuclearspin 12C atoms. Spinsensitive transport in doubledot devices grown using methane with the natural abundance (~ 1%) of 13C is compared with similar devices grown using an enhanced (~99%) concentration of 13C. We observe strong isotope effects in spinblockaded transport, and from the dependence on external magnetic field, estimate the hyperfine coupling in 13C nanotubes to be on the order of 100 microeV, two orders of magnitude larger than anticipated theoretically. 13Cenhanced nanotubes are an interesting new system for spinbased quantum information processing and memory, with nuclei that are strongly coupled to gatecontrolled electrons, differ from nuclei in the substrate, are naturally confined to one dimension, lack quadrupolar coupling, and have a readily controllable concentration from less than one to 10^5 per electron.
H. O. H. Churchill, A. J. Bestwick, J. W. Harlow, F. Kuemmeth, D. Marcos, C. H. Stwertka, S. K. Watson, C. M. Marcus Journal reference: Nature Physics 5, 321 (2009) [pdf] DOI: 10.1038/nphys1247

Relaxation and Dephasing in a Twoelectron 13C Nanotube Double Quantum
Dot 
Abstract
 We use charge sensing of Pauli blockade (including spin and isospin) in a twoelectron 13C nanotube double quantum dot to measure relaxation and dephasing times. The relaxation time, T1, first decreases with parallel magnetic field then goes through a minimum in a field of 1.4 T. We attribute both results to the spinorbitmodified electronic spectrum of carbon nanotubes, which suppresses hyperfine mediated relaxation and enhances relaxation due to soft phonons. The inhomogeneous dephasing time, T2*, is consistent with previous data on hyperfine coupling strength in 13C nanotubes.
H. O. H. Churchill, F. Kuemmeth, J. W. Harlow, A. J. Bestwick, E. I. Rashba, K. Flensberg, C. H. Stwertka, T. Taychatanapat, S. K. Watson, C. M. Marcus Journal reference: Phys. Rev. Lett. 102, 166802 (2009). [pdf] DOI: 10.1103/PhysRevLett.102.166802

Coupling of spin and orbital motion of electrons in carbon nanotubes 
Abstract
 Electrons in atoms possess both spin and orbital degrees of freedom. In nonrelativistic quantum mechanics, these are independent, resulting in large degeneracies in atomic spectra. However, relativistic effects couple the spin and orbital motion leading to the wellknown fine structure in their spectra. The electronic states in defectfree carbon nanotubes (NTs) are widely believed to be fourfold degenerate, due to independent spin and orbital symmetries, and to also possess electronhole symmetry. Here we report measurements demonstrating that in clean NTs the spin and orbital motion of electrons are coupled, thereby breaking all of these symmetries. This spinorbit coupling is directly observed as a splitting of the fourfold degeneracy of a single electron in ultraclean quantum dots. The coupling favours parallel alignment of the orbital and spin magnetic moments for electrons and antiparallel alignment for holes. Our measurements are consistent with recent theories that predict the existence of spinorbit coupling in curved graphene and describe it as a spindependent topological phase in NTs. Our findings have important implications for spinbased applications in carbonbased systems, entailing new design principles for the realization of qubits in NTs and providing a mechanism for allelectrical control of spins in NTs.
F. Kuemmeth, S. Ilani, D. C. Ralph, P. L. McEuen Journal reference: Nature 452, 448452 (27 March 2008) [pdf] DOI: 10.1038/nature06822

Measurement of Discrete EnergyLevel Spectra in Individual Chemically Synthesized Gold Nanoparticles 
Abstract
 2006

Anisotropic Magnetoresistance and Anisotropic Tunneling Magnetoresistance due to Quantum Interference in Ferromagnetic Metal Break Junctions 
Abstract
 We measure the lowtemperature resistance of permalloy break junctions as a function of contact size and the magnetic field angle, in applied fields large enough to saturate the magnetization. For both nanometerscale metallic contacts and tunneling devices we observe large changes in resistance with angle, as large as 25% in the tunneling regime. The pattern of magnetoresistance is sensitive to changes in bias on a scale of a few mV. We interpret the effect as a consequence of conductance fluctuations due to quantum interference.
Kirill I. Bolotin, Ferdinand Kuemmeth, D. C. Ralph Journal reference: Physical Review Letters 97, 127202 (2006) [ condmat/0602251v2 ] DOI: 10.1103/PhysRevLett.97.127202

Anisotropic Magnetoresistance and Anisotropic Tunneling Magnetoresistance due to Quantum Interference in Ferromagnetic Metal Break Junctions 
Abstract
 2005

From Ballistic Transport to Tunneling in Electromigrated Ferromagnetic Breakjunctions 
Abstract
 We fabricate ferromagnetic nanowires with constrictions whose cross section can be reduced gradually from 100 nm to the atomic scale and eventually to the tunneling regime by means of electromigration. These devices are mechanically stable against magnetostriction and magnetostatic effects. We measure magnetoresistances ~ 0.3% for 100*30 nm^2 constrictions, increasing to a maximum of 80% for atomicscale widths. These results are consistent with a geometricallyconstrained domain wall trapped at the constriction. For the devices in the tunneling regime we observe large fluctuations in MR, between 10 and 85%.
Kirill I. Bolotin, F. Kuemmeth, Abhay N. Pasupathy, D. C. Ralph Journal reference: Nano Letters 6, 123127 (2006) [ condmat/0510410v1 ] DOI: 10.1021/nl0522936

From Ballistic Transport to Tunneling in Electromigrated Ferromagnetic Breakjunctions 
Abstract
 2003

Metalnanoparticle singleelectron transistors fabricated using electromigration 
Abstract
 We have fabricated singleelectron transistors from individual metal nanoparticles using a geometry that provides improved coupling between the particle and the gate electrode. This is accomplished by incorporating a nanoparticle into a gap created between two electrodes using electromigration, all on top of an oxidized aluminum gate. We achieve sufficient gate coupling to access more than ten charge states of individual gold nanoparticles (515 nm in diameter). The devices are sufficiently stable to permit spectroscopic studies of the electroninabox level spectra within the nanoparticle as its charge state is varied.
K. I. Bolotin, F. Kuemmeth, A. N. Pasupathy, D. C. Ralph Journal reference: K.I. Bolotin et al, APL 84, 3154 (2004) [ condmat/0310594v1 ] DOI: 10.1063/1.1695203

Metalnanoparticle singleelectron transistors fabricated using electromigration 
Abstract