arXiv subjects

Alexander Shnirman

Publications and source records attributed to Alexander Shnirman.

At least 55 records · Page 3Linked to original sources

arXiv2016

Using Majorana spin-1/2 representation for the spin-boson model

The Majorana representation for spin operators enables efficient application of field-theoretical methods for the analysis of spin dynamics. Moreover, a wide class of spin correlation functions can be reduced to Majorana correlations of the same order, simplifying their calculation. For the spin-boson model, direct application of this method in the lowest order allows for a straightforward computation of the transverse-spin correlations, however, for the longitudinal-spin correlations it apparently fails in the long-time limit. Here we indicate the reason and discuss, how this method can be used as a convenient and accurate tool for generic spin correlations. Specifically, we demonstrate that accurate results are obtained by avoiding the use of the longitudinal Majorana fermion, and that correlations of the remaining transverse Majorana fermions can be easily evaluated using an effective Gaussian action.

cond-mat.mes-hall↗

arXiv2016

Decoherence of a quantum two-level system by spectral diffusion

We study the dephasing of an individual high-frequency tunneling two-level system (TLS) due to its interaction with an ensemble of low-frequency thermal TLSs which are described by the standard tunneling model (STM). We show that the dephasing by the bath of TLSs explains both the dependence of the Ramsey dephasing rate on an externally applied strain as well as its order of magnitude, as observed in a recent experiment [J. Lisenfeld et al.]. However, the theory based on the STM predicts the Hahn-echo protocol to be much more efficient, yielding too low echo dephasing rates, as compared to the experiment. Also the strain dependence of the echo dephasing rate predicted by the STM does not agree with the measured quadratic dependence, which would fit to a high-frequency white noise environment. We suggest that few fast TLSs which are coupled much more strongly to the strain fields than the usual TLSs of the STM give rise to such a white noise. This explains the magnitude and strong fluctuations of the echo dephasing rate observed in the experiment.

cond-mat.dis-nn↗

arXiv2016

Decoherence spectroscopy with individual two-level tunneling defects

Recent progress with microfabricated quantum devices has revealed that an ubiquitous source of noise originates in tunneling material defects that give rise to a sparse bath of parasitic two-level systems (TLSs). For superconducting qubits, TLSs residing on electrode surfaces and in tunnel junctions account for a major part of decoherence and thus pose a serious roadblock to the realization of solid-state quantum processors. Here, we utilize a superconducting qubit to explore the quantum state evolution of coherently operated TLSs in order to shed new light on their individual properties and environmental interactions. We identify a frequency-dependence of TLS energy relaxation rates that can be explained by a coupling to phononic modes rather than by anticipated mutual TLS interactions. Most investigated TLSs are found to be free of pure dephasing at their energy degeneracy points, around which their Ramsey and spin-echo dephasing rates scale linearly and quadratically with asymmetry energy, respectively. We provide an explanation based on the standard tunneling model, and identify interaction with incoherent low-frequency (thermal) TLSs as the major mechanism of the pure dephasing in coherent high-frequency TLS.

cond-mat.supr-con↗

arXiv2015

Current-phase relation and $h/e$-periodic critical current of a chiral Josephson contact between 1D Majorana modes

We explore a long Josephson contact transporting Cooper pairs between 1D charge-neutral chiral Majorana modes in the leads via charged Dirac chiral modes in the normal region. We investigate the regimes of (i) transparent contacts and (ii) tunnel junctions implemented in 3D topological insulator/superconductor/magnet hybrid structures. The setup acts as a SQUID controlled by the magnetic flux enclosed by the chiral loop of the normal region. This chirality leads to the fractional $h/e$-periodic pattern of critical current. The current-phase relation can have sawtooth-like shape with spikes at unusual even phases of $2πn$.

cond-mat.supr-con↗

arXiv2015

Depinning of disordered bosonic chains

We consider one-dimensional bosonic chains with a repulsive boson-boson interaction that decays exponentially on large length-scales. This model describes transport of Cooper-pairs in a Josepshon junction array, or transport of magnetic flux quanta in quantum-phase-slip ladders, i.e. arrays of superconducting wires in a ladder-configuration that allow for the coherent tunnelling of flux quanta. In the low-frequency, long wave-length regime these chains can be mapped to an effective model of a one-dimensional elastic field in a disordered potential. The onset of transport in these systems, when biased by external voltage, is described by the standard depinning theory of elastic media in disordered pinning potentials. We numerically study the regimes that are of relevance for quantum-phase-slip ladders. These are (i) very short chains and (ii) the regime of weak disorder. For chains shorter than the typical pinning length, i.e., the Larkin length, the chains reach a saturation regime where the depinning voltage does not depend on the decay length of the repulsive interaction. In the regime of weak disorder we find an emergent correlation length-scale that depends on the disorder strength. For arrays shorter than this length the onset of transport is similar to the clean arrays, i.e., is due to the penetration of solitons into the array. We discuss the depinning scenarios for longer arrays in this regime.

