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arXiv:2107.04278 · AVS Quantum Science

Charge dynamics in quantum-circuit refrigeration: Thermalization and microwave gain

Hao Hsu, Matti Silveri, Vasilii Sevriuk, Mikko Möttönen, Gianluigi Catelani

Published Oct 8, 2021• 9 citations
arXivHTMLPDF

Abstract

Previous studies of photon-assisted tunneling through normal-metal–insulator–superconductor junctions have exhibited potential for providing a convenient tool to control the dissipation of quantum-electric circuits in situ. However, the current literature on such a quantum-circuit refrigerator (QCR) does not present a detailed description for the charge dynamics of the tunneling processes or the phase coherence of the open quantum system. Here, we derive a master equation describing both quantum-electric and charge degrees of freedom, and discover that typical experimental parameters of low temperature and yet lower charging energy yield a separation of time scales for the charge and quantum dynamics. Consequently, the minor effect of the different charge states can be taken into account by averaging over the charge distribution. We also consider applying an ac voltage to the tunnel junction, which enables control of the decay rate of a superconducting qubit over four orders of magnitude by changing the drive amplitude; we find an order-of-magnitude drop in the qubit excitation in 40 ns and a residual reset infidelity below 10−4. Furthermore, for the normal island, we consider the case of charging energy and single-particle level spacing large compared to the superconducting gap, i.e., a quantum dot. Although the decay rates arising from such a dot QCR appear low for use in qubit reset, the device can provide effective negative damping (gain) to the coupled microwave resonator. The Fano factor of such a millikelvin microwave source may be smaller than unity, with the latter value being reached close to the maximum attainable power.

