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arXiv:cond-mat/9910506

Andreev Spectroscopy for Superconducting Phase Qubits

M. V. Feigel’man, L. B. Ioffe, V. B. Geshkenbeǐn, G. Blatter

Published Oct 31, 1999• 1 citation
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Abstract

We propose a new method to measure the coherence time of superconducting phase qubits based on the analysis of the magnetic-field dependent dc nonlinear Andreev current across a high-resistance tunnel contact between the qubit and a dirty metal wire and derive a quantitative relation between the subgap I-V characteristic and the internal correlation function of the qubit.

DOI
10.48550/arxiv.cond-mat/9910506

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A study of the Andreev level current through a weakly voltage-biased single-mode superconducting quantum point contact under microwave irradiation is presented. The applied microwave field induces resonant transitions between the current carrying Andreev states localized to the contact region, which results in an increase of the dc subgap current by several orders of magnitude. The applied voltage-bias couples to the superconductor phase difference across the junction, which will evolve in time. In turn the Andreev levels will oscillate adiabatically within the superconductor energy gap. Depending on the frequency of the applied field there can be either one or two resonances per oscillation period. When considering the case of two resonances the calculated dc-current exhibits an interference pattern as a function of inverse voltage. A measurement of the oscillation period would make it possible to reconstruct the Andreev level spectrum. Further, a detailed study is conducted concerning the microwave-induced current as a function of voltage bias, and the amplitude and frequency of the applied field. In realistic experimental situations there are equilibrium fluctuations of the applied voltage bias and sometimes impurity induced noise in the contact transparency. The amount of dephasing induced on the interference pattern by these fluctuations is estimated. In most cases the interference pattern will be subject to some amount of decay. However, there are parameter values for which this decay will be small. The decay originating from equilibrium fluctuations is predicted to have a non-monotonic dependence on the position of the resonances, while the decay induced by impurities should increase linearly when the separation between the resonances is increased. This difference could be used to distinguish between the two sources. The results also indicate that it should be possible to experimentally investigate the coupling between Andreev states and their environment, explicitly the impedance which the contact "sees" and the coupling strength between impurities and Andreev states.

