Chemical potential for light by parametric coupling

TL;DR

This paper demonstrates how parametric coupling can induce an effective chemical potential for photons, enabling new thermodynamic control and quantum simulation capabilities in photonic systems.

Contribution

It introduces a method to generate a tunable chemical potential for photons through system-bath parametric coupling, a novel approach in photonic thermodynamics.

Findings

Photons can be made to equilibrate with a chemical potential using parametric oscillation.

The chemical potential is tunable via the frequency of the parametric coupler.

Implementation is feasible with current circuit-QED and optomechanical technologies.

Abstract

Usually photons are not conserved in their interaction with matter. Consequently, for the thermodynamics of photons, while we have a concept of temperature for energy conservation, there is no equivalent chemical potential for particle number conservation. However, the notion of a chemical potential is crucial in understanding a wide variety of single- and many-body effects, from transport in conductors and semiconductors to phase transitions in electronic and atomic systems. Here we show how a direct modification of the system-bath coupling via parametric oscillation creates an effective chemical potential for photons even in the thermodynamic limit. In particular, we show that the photonic system equilibrates to the temperature of the bath, with a tunable chemical potential that is set by the frequency of the parametric coupler. Specific implementations, using circuit-QED or optomechanics, are feasible using current technologies, and we show a detailed example demonstrating the emergence of Mott insulator-superfluid transition in a lattice of nonlinear oscillators. Our approach paves the way for quantum simulation, quantum sources, and even electron-like circuits with light.