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Microwave Sensing of Andreev Bound States in a Gate-Defined Superconducting Quantum Point Contact

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 Added by Malcolm Connolly
 Publication date 2021
  fields Physics
and research's language is English




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We use a superconducting microresonator as a cavity to sense absorption of microwaves by a superconducting quantum point contact defined by surface gates over a proximitized two-dimensional electron gas. Renormalization of the cavity frequency with phase difference across the point contact is consistent with adiabatic coupling to Andreev bound states. Near $pi$ phase difference, we observe random fluctuations in absorption with gate voltage, related to quantum interference-induced modulations in the electron transmission. We identify features consistent with the presence of single Andreev bound states and describe the Andreev-cavity interaction using a dispersive Jaynes-Cummings model. By fitting the weak Andreev-cavity coupling, we extract ~GHz decoherence consistent with charge noise and the transmission dispersion associated with a localized state.



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We present a microscopic theory for the current through a tunnel Josephson junction coupled to a non-linear environment, which consists of an Andreev two-level system coupled to a harmonic oscillator. It models a recent experiment [Bretheau, Girit, Pothier, Esteve, and Urbina, Nature (London) 499, 312 (2013)] on photon spectroscopy of Andreev bound states in a superconducting atomic-size contact. We find the eigenenergies and eigenstates of the environment and derive the current through the junction due to inelastic Cooper pair tunneling. The current-voltage characteristic reveals the transitions between the Andreev bound states, the excitation of the harmonic mode that hybridizes with the Andreev bound states, as well as multi-photon processes. The calculated spectra are in fair agreement with the experimental data.
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Sub-gap transport properties of a quantum dot (QD) coupled to two superconducting and one metallic leads are studied theoretically, solving the time-dependent equation of motion by the Laplace transform technique. We focus on time-dependent response of the system induced by a sudden switching on the QD-leads couplings, studying the influence of initial conditions on the transient currents and the differential conductance. We derive analytical expressions for measurable quantities and find that they oscillate in time with the frequency governed by the QD-superconducting lead coupling and acquire damping, due to relaxation driven by the normal lead. Period of these oscillations increases with the superconducting phase difference $phi$. In particular, for $phi=pi$ the QD occupancy and the normal current evolve monotonically (without any oscillations) to their stationary values. In such case the induced electron pairing vanishes and the superconducting current is completely blocked. We also analyze time-dependent development of the Andreev bound states. We show, that the measurable conductance peaks do not appear immediately after sudden switching of the QD coupling to external leads but it takes some finite time-interval for the system needs create these Andreev states. Such time-delay is mainly controlled by the QD-normal lead coupling.
The superconducting proximity effect in semiconductor nanowires has recently enabled the study of new superconducting architectures, such as gate-tunable superconducting qubits and multiterminal Josephson junctions. As opposed to their metallic counterparts, the electron density in semiconductor nanosystems is tunable by external electrostatic gates providing a highly scalable and in-situ variation of the device properties. In addition, semiconductors with large $g$-factor and spin-orbit coupling have been shown to give rise to exotic phenomena in superconductivity, such as $varphi_0$ Josephson junctions and the emergence of Majorana bound states. Here, we report microwave spectroscopy measurements that directly reveal the presence of Andreev bound states (ABS) in ballistic semiconductor channels. We show that the measured ABS spectra are the result of transport channels with gate-tunable, high transmission probabilities up to $0.9$, which is required for gate-tunable Andreev qubits and beneficial for braiding schemes of Majorana states. For the first time, we detect excitations of a spin-split pair of ABS and observe symmetry-broken ABS, a direct consequence of the spin-orbit coupling in the semiconductor.
We study coherent transport and bound-state formation of Bogoliubov quasiparticles in a high-mobility In$_{0.75}%$Ga$_{0.25}$As two-dimensional electron gas (2DEG) coupled to a superconducting Nb electrode by means of a quantum point contact (QPC) as a tunable single-mode probe. Below the superconducting critical temperature of Nb, the QPC shows a single-channel conductance greater than the conductance quantum $2e^{2}/h$ at zero bias, which indicates the presence of Andreev-reflected quasiparticles, time-reversed states of the injected electron, returning back through the QPC. The marked sensitivity of the conductance enhancement to voltage bias and perpendicular magnetic field suggests a mechanism analogous to reflectionless tunneling--a hallmark of phase-coherent transport, with the boundary of the 2DEG cavity playing the role of scatters. When the QPC transmission is reduced to the tunneling regime, the differential conductance vs bias voltage probes the single-particle density of states in the proximity area. Measured conductance spectra show a double peak within the superconducting gap of Nb, demonstrating the formation of Andreev bound states in the 2DEG. Both of these results, obtained in the open and closed geometries, underpin the coherent nature of quasiparticles, i.e., phase-coherent Andreev reflection at the InGaAs/Nb interface and coherent propagation in the ballistic 2DEG.
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