•Jan 1, 2000•1 citation
We propose a new method to measure the coherence time of superconducting phase qubits based on the analysis of the magnetic-field dependent dc nonlinear Andreev current across a high-resistance tunnel contact between the qubit and a dirty metal wire and derive a quantitative relation between the subgap I-V characteristic and the internal correlation function of the qubit.
New method to probe quantum dynamics of the order parameter phase of a small superconductive island is proposed. The idea is to measure Andreev subgap conductance between the island and a dirty normal-metal wire connected with the island by very high-resistance tunnel barrier. The phase on the island is supposed to stay primarly in one of the two nearly degenerate classical minima i.e. the island is an active element of the Superconductive Phase Qubit. Voltage-dependence of the differential subgap conductance measured at low temperatures are predicted to demonstrate crucially different behavior depending on the type of the internal dynamics of phase (coherent tunnelling of phase, non-coherent tunnelling, or no tunneling). Thus the measurements of nonliner Andreev conductance is a tool to probe the type of quantum behavior of the artificial two-level system.
In this thesis we present theoretical investigations of the effects of Andreev bound states on the current transport in superconducting interferometers. We also investigate the slow dynamics of the Andreev states in a superconducting point contact, and the possible application as a quantum bit. We consider superconductor-normal metal-superconductor (SNS) and normal metalsuperconductor (NS) interferometers, where the contact region is a Y-shaped normal metal wave guide, and the two connection points to the same superconducting electrode can have different phases. The electric current in the interferometer is calculated as a function of the applied voltage and the phase difference . Andreev reflection in SNS and NS interferometers incorporates two features: interference in the arms of the Y-shaped normal region, and interplay with Andreev resonances. The latter feature yields rich phase dependent current structures in the subgap voltage region. The interference effect leads to a suppression of the current structures at . We investigate the effects on the Josephson current in NS interferometers due to current injection from the normal electrode. The two main effects of the nonequilibrium situation are: nonequilibrium population of the Andreev levels, which can result in enhancement, suppression, or even sign reversal of the Josephson current, and an anomalous interference Josephson effect, which gives rise to a long range Josephson effect, increasing with the voltage up to the superconducting gap . The two Andreev states in a superconducting quantum point contact can be accessed for manipulation and measurement by embedding the point contact in a superconducting loop. We calculate an effective Hamiltonian for the slow dynamics of the Andreev two-level system in the ring. Furthermore, we discuss methods of manipulation of the Andreev levels, and coupling of qubits. The state of the Andreev two-level system can be read out by monitoring the macroscopic quantum tunneling in a current biased Josephson junction, which is embedded in the superconducting ring of the qubit. We discuss the effects on the qubit, the readout scheme and the signal-to-noise ratio. THESIS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY Coherent processes in Superconducting quantum interferometers and qubits
In this talk I will address the problem of supercurrent instability in highly transparent weak links. I will demonstrate that at subgap energies quantum behavior of superconducting weak links can be exactly accounted for by an effective Hamiltonian for a Josephson particle in a quantum dissipative environment formed by Andreev levels. I will identify several macroscopic quantum tunneling (MQT) regimes and predict a non-trivial non-monotonous dependence of the switching current distribution on temperature which can be observed in MQT experiments with transparent superconducting weak links. I will also argue that intrinsic dissipation in such weak links can be studied by means of qubit spectroscopy. Varying either the bias current or magnetic flux through a superconducting ring in the rf-SQUID setup, one can tune the level splitting value close to the bottom of the Josephson potential well. Monitoring the qubit energy relaxation time one can probe the spectral density of the effective dissipative bath and unambiguously identify the contribution emerging from Andreev levels.
We theoretically study the dephasing of an Andreev spin qubit (ASQ) due to electric and magnetic noise. Using a tight-binding model, we calculate the Andreev states formed in a Josephson junction where the link is a semiconductor with strong spin-orbit interaction. As a result of both the spin-orbit interaction and induced superconductivity, the local charge and spin of these states vary as a function of externally controllable parameters: the phase difference between the superconducting leads, an applied magnetic field, and filling of the underlying semiconductor. Concomitantly, coupling to fluctuations of the electric or magnetic environment will vary, which informs the rate of dephasing. We qualitatively predict the dependence of dephasing on the nature of the environment, magnetic field, phase difference between the junction, and filling of the semiconductor. Comparing the simulated electric- and magnetic-noise-induced dephasing rate to experiment suggests that the dominant source of noise is magnetic. Moreover, by appropriately tuning these external parameters, we find sweet spots at which we predict an enhancement in ASQ coherence times.
We calculate the current-voltage ($I\ensuremath{-}V$) characteristic of a Josephson junction containing a resonant level in the weakly coupled regime (resonance width small compared to the superconducting gap). The phase $\ensuremath{\phi}$ across the junction becomes time dependent in response to a DC current bias. Rabi oscillations in the Andreev levels produce a staircase $I\ensuremath{-}V$ characteristic. The number of voltage steps counts the number of Rabi oscillations per $2\ensuremath{\pi}$ increment of $\ensuremath{\phi}$, providing a way to probe the coherence of the qubit in the absence of any external AC driving. The phenomenology is the same as the Majorana-induced DC Shapiro steps in topological Josephson junctions of Choi et al. [Phys. Rev. B 102, 140501(R) (2020)]---but now for a nontopological Andreev qubit.
A study of the Andreev level current through a weakly voltage-biased single-mode superconducting quantum point contact under microwave irradiation is presented. The applied microwave field induces resonant transitions between the current carrying Andreev states localized to the contact region, which results in an increase of the dc subgap current by several orders of magnitude. The applied voltage-bias couples to the superconductor phase difference across the junction, which will evolve in time. In turn the Andreev levels will oscillate adiabatically within the superconductor energy gap. Depending on the frequency of the applied field there can be either one or two resonances per oscillation period. When considering the case of two resonances the calculated dc-current exhibits an interference pattern as a function of inverse voltage. A measurement of the oscillation period would make it possible to reconstruct the Andreev level spectrum. Further, a detailed study is conducted concerning the microwave-induced current as a function of voltage bias, and the amplitude and frequency of the applied field. In realistic experimental situations there are equilibrium fluctuations of the applied voltage bias and sometimes impurity induced noise in the contact transparency. The amount of dephasing induced on the interference pattern by these fluctuations is estimated. In most cases the interference pattern will be subject to some amount of decay. However, there are parameter values for which this decay will be small. The decay originating from equilibrium fluctuations is predicted to have a non-monotonic dependence on the position of the resonances, while the decay induced by impurities should increase linearly when the separation between the resonances is increased. This difference could be used to distinguish between the two sources. The results also indicate that it should be possible to experimentally investigate the coupling between Andreev states and their environment, explicitly the impedance which the contact "sees" and the coupling strength between impurities and Andreev states.