Refrigeration of a 1D gas of microwave photons

We propose a circuit-QED setup that, within experimentally accessible parameters, cools a photon gas to temperatures below 1 mK while simultaneously introducing a chemical potential for the photons. The setup consists of a multimode transmission-line resonator hosting a one-dimensional photon gas, coupled to an engineered reservoir that is both colder than the environment and conserves the total photon number. The overall photon population is instead controlled by the physical environment of the transmission line. These two reservoirs independently tune the temperature and chemical potential of the photons, enabling the stabilization of condensate states. The core element of the engineered bath is a SNAIL-based coupler that realizes a pure three-wave mixing interaction, linking the transmission line to a waste mode that facilitates energy dissipation. We demonstrate numerically that this system can prepare the photon gas at temperatures and energy scales required for analog many-body simulations on superconducting hardware—regimes that are otherwise inaccessible via conventional cryogenic cooling. Our results pave the way for realizing analog many-body simulators on superconducting platforms.