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arXiv:1303.2918 · Physical Review B

Frequency-dependent admittance of a short superconducting weak link

Filip Kos, Simon E. Nigg, L. I. Glazman

Published May 28, 2013• 61 citations
arXivHTMLPDF

Abstract

We consider the linear and nonlinear electromagnetic responses of a nanowire connecting two bulk superconductors. The Andreev states appearing at a finite phase bias substantially affect the finite-frequency admittance of such a wire junction. Electron transitions involving the Andreev levels are easily saturated, leading to the nonlinear effects in photon absorption for the subgap photon energies. We evaluate the complex admittance analytically at an arbitrary frequency and arbitrary, possibly nonequilibrium, occupation of the Andreev levels. Special care is given to the limits of a single-channel contact and a disordered metallic weak link. We also evaluate the quasistatic fluctuations of admittance induced by fluctuations of the occupation factors of the Andreev levels. In view of possible qubit applications, we compare properties of a weak link with those of a tunnel Josephson junction. Compared to the latter, a weak link has smaller low-frequency dissipation. However, because of the deeper Andreev levels, the low-temperature quasistatic fluctuations of the inductance of a weak link are exponentially larger than of a tunnel junction. These fluctuations limit the applicability of nanowire junctions in superconducting qubits.

DOI
10.1103/physrevb.87.174521

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We consider the linear and nonlinear electromagnetic responses of a nanowire connecting two bulk superconductors. The Andreev states appearing at a finite phase bias substantially affect the finite-frequency admittance of such a wire junction. Electron transitions involving the Andreev levels are easily saturated, leading to the nonlinear effects in photon absorption for the subgap photon energies. We evaluate the complex admittance analytically at an arbitrary frequency and arbitrary, possibly nonequilibrium, occupation of the Andreev levels. Special care is given to the limits of a single-channel contact and a disordered metallic weak link. We also evaluate the quasistatic fluctuations of admittance induced by fluctuations of the occupation factors of the Andreev levels. In view of possible qubit applications, we compare properties of a weak link with those of a tunnel Josephson junction. Compared to the latter, a weak link has smaller low-frequency dissipation. However, because of the deeper Andreev levels, the low-temperature quasistatic fluctuations of the inductance of a weak link are exponentially larger than of a tunnel junction. These fluctuations limit the applicability of nanowire junctions in superconducting qubits.
By coupling a superconducting weak link to a microwave resonator, recent experiments probed the spectrum and achieved the quantum manipulation of Andreev states in various systems. However, the quantitative understanding of the response of the resonator to changes in the occupancy of the Andreev levels, which are of fermionic nature, is missing. Here, using Bogoliubov-de Gennes formalism to describe the weak link and a general formulation of the coupling to the resonator, we calculate the shift of the resonator frequency as a function of the levels occupancy and describe how transitions are induced by phase or electric field microwave drives. We apply this formalism to analyze recent experimental results obtained using circuit-QED techniques on superconducting atomic contacts and semiconducting nanowire Josephson junctions.
By coupling a superconducting weak link to a microwave resonator, recent experiments probed the spectrum and achieved the quantum manipulation of Andreev states in various systems.However, the quantitative understanding of the response of the resonator to changes in the occupancy of the Andreev levels, which are of fermionic nature, is missing.Here, using Bogoliubov-de Gennes formalism to describe the weak link and a general formulation of the coupling to the resonator, we calculate the shift of the resonator frequency as a function of the levels occupancy and describe how transitions are induced by phase or electric field microwave drives.We apply this formalism to analyze recent experimental results obtained using circuit-QED techniques on superconducting atomic contacts and semiconducting nanowire Josephson junctions.
Inspired by recent experiments, we study a short superconducting junction of length $L\ensuremath{\ll}\ensuremath{\xi}$ (coherence length) inserted in a dc-SQUID containing an ancillary Josephson tunnel junction. We evaluate the nonequilibrium occupation of the Andreev bound states (ABS) for the case of a conventional junction and a topological junction, with the latter case of ABS corresponding to a Majorana mode. We take into account small phase fluctuations of the Josephson tunnel junction, acting as a damped LC resonator, and analyze the role of the distribution of the quasiparticles of the continuum assuming that these quasiparticles are in thermal distribution with an effective temperature different from the environmental temperature. We also discuss the effect of strong photon irradiation in the junction leading to a nonequilibrium occupation of the ABS. We systematically compare the occupations of the bound states and the supercurrents carried by these states for conventional and topological junctions.
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
Josephson junctions formed in semiconductor nanowires host Andreev bound states and serve as a physical platform to realize Andreev qubits tuned by electrostatic gating. With the Andreev bound state being confined to the nanoscale weak link, it couples to a circuit-QED architecture via the state-dependent supercurrent flowing through the weak link. Thus, increasing this coupling strength is a crucial challenge for this architecture. Here, we demonstrate the fabrication and microwave characterization of a weak link which is defined in an In As - Al (core-half shell) nanowire and embedded in a superconducting loop with a lumped-element resonator patterned from a thin Nb Ti N film with high kinetic inductance. We investigate several devices with various weak-link lengths and performed spectroscopy that revealed pair transitions and single-quasiparticle transitions arising from spin-orbit-split Andreev bound states. Our approach offers a compact geometry and a large resonator impedance above 12 k Ω at a resonator frequency of 8 GHz, which facilitates large coupling in the system. For the pair transitions, the experimentally observed energy level splitting demonstrates the coupling to an Andreev level of 490 MHz. We apply a perturbative model that shows good agreement with the experimental data and extract the maximum coupling of 968 MHz. Moreover, we show that the coupling is even stronger to an Andreev level with a higher transmission. In addition, spectroscopy of single-quasiparticle transitions reveals spin-orbit-split Andreev bound states with the extracted spin-photon coupling of 77 MHz.
Excess quasiparticles play a crucial role in superconducting quantum devices ranging from qubits to quantum sensors. In this work we analyze their dynamics for phase-biased finite-length weak links with several Andreev subgap states, where the coupling to a microwave resonator allows for parity state (even or odd) readout. Our theory shows that almost perfect dynamical polarization in a given parity sector is achievable by applying a microwave pulse matching a transition in the opposite parity sector. Our results qualitatively explain key features of recent experiments on hybrid semiconducting nanowire Josephson junctions and provide theoretical guidelines for efficiently controlling the parity state of Andreev qubits.