Calorimetry of a Bose-Einstein-condensed photon gas.

Tobias Damm,David Dung,Martin Weitz,Frank Vewinger,Julian Schmitt,Jan Klaers,Qi Liang

doi:10.1038/ncomms11340

Abstract

Phase transitions, as the condensation of a gas to a liquid, are often revealed by a discontinuous behaviour of thermodynamic quantities. For liquid helium, for example, a divergence of the specific heat signals the transition from the normal fluid to the superfluid state. Apart from liquid helium, determining the specific heat of a Bose gas has proven to be a challenging task, for example, for ultracold atomic Bose gases. Here we examine the thermodynamic behaviour of a trapped two-dimensional photon gas, a system that allows us to spectroscopically determine the specific heat and the entropy of a nearly ideal Bose gas from the classical high temperature to the Bose-condensed quantum regime. The critical behaviour at the phase transition is clearly revealed by a cusp singularity of the specific heat. Regarded as a test of quantum statistical mechanics, our results demonstrate a quantitative agreement with its predictions at the microscopic level.

Highlights

Phase transitions, as the condensation of a gas to a liquid, are often revealed by a discontinuous behaviour of thermodynamic quantities
It has been proposed that superfluid helium forms a macroscopic matter wave as a consequence of Bose–Einstein condensation[3], which describes the condensation of the ideal Bose gas at low temperatures due to quantum statistics[4]
Evidence for a non-classical specific heat has been reported[10,11], but the accuracy obtained in experiments with weakly interacting atomic Bose gases has not been sufficient for an unambiguous determination of the temperature dependence of the heat capacity

Summary

Introduction

As the condensation of a gas to a liquid, are often revealed by a discontinuous behaviour of thermodynamic quantities. 2.2 K, liquid helium shows peculiar hydrodynamic properties, such as a flow without viscosity, the fountain effect or the formation of vortices[1] This transition from a normal fluid to a superfluid has been named l-transition, which originates from the fact that plotting the heat capacity versus temperature[2] results in a graph resembling the greek letter l. Soon after this discovery, it has been proposed that superfluid helium forms a macroscopic matter wave as a consequence of Bose–Einstein condensation[3], which describes the condensation of the ideal (interaction-free) Bose gas at low temperatures due to quantum statistics[4]. The observed specific heat shows a cusp singularity, illustrating critical behaviour for a photon gas analogous to the l-transition of liquid helium

Methods

Results

Conclusion