Calorimetry of Photon Gases in Nonlinear Multimode Optical Fibers

Recent studies have shown that light propagating in a nonlinear, highly multimode system can thermalize in a manner totally analogous to that encountered in traditional statistical mechanics. At thermal equilibrium, the system’s entropy is at a maximum, in full accord with the second law of thermodynamics. In such arrangements, the entropy is extremized once the statistical power allocation among modes associated with this photon gas attains a Rayleigh-Jeans distribution that is fully characterized by an optical temperature $T$ and a chemical potential $\mu$. However, it has been theoretically argued that the variables $T$ and $\mu$ represent actual thermodynamic forces that control the exchange of the respective conjugate quantities between two subsystems. In this work, we report, for the first time, optical calorimetric measurements in nonlinear multimode fibers, which unambiguously demonstrate that both the temperature $T$ and the chemical potential $\mu$ dictate the flow of their associated extensive quantities, i.e., the energy and the optical power. Specifically, we study the process of light thermalization associated with two orthogonally polarized laser beams. Our observations are enabled by recently developed techniques that allow one to judiciously multiplex/demultiplex the optical power within various mode groups. Our results indicate that because of photon-photon collisions, “heat” only flows from a hot to a cold photon gas subsystem—thus providing an unequivocal demonstration of the second law in such all-optical thermodynamic arrangements. In addition to being fundamental, our findings provide a new approach to manipulate laser beams using thermodynamic principles.