Quantum thermodynamic properties of a cold atom coupled to a heat bath in non-Abelian gauge potentials

TL;DR

This paper investigates how a cold atom in a non-Abelian gauge field interacts thermodynamically with a quantum heat bath, revealing unique effects on free energy, specific heat, and entropy compared to Abelian cases.

Contribution

It provides explicit expressions for quantum thermodynamic functions of a cold atom under non-Abelian gauge fields with different coupling schemes and bath models.

Findings

Non-Abelian magnetic fields alter free energy expressions.

Quantum thermodynamic functions depend on gauge potential even if uniform.

Explicit low-temperature formulas for different bath models are derived.

Abstract

In this work, we study different quantum thermodynamic functions (QTFs) of a cold atom subjected to an artificial non-Abelian uniform magnetic field and linearly coupled to a quantum heat bath through either usual coordinate-coordinate coupling or through momentum variables. The bath is modelled as a collection of independent quantum harmonic oscillators. In each of the coupling scheme, the effect of the non-Abelian magnetic field on different QTFs are explicitly demonstrated for a U(2) gauge transformation. In each case, we show that the free energy has a different expression than that for the Abelian case. We consider two illustrative heat bath spectrum (Ohmic bath and Drude model) to evaluate explicit closed form expressions of free energy (F), specific heat (C), and entropy (S) in the low temperature limit for each of the above mentioned coupling scheme. The dependence of different QTFs on the non-Abelian magnetic field are pointed out even if the gauge potential is uniform in space.