cond-mat.mes-hall↗

arXiv2015

U(1) and SU(2) quantum dissipative systems: The Caldeira-Leggett vs. the Amegaokar-Eckern-Schön approaches

There are two paradigmatic frameworks for treating quantum systems coupled to a dissipative environment: the Caldeira-Leggett and the Ambegaokar-Eckern-Schön approaches. Here we recall the differences between them, and explain the consequences when each is applied to a zero dimensional spin (possessing an SU(2) symmetry) in a dissipative environment (a dissipative quantum dot near or beyond the Stoner instability point).

cond-mat.mes-hall↗

arXiv2015

Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits

Since the very first experiments, superconducting circuits have suffered from strong coupling to environmental noise, destroying quantum coherence and degrading performance. In state-of-the-art experiments, it is found that the relaxation time of superconducting qubits fluctuates as a function of time. We present measurements of such fluctuations in a 3D-Transmon circuit and develop a qualitative model based on interactions within a bath of background two-level systems (TLS) which emerge from defects in the device material. In our model, the time-dependent noise density acting on the qubit emerges from its near-resonant coupling to high-frequency TLS which experience energy fluctuations due to their interaction with thermally fluctuating TLS at low frequencies. We support the model by providing experimental evidence of such energy fluctuations observed in a single TLS in a phase qubit circuit.

cond-mat.mes-hall↗

arXiv2015

One-dimensional Josephson junction arrays: Lifting the Coulomb blockade by depinning

Experiments with one-dimensional arrays of Josephson junctions in the regime of dominating charging energy show that the Coulomb blockade is lifted at the threshold voltage, which is proportional to the array's length and depends strongly on the Josephson energy. We explain this behavior as de-pinning of the Cooper-pair-charge-density by the applied voltage. We assume strong charge disorder and argue that physics around the de-pinning point is governed by a disordered sine-Gordon-like model. This allows us to employ the well-known theory of charge density wave de-pinning. Our model is in good agreement with the experimental data.

cond-mat.mes-hall↗

arXiv2015

Geometric Quantum Noise of Spin

The presence of geometric phases is known to affect the dynamics of the systems involved. Here we consider a quantum degree of freedom, moving in a dissipative environment, whose dynamics is described by a Langevin equation with quantum noise. We show that geometric phases enter the stochastic noise terms. Specifically, we consider small ferromagnetic particles (nano-magnets) or quantum dots close to Stoner instability, and investigate the dynamics of the total magnetization in the presence of tunneling coupling to the metallic leads. We generalize the Ambegaokar-Eckern-Schön (AES) effective action and the corresponding semiclassical equations of motion from the U(1) case of the charge degree of freedom to the SU(2) case of the magnetization. The Langevin forces (torques) in these equations are strongly influenced by the geometric phase. As a first but nontrivial application we predict low temperature quantum diffusion of the magnetization on the Bloch sphere, which is governed by the geometric phase. We propose a protocol for experimental observation of this phenomenon.

cond-mat.mes-hall↗

arXiv2014

Superconductor-insulator transition in nanowires and nanowire arrays

Superconducting nanowires are the dual elements to Josephson junctions, with quantum phase-slip processes replacing the tunneling of Cooper pairs. When the quantum phase-slip amplitude ES is much smaller than the inductive energy EL, the nanowire responds as a superconducting inductor. When the inductive energy is small, the response is capacitive. The crossover at low temperatures as a function of ES/EL is discussed and compared with earlier experimental results. For one-dimensional and two-dimensional arrays of nanowires quantum phase transitions are expected as a function of ES/EL. They can be tuned by a homogeneous magnetic frustration.

cond-mat.supr-con↗

arXiv2014

Flux $1/f^α$ noise in 2D Heisenberg spin glasses: effects of weak anisotropic interactions

We study the dynamics of a two-dimensional ensemble of randomly distributed classical Heisenberg spins with isotropic RKKY and weaker anisotropic dipole-dipole couplings. Such ensembles may give rise to the flux noise observed in SQUIDs with a $1/f^α$ power spectrum ($α\lesssim 1$). We solve numerically the Landau-Lifshiftz-Gilbert equations of motion in the dissipationless limit. We find that Ising type fluctuators, which arise from spin clustering close to a spin-glass critical behavior with $T_c =0$, give rise to $1/f^α$ noise. Even weak anisotropic interactions lead to a crossover from the Heisenberg-type criticality to the much stronger Ising-type criticality. The temperature dependent exponent $α(T) \lesssim 1$ grows and approaches unity when the temperature is lowered. This mechanism acts in parallel to the spin diffusion mechanism. Whereas the latter is sensitive to the device geometry, the spin-clustering mechanism is largely geometry independent.

