Investigation of Photon Condensation in a Four-Site Lattice Unit Cell

Abstract

Since the first experimental realization of Bose-Einstein condensation in ultracold, dilute atomic gases in 1995, a broad research field exploring the physics of various intriguing quantum phenomena has developed. The Bose-Einstein condensate is a collective state occupied by many thousand atoms, forming a giant, coherent matter wave, which is formed due to quantum statistics and makes quantum effects observable at the macroscopic scale. <br/> Apart from material particles, Bose-Einstein condensation can also be realized with gases of photons or photon-like quasiparticles in highly reflective microresonators. However, in contrast to atoms, where thermalisation is achieved by contact interactions, photonic condensates need to be coupled to a material component to exchange energy and thereby reach thermal equilibrium. The radiative coupling to a fluorescent dye solution inside the microcavity, where the broadband absorption and emission coefficients are connected by a Boltzmann-like frequency scaling, can provide such a thermalisation mechanism for photons. <br/> The present thesis investigates Bose-Einstein condensation of photons into the ground state provided by a square lattice potential in the form of a unit cell with four sites, which is imprinted onto one of the cavity mirrors using a static structuring technique. The lattice structure is surrounded by a shallow harmonic potential, to provide a suitable density of states such that a Bose-Einstein condensate can exist. The eigenstates of the trapping potential are thoroughly characterized numerically as well as experimentally by selectively exciting the individual states and analysing the spectral photon distribution. Spatial and spectral photon distributions are recorded for different total photon numbers in the dye microcavity and good agreement with theoretical Bose-Einstein distributions at room temperature is found. It is verified that the condensate is indeed formed in the delocalized ground state of the lattice potential and the condensate is probed for phase coherence between lattice sites in a Mach-Zehnder type, multi-path interferometer. Remaining small deviations between the experiment and the theoretical expectations in terms of the precise photon distributions, photon numbers and finite saturation of the excited states are analysed and explained by taking into account the driven-dissipative nature of the microcavity environment. The experiments are performed in a regime where cavity loss and photon reabsorption occur on a comparable timescale. The rates of these competing processes can be experimentally tuned by varying the cavity cutoff. Close to equilibrium conditions can be obtained, when photon reabsorption is much faster than the loss of photons from the cavity, which corresponds to the regime of good thermalisation. In further work carried out in this thesis, the pump power required to reach the threshold for condensation or lasing-like behaviour is investigated theoretically and experimentally as a function of the cavity cutoff wavelength. It is found for the experimental parameters, that the cutoff wavelength at which the pump threshold reaches its minimum value is almost identical to the point, where the absorption rate of photons is the same as the cavity loss rate, i.e. at the crossover between condensation and lasing-like behaviour.