Analytic Theory and cQED Implementation of a Two-Qubit Refrigerator: Sub-100 mK Cavity Cooling from a 4 K Bath

Abstract

We develop a theoretical framework for cooling a microwave cavity mode using a Poisson stream of internally correlated pairs of two-level systems and analyze its performance under realistic dissipation. Starting from a Lindblad model of a phonon-tethered cavity interacting with sequentially injected atom pairs, we derive closed-form expressions for the steady-state cavity occupation and effective temperature. Two coupling geometries are examined: a one-atom configuration, where only one member of each pair interacts with the cavity, and a two-atom configuration, where both atoms couple collectively. The single-atom model enables cooling below the phonon bath but not below the reservoir temperature, whereas the two-atom scheme exhibits enhanced refrigeration - pair correlations modify the cavity's upward and downward transition rates so that the steady-state temperature can fall well below that of the reservoir for weak phonon damping. We map the parameter space including detuning, coupling strength, damping, and intra-pair exchange, identifying cooling valleys near resonance and the crossover between reservoir- and phonon-dominated regimes. The two-atom configuration thus realizes a genuine quantum-enhanced cooling mechanism absent in the single-atom case. We further outline an experimental implementation using two superconducting qubits repeatedly prepared, coupled, and reset inside a 3D cavity. Realistic reset and flux-tuning protocols support MHz-rate interaction cycles, enabling engineered reservoirs to impose cavity temperatures of 50-120 mK even when the cryostat is at ~1 K, offering a pathway to autonomous, on-chip refrigeration of microwave modes in scalable quantum hardware.