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Optics and Spectroscopy

Thermalization of Photons in a Microcavity

Evgenii Dmitrievich Trifonov

Published Jan 1, 2018• 3 citations
Publisher

Abstract

A theoretical interpretation of the spectral condensation of photons in a microcavity based on solution of kinetic equations describing photon-gas thermalization as a result of Raman scattering from an atomic-gas thermostat is proposed.
DOI
10.1134/s0030400x18010204

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We report a time-resolved study of the thermalization dynamics and the lasing to photon Bose-Einstein condensation crossover by in situ monitoring the photon kinetics in a dye microcavity. When the equilibration of the light to the dye temperature by absorption and reemission is faster than photon loss in the cavity, the optical spectrum becomes Bose-Einstein distributed and photons accumulate at low-energy states, forming a Bose-Einstein condensate. The thermalization of the photon gas and its evolution from nonequilibrium initial distributions to condensation is monitored in real time. In contrast, if photons leave the cavity before they thermalize, the system operates as a laser.
The experimental realization of a Bose-Einstein condensate of photons, first achieved in 2010 at Bonn University, allowed for new ways to probe the properties of condensates. For thermal light in free space the chemical potential is zero and condensation is not possible. By confining light to a microcavity, the transverse degrees of freedom behave as massive bosons which can have nonzero chemical potential. The gas of thermal photons can be brought to thermalize with a fluorescent dye though absorption and emission cycles. By pumping the dye molecules with a laser, the chemical potential can be increased and the photons will condense. \nWe have built a setup with which we can spatially and spectrally resolve the photon distribution in such a dye-filled microcavity. This allows us to study the shape and occupation of the low energy transverse modes of the cavity. We use this to investigate the thermalization process of the photon gas. A rate equation model is presented and qualitatively compared to experimental data. We find that the photon gas is not in thermal equilibrium.\nWe also investigate effective photon-photon interactions by measuring the spatial extent of the condensate. We find an effective interaction in the form of thermal lensing. As the thermal lensing depends on the interaction between the photon gas and the dye, we find that the model used for thermalization can also make good predictions about effective photon-photon interactions.
This paper provides, first, a succinct theoretical derivation of Bose-Einstein condensation in a grand-canonical ideal photon gas elaborating on previous results [M\"uller, Ann. Phys. 184, 219 (1988); Physica A (Amsterdam, Neth.) 139, 165 (1986)] additionally including new results on the condensate function and, second, applies this framework to consistently explain experimental findings on Bose-Einstein condensation of photons in an optical microcavity [Klaers, Schmitt, Vewinger, and Weitz, Nature 468, 545 (2010)]. A grand-canonical photon gas is realized by a steady state of a photon flux deviating from a canonical thermodynamic Planck equilibrium. The theoretical approach presented here invites to significantly widen the experimental framework for Bose-Einstein condensation of photons including three-dimensional photon resonators and thermalization mechanisms different from a dye medium in the cavity.
Photons can come to thermal equilibrium at room temperature by scattering multiple times from a fluorescent dye. By confining the light and dye in a microcavity, a minimum energy is set and the photons can then show Bose–Einstein condensation. We present here the physical principles underlying photon thermalization and condensation, and review the literature on the subject. We then explore the ‘small’ regime where very few photons are needed for condensation. We compare thermal equilibrium results to a rate-equation model of microlasers, which includes spontaneous emission into the cavity, and we note that small systems result in ambiguity in the definition of threshold.
We examine in detail the mechanisms behind thermalization and Bose-Einstein condensation (BEC) of a gas of photons in a dye-filled microcavity. We derive a microscopic quantum model, based on that of a standard laser, and show how this model can reproduce the behavior of recent experiments. Using the rate-equation approximation of this model, we show how a thermal distribution of photons arises. We go on to describe how the nonequilibrium effects in our model can cause thermalization to break down as one moves away from the experimental parameter values. In particular, we examine the effects of changing cavity length, and of altering the vibrational spectrum of the dye molecules. We are able to identify two measures which quantify whether the system is in thermal equilibrium. Using these, we plot ``phase diagrams'' distinguishing BEC and standard lasing regimes. Going beyond the rate-equation approximation, our quantum model allows us to investigate both the second-order coherence g(2){g}^{(2)}g(2) and the linewidth of the emission from the cavity. We show how the linewidth collapses as the system transitions to a Bose condensed state, and compare the results to the Schawlow-Townes linewidth.
This chapter reviews recent work on the Bose–Einstein condensation of photons in a dye microcavity environment. The chapter is organized as follows. Section 6.2 describes the fluorescence induced thermalization mechanism of the photon gas. Section 6.3 discusses the statistical theory of the trapped photon gas. Section 6.4 reviews experiments on the thermalization process. Section 6.5 presents the corresponding results on Bose–Einstein condensation, and Section 6.6 concludes. A fluorescence induced thermalization process leads to a thermal photon gas at room temperature with freely adjustable chemical potential.