[Paper Review] Quantum-circuit refrigeration of a superconducting microwave resonator well below a single quantum

A.J. Viitanen, Timm Mörstedt+5 more|arXiv (Cornell University)|Aug 1, 2023

Quantum and electron transport phenomenaPhysics and Astronomy31 references3 citations

TL;DR

This paper experimentally demonstrates a single-junction quantum-circuit refrigerator (QCR) that cools a superconducting microwave resonator to below one photon on average, using voltage or rf drive control. By coupling the QCR to a transmon qubit for Fock state readout, the authors achieve fast, tunable dissipation and demonstrate refrigeration from above 1 K to sub-single-photon states with both continuous and 10-ns pulsed drives, resolving prior issues with slow charging dynamics.

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.

Motivation & Objective

• To address the slow charging dynamics and non-exponential decay in prior double-junction QCRs due to charge island effects.
• To implement and validate a theoretically proposed single-junction QCR design with a ground-return path via a quarter-wave resonator.
• To enable in-situ, voltage- or rf-driven dissipation control for real-time refrigeration of resonator states.
• To characterize the refrigerated resonator at the Fock state level, resolving the thermal state population with high fidelity.
• To demonstrate robust refrigeration under both continuous and ultra-short (10-ns) pulsed rf drives, confirming broad operational bandwidth.

Proposed method

• A single-junction NIS tunnel junction is galvanically connected to a quarter-wave superconducting coplanar-waveguide resonator, providing a ground return path for dc current.
• The QCR operates via photon-assisted quasiparticle tunneling, where bias voltage or rf drive induces resonant photon absorption from the resonator.
• A transmon qubit is dispersively coupled to the resonator to perform number-splitting spectroscopy and resolve individual Fock states.
• The system is modeled using transition rates derived from quasiparticle tunneling rates, with effective temperature and coupling strength defined via the normalized forward tunneling rate $\overrightarrow{F}(E)$.
• Both dc bias and 2.9-GHz rf drives (continuous and 10-ns pulsed) are used to control dissipation, with identical refrigeration performance observed.
• Theoretical modeling assumes a lumped-element resonator with $Z_r = \frac{4}{\pi}Z_0$, and the limit $C_c/C_N = 1$, $E_N = 0$ is used for direct attachment.

Experimental results

Research questions

• RQ1 Can a single-junction QCR achieve fast, clean, and tunable dissipation without the charge island nonlinearity of prior double-junction designs?
• RQ2 To what extent can the QCR cool a resonator to sub-single-photon states, and can this be achieved with both continuous and ultra-short pulsed drives?
• RQ3 How accurately can the Fock state populations of the resonator be measured during refrigeration, and what does this reveal about the thermalization process?
• RQ4 Does the QCR maintain consistent performance across different drive types (dc vs. rf), and is the bandwidth limited by the circuit?
• RQ5 Can the QCR actively cool a resonator that is artificially heated to a 1-K thermal state, demonstrating robustness against external heating?

Key findings

• The single-junction QCR successfully cools a 4.7-GHz superconducting resonator to an average photon number well below one, achieving sub-single-photon states.
• The QCR demonstrates identical refrigeration performance with both continuous 2.9-GHz rf drive and 10-ns pulsed rf drive, confirming a broad operational bandwidth beyond circuit limitations.
• Fock state populations are resolved via transmon qubit number-splitting spectroscopy, enabling direct measurement of the resonator's thermal state during refrigeration.
• The system achieves fast, exponential-like decay dynamics, resolving the slow charging issue of previous double-junction QCRs.
• The QCR effectively cools a resonator heated to a 1-K thermal state (approximately one photon on average), reducing it to a small fraction of a photon.
• Both dc bias and rf drive can be used to tune the dissipation rate, with no observed degradation in performance, confirming the QCR’s versatility.