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arXiv:1706.07188 · Physical review. B./Physical review. B

Theory of quantum-circuit refrigeration by photon-assisted electron tunneling

Matti Silveri, Hermann Grabert, Shumpei Masuda, Kuan Yen Tan, Mikko Möttönen

Published Sep 22, 2017• 41 citations
arXivHTMLPDF

Abstract

We focus on a recently experimentally realized scenario of normal-metal--insulator--superconductor tunnel junctions coupled to a superconducting resonator. We develop a first-principles theory to describe the effect of photon-assisted electron tunneling on the quantum state of the resonator. Our results are in very good quantitative agreement with the previous experiments on refrigeration and heating of the resonator using the photon-assisted tunneling, thus providing a stringent verification of the developed theory. Importantly, our results provide simple analytical estimates of the voltage-tunable coupling strength and temperature of the thermal reservoir formed by the photon-assisted tunneling. Consequently, they are used to introduce optimization principles for initialization of quantum devices using such a quantum-circuit refrigerator. Thanks to the first-principles nature of our approach, extension of the theory to the full spectrum of quantum electric devices seems plausible.

DOI
10.1103/physrevb.96.094524

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We focus on a recently experimentally realized scenario of normal-metal--insulator--superconductor tunnel junctions coupled to a superconducting resonator. We develop a first-principles theory to describe the effect of photon-assisted electron tunneling on the quantum state of the resonator. Our results are in very good quantitative agreement with the previous experiments on refrigeration and heating of the resonator using the photon-assisted tunneling, thus providing a stringent verification of the developed theory. Importantly, our results provide simple analytical estimates of the voltage-tunable coupling strength and temperature of the thermal reservoir formed by the photon-assisted tunneling. Consequently, they are used to introduce optimization principles for initialization of quantum devices using such a quantum-circuit refrigerator. Thanks to the first-principles nature of our approach, extension of the theory to the full spectrum of quantum electric devices seems plausible.
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.
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 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.
We experimentally realize an incoherent microwave source driven by voltage-controlled quantum tunneling of electrons through nanoscale normal-metal--insulator--superconductor junctions coupled to a resonator. We observe the direct conversion of the electronic energy into microwave photons by measuring the power spectrum of the microwave radiation emitted from the resonator. The demonstrated total output power exceeds that of 2.5-K thermal radiation although the photon and electron reservoirs are at subkelvin temperatures. Measurements of the output power quantitatively agree with a theoretical model in a wide range of the bias voltages providing information on the electrically-controlled photon creation. The developed photon source is fully compatible with low-temperature electronics and offers convenient in-situ electrical control of the photon emission rate with a predetermined frequency, without relying on intrinsic voltage fluctuations of heated normal-metal components nor suffering from unwanted dissipation in room temperature cables. In addition to its potential applications in microwave photonics, our results provide complementary verification of the working principles of the recently discovered quantum-circuit refrigerator.
Quantum technology promises revolutionizing applications in information processing, communications, sensing and modelling.However, efficient on-demand cooling of the functional quantum degrees of freedom remains challenging in many solid-state implementations, such as superconducting circuits.Here we demonstrate direct cooling of a superconducting resonator mode using voltage-controllable electron tunnelling in a nanoscale refrigerator.This result is revealed by a decreased electron temperature at a resonator-coupled probe resistor, even for an elevated electron temperature at the refrigerator.Our conclusions are verified by control experiments and by a good quantitative agreement between theory and experimental observations at various operation voltages and bath temperatures.In the future, we aim to remove spurious dissipation introduced by our refrigerator and to decrease the operational temperature.Such an ideal quantum-circuit refrigerator has potential applications in the initialization of quantum electric devices.In the superconducting quantum computer, for example, fast and accurate reset of the quantum memory is needed.
Quantum technology promises revolutionizing applications in information processing, communications, sensing and modelling. However, efficient on-demand cooling of the functional quantum degrees of freedom remains challenging in many solid-state implementations, such as superconducting circuits. Here we demonstrate direct cooling of a superconducting resonator mode using voltage-controllable electron tunnelling in a nanoscale refrigerator. This result is revealed by a decreased electron temperature at a resonator-coupled probe resistor, even for an elevated electron temperature at the refrigerator. Our conclusions are verified by control experiments and by a good quantitative agreement between theory and experimental observations at various operation voltages and bath temperatures. In the future, we aim to remove spurious dissipation introduced by our refrigerator and to decrease the operational temperature. Such an ideal quantum-circuit refrigerator has potential applications in the initialization of quantum electric devices. In the superconducting quantum computer, for example, fast and accurate reset of the quantum memory is needed.