Quantum-circuit refrigeration of a superconducting microwave resonator well below a single quantum

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Quantum-circuit refrigeration of a superconducting microwave resonator well below a single quantum

Arto Viitanen, Timm Mörstedt, Wallace S. Teixeira, Maaria Tiiri, Jukka Räbinä, Matti Silveri, and Mikko Möttönen

Phys. Rev. Research 6, 023262 – Published 10 June 2024

Abstract

We experimentally demonstrate a recently proposed single-junction quantum-circuit refrigerator (QCR) as an in situ 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.

Received 30 June 2023
Revised 5 January 2024
Accepted 16 April 2024

DOI:https://doi.org/10.1103/PhysRevResearch.6.023262

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Quantum circuits

Quantum heat engines & refrigerators Superconducting devices Superconducting qubits Tunnel junctions

Quantum Information, Science & TechnologyCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Arto Viitanen ^1,*, Timm Mörstedt ¹, Wallace S. Teixeira ¹, Maaria Tiiri¹, Jukka Räbinä ², Matti Silveri ³, and Mikko Möttönen ^1,4,†

¹QCD Labs, QTF Centre of Excellence, Department of Applied Physics, Aalto University, P.O. Box 13500, FI-00076 Aalto, Finland
²IQM Quantum Computers, FI-02150 Espoo, Finland
³Nano and Molecular Systems Research Unit, University of Oulu, P.O. Box 3000, FI-90014 Oulu, Finland
⁴QTF Centre of Excellence, VTT Technical Research Centre of Finland Ltd., P.O. Box 1000, 02044 VTT, Finland

^*Corresponding author: arto.viitanen@aalto.fi
^†Corresponding author: mikko.mottonen@aalto.fi

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Vol. 6, Iss. 2 — June - August 2024

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Images

Figure 1
Experimental device and setup. (a) False-color micrograph of a representative chip. The quarter-wave resonator (light blue) with an attached QCR at the top end is probed with a transmon qubit (green) setup consisting of a readout resonator (dark blue), a transmission line (right), a qubit drive line (top), and a flux line (bottom). (b) Simplified circuit diagram of the chip and the experimental setup with colors matching to those in (a). Each Josephson junction of the qubit is denoted by a crossed square, whereas the QCR junction has a half of a cross (superconductor side) and a blank rectangle (normal-metal side). (c) Current through the QCR as a function of its bias voltage $V$ without excitation applied elsewhere in the circuit. (d) Phase of the readout resonator signal as a function of the external flux bias $Φ$ of the qubit and the excitation frequency of the qubit. Owing to a relatively high qubit-drive power, the two-photon transition from the ground state to the second excited state is visible below the primary ground-state-to-excited-state line.
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Figure 2
Control of dissipation of a coherently driven resonator. (a) Phase of the readout signal as a function of the qubit excitation frequency and the power of a coherent drive tone at the resonator frequency. (b) Phase of the readout signal as a function of the qubit excitation frequency and the QCR bias voltage $V$ for the resonator driven at $- 130$ dBm power. The right inset shows the measured populations $P_{n}$ (bars) of the Fock states $| n 〉$ at $V = 68 µ V$ and a fit to a Poisson distribution (dots) yielding $\bar{n} = \sum_{n} n P_{n} = 1.21$ . (c) Mean resonator population $\bar{n}$ (blue dots, left axis) and the corresponding QCR-induced decay rate (orange dots, right axis) as functions of the QCR bias voltage extracted from the data of panel (b). The line shows our theoretical decay rate model $γ_{QCR} + γ_{V = 0}$ , for which some of the parameters are shown in Table 1 and the superconductor gap parameter $Δ = 220 µ eV$ , normal-metal temperature $T_{N} = 150$ mK, junction capacitance $C_{NIS} = 0.54$ fF, and resonator characteristic impedance $Z_{r} = 63.7 Ω$ . The crosses show results of an identical experiment except with an additional continuous 9.25 GHz drive applied at the junction.
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Figure 3
Continuous and pulsed rf operated QCR and cooling of a thermal state. (a) Phase of the readout signal as a function of the power of a 10 ns pulsed rf excitation at the QCR and the qubit excitation frequency. The pulses have $50 %$ duty cycle and 2.9 GHz carrier frequency. The resonator is coherently driven with $- 130$ dBm power. (b) Mean photon number (blue markers, left axis) and corresponding QCR-induced decay rate (orange markers, right axis) for pulsed (crosses) and continuous (dots) 2.9 GHz excitation as functions of the QCR rf tone strength. The QCR is not dc biased in panels (a) and (b). (c) Phase of the readout signal as a function of the QCR dc bias voltage and the qubit excitation frequency in the case of a hot attenuator. The attenuator is intentionally heated by a detuned rf signal with power tuned to have roughly a single thermal photon on average in the resonator. (d) Mean photon number (blue dots, left axis) and the corresponding effective temperature of the resonator environment (orange dots, right axis) as functions of the QCR bias voltage. The line shows our decay rate model with values as in Table 1 and in Fig. 2 except for $T_{N} = 150$ mK, $γ_{dr} / (2 π) = 2$ MHz, and ${\bar{n}}_{dr} = 1$ .
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Figure 4
Cooling of an intentionally heated resonator. (a) Phase of the readout signal as a function of the artificial thermal-noise power and the qubit excitation frequency. (b) Phase of the readout signal as a function of the QCR bias voltage and the qubit excitation frequency. The resonator is driven with artificial noise of approximately $- 105$ dBm. (c) Mean resonator population and the corresponding temperature as a function of the QCR bias voltage. The line shows our model with values given in Table 1 and in Fig. 2 except for $T_{N} = 280$ mK, $γ_{dr} / (2 π) = 2$ MHz, and ${\bar{n}}_{dr} = 4$ .
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