cond-mat.mes-hall↗

arXiv2014

Nonequilibrium Spin Noise and Noise of Susceptibility

We analyze out-of-equilibrium fluctuations in a driven spin system and relate them to the noise of spin susceptibility. In the spirit of the linear response theory we further relate the noise of susceptibility to a $4$-spin correlation function in equilibrium. We show that, in contrast to the second noise (noise of noise), the noise of susceptibility is a direct measure of non-Gaussian fluctuations in the system. We develop a general framework for calculating the noise of susceptibility using the Majorana representation of spin-1/2 operators. We illustrate our approach by a simple example of non-interacting spins coupled to a dissipative (Ohmic) bath.

cond-mat.mes-hall↗

arXiv2014

Distribution of energy dissipated by a driven two-level system

In the context of fluctuation relations, we study the distribution of energy dissipated by a driven two-level system. Incorporating an energy counting field into the well known spin-boson model enables us to calculate the distribution function of the amount of energy exchanged between the system and the bath. We also derive the conditional distribution functions of the energy exchanged with the bath for particular initial and/or final states of the two-level system. We confirm the symmetry of the conditional distribution function expected from the theory of fluctuation relations. We also find that the conditional distribution functions acquire considerable quantum corrections at times shorter or of the order of the dephasing time. Our findings can be tested using solid-state qubits.

cond-mat.mes-hall↗

arXiv2014

Statistics of energy dissipation in a quantum dot operating in the cotunneling regime

At Coulomb blockade valleys inelastic cotunneling processes generate particle-hole excitations in quantum dots (QDs), and lead to energy dissipation. We have analyzed the probability distribution function (PDF) of energy dissipated in a QD due to such processes during a given time interval. We obtained analytically the cumulant generating function, and extracted the average, variance and Fano factor. The latter diverges as $T^3/(eV)^2$ at bias $eV$ smaller than the temperature $T$, and reaches the value $3 eV / 5$ in the opposite limit. The PDF is further studied numerically. As expected, Crooks fluctuation relation is not fulfilled by the PDF. Our results can be verified experimentally utilizing transport measurements of charge.

cond-mat.mes-hall↗

arXiv2013

Lasing and transport in a coupled quantum dot-resonator system

We investigate a double quantum dot coupled to a transmission line resonator. By driving a current through the double dot, a population inversion between the dot levels can be created, and a lasing state of the radiation field is generated within a sharp resonance window. The transport current correlates with the lasing state. The sharp resonance condition allows for resolving small differences in the dot properties. Dissipative processes in the quantum dots and their effect on the lasing and transport behavior are investigated.

cond-mat.mes-hall↗

arXiv2013

Measuring fermion parity correlations and relaxation rates in 1D topological superconducting wires

Zero energy Majorana fermion states (Majoranas) can arise at the ends of a semiconducting wire in proximity with a superconductor. A first generation of experiments has detected a zero bias conductance peak in these systems that strongly suggests these Majoranas do exist; however, a definitive demonstration of the long-ranged entanglement that is crucial for potential applications in quantum computing has yet to be carried out. This work discusses two possible measurement schemes to detect this long-ranged entanglement in a wire system with two coupled pairs of Majoranas, by varying the coupling between one pair while measuring the fermion parity of the second pair. First, in a system with two coupled pairs of Majoranas, we discuss how varying the coupling of one pair in time, while measuring temporal fermion parity correlations of the second pair, allows for an experimental probe of long-ranged Majorana entanglement. Second, we show that the power spectrum of the charge noise (fermion parity noise) of one pair contains signatures of these correlations, as well as allowing one to infer the parity relaxation rate.

cond-mat.str-el↗

arXiv2013

Non-adiabatic processes in Majorana qubit systems

We investigate the non-adiabatic processes occurring during the manipulations of Majorana qubits in 1-D semiconducting wires with proximity induced superconductivity. Majorana qubits are usually protected by the excitation gap. Yet, manipulations performed at a finite pace can introduce both decoherence and renormalization effects. Though exponentially small for slow manipulations, these effects are important as they may constitute the ultimate decoherence mechanism. Moreover, as adiabatic topological manipulations fail to produce a universal set of quantum gates, non-adiabatic manipulations might be necessary to perform quantum computation.

cond-mat.mes-hall↗

arXiv2013

Adiabatic pumping through an interacting quantum dot with spin-orbit coupling

We study adiabatic pumping through a two-level quantum dot with spin-orbit coupling. Using a diagrammatic real-time approach, we calculate both the pumped charge and spin for a periodic variation of the dot's energy levels in the limit of weak tunnel coupling. Thereby, we compare the two limits of vanishing and infinitely large charging energy on the quantum dot. We discuss the dependence of the pumped charge and pumped spin on gate voltages, the symmetry in the tunnel-matrix elements and spin-orbit coupling strength. We identify the possibility to generate pure spin currents in the absence of charge currents.

cond-mat.mes-hall↗