Final Report Summary - INPEC (Interacting Photon Bose-Einstein Condensates in Variable Potentials) Bose-Einstein condensation has been achieved with cold atomic gases, exciton-polaritons, and more recently, in to date three different laboratories, also with photons in dye-solution filled optical microcavities. The aim of this project has been the study of interacting photon condensates in variable potentials realized in the microcavity environment.In the course of the project works, photon condensates have been successfully trapped in variable potentials created within the dye microcavity environment. We have realized both thermo-optically imprinted as well as permanently structured cavity mirrors to realize trapping potentials for the two-dimensional photon gas, and demonstrated both double-well potentials and periodic lattice potentials.For quantitative observations, we have concentrated on a double-well potential, realizing a Josephson geometry. The photon trapping potential was realized by thermo-optically imprinting refractive index changes within the microcavity. To enhance the thermo-optic response, a thermo-optic polymer was added to the dye solution, and transverse variations of the refractive index were induced through irradiation with a focused laser beam causing heating form absorption in a thin silicon layer placed below one of the mirror reflecting surfaces. Photons thermalize by absorption re-emission processes on the dye molecules, and despite the variable structuring the photon lifetime is long enough to allow for a thermalization of photons. In a single lattice site, we observe a microscopic photon Bose-Einstein condensate with a critical photon number of 68. Effective interactions between the photons are observed due to thermo-optic effects, and in the double-well trapping geometry tunnel coupling between the microsites is observed, as well as the hybridization of eigenstates.In more recent work, we have demonstrated Bose-Einstein condensation into a superposition state of the localized optical wavefunctions of a double-well system. To yield the correct density of states to allow for Bose-Einstein condensation of the two-dimensional photon gas, for this the double-well potential was superimposed by a shallow harmonic trapping potential, with the symmetric linear combination of the optical wavefunction of photons localized in the two sites constituting the lowest energy available system eigenstate. As the photon number of the thermalized cloud in the microcavity exceeds the critical number for condensation, we observe the macroscopic accumulation of photons in the symmetric superposition state of the double-well system, meaning that Bose-Einstein condensation allows to accumulate photons in this superposition state by cooling alone.In other work, the thermalization dynamics of the light condensate in the dye microcavity has been studied. As expected, a photon Bose-Einstein condensate is observed when thermalization by absorption and re-emission proceeds faster than photon loss by e.g. mirror transmission, while in the opposite limit the device operates as a usual laser. Operating in the near equilibrium regime of fast thermalization with respect to photon loss, we have moreover determined calorimetric properties of the photon gas, as most notable the heat capacity, with an observed cusp-like singularity signaling the Bose-Einstein phase transition. Also, for the first time in an optical quantum gas experiment, the genuine thermal de Broglie wavelength has been determined.Additionally. grand canonical number statistics of the optical condensate has been demonstrated, as well understood from coupling of the photon gas to the photo-excitable dye molecules, which allow for effective particle exchange between condensate photons and dye-electronic excitations acting as a reservoir. The first order coherence of the condensate has been determined both in the usual canonical as well as in the grand canonical statistical regime, with the latter exhibiting remarkably large statistical number fluctuations deep in the Bose-Einstein condensed phase.