DOI
10.1116/5.0062868

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Previous studies of photon-assisted tunneling through normal-metal–insulator–superconductor junctions have exhibited potential for providing a convenient tool to control the dissipation of quantum-electric circuits in situ. However, the current literature on such a quantum-circuit refrigerator (QCR) does not present a detailed description for the charge dynamics of the tunneling processes or the phase coherence of the open quantum system. Here, we derive a master equation describing both quantum-electric and charge degrees of freedom, and discover that typical experimental parameters of low temperature and yet lower charging energy yield a separation of time scales for the charge and quantum dynamics. Consequently, the minor effect of the different charge states can be taken into account by averaging over the charge distribution. We also consider applying an ac voltage to the tunnel junction, which enables control of the decay rate of a superconducting qubit over four orders of magnitude by changing the drive amplitude; we find an order-of-magnitude drop in the qubit excitation in 40 ns and a residual reset infidelity below 10−4. Furthermore, for the normal island, we consider the case of charging energy and single-particle level spacing large compared to the superconducting gap, i.e., a quantum dot. Although the decay rates arising from such a dot QCR appear low for use in qubit reset, the device can provide effective negative damping (gain) to the coupled microwave resonator. The Fano factor of such a millikelvin microwave source may be smaller than unity, with the latter value being reached close to the maximum attainable power.
We propose a quantum-circuit refrigerator (QCR) based on photon-assisted quasiparticle tunneling through a single normal-metal–insulator–superconductor (NIS) junction. In contrast to previous studies with multiple junctions and an additional charge island for the QCR, we directly connect the NIS junction to an inductively shunted electrode of a superconducting microwave resonator making the device immune to low-frequency charge noise. At low characteristic impedance of the resonator and parameters relevant to a recent experiment, we observe that a semiclassical impedance model of the NIS junction reproduces the bias voltage dependence of the QCR-induced damping rate and frequency shift. For high characteristic impedances, we derive a Born–Markov master equation and use it to observe significant non-linearities in the QCR-induced dissipation and frequency shift. We further demonstrate that, in this regime, the QCR can be used to initialize the linear resonator into a non-thermal state even in the absence of any microwave drive.
We experimentally demonstrate a recently proposed single-junction quantum-circuit refrigerator (QCR) as an tunable low-temperature environment for a superconducting 4.7 GHz resonator. With the help of a transmon qubit, we measure the populations of the different resonator Fock states, thus providing reliable access to the temperature of the engineered electromagnetic environment and its effect on the resonator. We demonstrate coherent and thermal resonator states and that the on-demand dissipation provided by the QCR can drive these to a small fraction of a photon on average, even if starting above 1 K. We observe that the QCR can be operated either with a dc bias voltage or a gigahertz rf drive, or a combination of these. The bandwidth of the rf drive is not limited by the circuit itself and consequently, we show that 2.9 GHz continuous and 10 ns pulsed drives lead to identical desired refrigeration of the resonator. These observations answer to the shortcomings of previous works where the Fock states were not resolvable and the QCR exhibited slow charging dynamics. Thus, this work introduces a versatile tool to study open quantum systems, quantum thermodynamics, and to quickly reset superconducting qubits. Published by the American Physical Society 2024
We present here our recent results on qubit reset scheme based on a quantum-circuit refrigerator (QCR). In particular, we use the photon-assisted quasiparticle tunneling through a superconductor–insulator–normal-metal–insulator–superconductor junction to controllably decrease the energy relaxation time of the qubit during the QCR operation. In our experiment, we use a transmon qubit with dispersive readout. The QCR is capacitively coupled to the qubit through its normal-metal island. We employ rapid, square-shaped QCR control voltage pulses with durations in the range of 2–350 ns and a variety of amplitudes to optimize the reset time and fidelity. Consequently, we reach a qubit ground-state probability of roughly 97% with 80-ns pulses starting from the first excited state. The qubit state probability is extracted from averaged readout signal, where the calibration is based on Rabi oscillations, thus not distinguishing the residual thermal population of the qubit.
Abstract The recent progress in direct active cooling of the quantum‐electric degrees of freedom in engineered circuits, or quantum‐circuit refrigeration is reviewed. In 2017, the discovery of a quantum‐circuit refrigerator (QCR) based on photon‐assisted tunneling of quasiparticles through normal‐metal–insulator–superconductor junctions inspired a series of experimental studies demonstrating the following main properties: i) the direct‐current (dc) bias voltage of the junction can change the QCR‐induced damping rate of a superconducting microwave resonator by orders of magnitude and give rise to nontrivial Lamb shifts, ii) the damping rate can be controlled in nanosecond time scales, and ii) the dc bias can be replaced by a microwave excitation, the amplitude of which controls the induced damping rate. Theoretically, it is predicted that state‐of‐the‐art superconducting resonators and qubits can be reset with an infidelity lower than 10−4 in tens of nanoseconds using experimentally feasible parameters. A QCR‐equipped resonator has also been demonstrated as an incoherent photon source with an output temperature above 1 K yet operating at millikelvin. This source has been used to calibrate cryogenic amplification chains. In the future, the QCR may be experimentally used to quickly reset superconducting qubits, and hence assist in the great challenge of building a practical quantum computer.
Superconducting microwave circuits are promising candidates for a variety of different applications, ranging from extremely sensitive photon detectors to large-scale quantum computer. Thus, they may revolutionize our everyday lives in the future through substantial technological development. Superconducting quantum circuits typically operate at low power levels and consist of linear and nonlinear resonators. In order to enhance their operation fidelity, they need to be cooled efficiently, and the dissipation of the circuit needs to be well engineered. In this chapter, we describe a refrigerator for electric quantum circuits based on photon-assisted electron tunneling in hybrid superconductor–insulator–normal-metal junctions. Furthermore, such junctions can also serve as incoherent microwave sources. Importantly, the photon absorption and emission rates can be tuned over several orders of magnitude. In addition, these junctions are used for refrigeration and heating of the normal-metal electrons as well as for probing the electron temperature. Here, we present their operation principle and provide insight to their potential applications as well as briefly describe fabrication methods.
Recent advancements in circuit quantum electrodynamics have enabled precise manipulation and detection of the single energy quantum in quantum systems. A quantum circuit refrigerator (QCR) is capable of electrically cooling the excited population of quantum systems, such as superconducting resonators and qubits, through photon-assisted tunneling of quasi-particles within a superconductor-insulator-normal metal junction. In this study, we demonstrated instantaneous QCR in the quantum regime. We performed the time-resolved measurement of the QCR-induced cooling of photon number inside the superconducting resonator by harnessing a qubit as a photon detector. From the enhanced photon loss rate of the resonator estimated from the amount of the AC Stark shift, the QCR was shown to have a cooling power of approximately 300 aW. Furthermore, even below the single energy quantum, the QCR can reduce the number of photons inside the resonator with 100 ns pulse from thermal equilibrium. Numerical calculations based on the Lindblad master equation successfully reproduced these experimental results.