Gibbs mixing of partially distinguishable photons with a polarising beamsplitter membrane

TL;DR

This paper extends Gibbs' classical gas mixing thought experiment to the quantum domain, analyzing how partial distinguishability of photon gases affects the work extracted and the associated fluctuations, using an optomechanical model.

Contribution

It introduces a quantum model of gas mixing with non-orthogonal polarizations and derives a continuous quantum mixing work expression based on distinguishability.

Findings

Quantum mixing work varies continuously with photon distinguishability.

Work fluctuations are significant for Fock and thermal states.

The model generalizes Gibbs' classical mixing to quantum gases.

Abstract

For a thought experiment concerning the mixing of two classical gases, Gibbs concluded that the work that can be extracted from mixing is determined by whether or not the gases can be distinguished by a semi-permeable membrane; that is, the mixing work is a discontinuous function of how similar the gases are. Here we describe an optomechanical setup that generalises Gibbs' thought experiment to partially distinguishable quantum gases. Specifically, we model the interaction between a polarising beamsplitter, that plays the role of a semi-permeable membrane, and two photon gases of non-orthogonal polarisation. We find that the work arising from the mixing of the gases is related to the potential energy associated with the displacement of the microscopic membrane, and we derive a general quantum mixing work expression, valid for any two photon gases with the same number distribution. The quantum mixing work is found to change continuously with the distinguishability of the two polarised gases. In addition, fluctuations of the work on the microscopic membrane become important, which we calculate for Fock and thermal states of the photon gases. Our findings generalise Gibbs' mixing to the quantum regime and open the door for new quantum thermodynamic (thought) experiments with quantum gases with non-orthogonal polarisations and microscopic pistons that can distinguish orthogonal polarisations.