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arXiv:1309.7575 · Physical Review A

Condensation of photons coupled to a Dicke field in an optical microcavity

Eran Sela, Achim Rosch, V. Fleurov

Published Apr 30, 2014• 12 citations
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Abstract

Motivated by recent experiments reporting Bose-Einstein condensation of light coupled to incoherent dye molecules in a microcavity, we show that due to a dimensionality mismatch between the two-dimensional cavity photons and the three-dimensional arrangement of molecules, the system permits superfluid regimes where the relevant molecular degrees of freedom are collective Dicke states rather than individual excitations. For sufficiently high dye concentration, Dicke states become robust against local decoherence. In the limit when all dye molecules become excited, this system also shows Mott-Hubbard physics, despite the absence of an underlying lattice.

DOI
10.1103/physreva.89.043844

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Motivated by recent experiments reporting Bose-Einstein condensation of light coupled to incoherent dye molecules in a microcavity, we show that due to a dimensionality mismatch between the two-dimensional cavity photons and the three-dimensional arrangement of molecules, the system permits superfluid regimes where the relevant molecular degrees of freedom are collective Dicke states rather than individual excitations. For sufficiently high dye concentration, Dicke states become robust against local decoherence. In the limit when all dye molecules become excited, this system also shows Mott-Hubbard physics, despite the absence of an underlying lattice.
We theoretically analyze the temperature behavior of paraxial light in thermal equilibrium with a dye-filled optical microcavity. At low temperatures the photon gas undergoes Bose-Einstein condensation, and the photon number in the cavity ground state becomes macroscopic with respect to the total photon number. Owing to a grand-canonical excitation exchange between the photon gas and the dye molecule reservoir, a regime with unusually large fluctuations of the condensate number is predicted for this system that is not observed in present atomic physics Bose-Einstein condensation experiments.
The advent of controlled experimental accessibility of Bose-Einstein condensates, as realized with e.g. cold atomic gases, exciton-polaritons, and more recently photons in a dye-filled optical microcavity, has paved the way for new studies and tests of a plethora of fundamental concepts in quantum physics. We here describe recent experiments studying a transition between laser-like dynamics and Bose-Einstein condensation of photons in the dye microcavity system. Further, measurements of the second-order coherence of the photon condensate are presented. In the condensed state we observe photon number fluctuations of order of the total particle number, as understood from effective particle exchange with the photo-excitable dye molecules. The observed intensity fluctuation properties give evidence for Bose-Einstein condensation occurring in the grand-canonical statistical ensemble regime.
We consider Bose-Einstein condensation of photons in an optical cavity filled with dye molecules that are excited by laser light. By using the Schwinger-Keldysh formalism we derive a Langevin field equation that describes the dynamics of the photon gas and, in particular, its equilibrium properties and relaxation towards equilibrium. Furthermore we show that the finite lifetime effects of the photons are captured in a single dimensionless damping parameter that depends on the power of the external laser pumping the dye. Finally, as applications of our theory we determine spectral functions and collective modes of the photon gas in both the normal and the Bose-Einstein condensed phases.
A theory of Bose-Einstein condensation (BEC) of light in a dye microcavity is developed. The photon polarization degeneracy and the interaction between dye molecules and photons in all of the cavity modes are taken into account. The theory goes beyond the grand canonical approximation and allows one to determine the statistical properties of the photon gas for all numbers of dye molecules and photons at all temperatures, thus describing the microscopic, mesoscopic, and macroscopic light BEC from a general perspective. A universal relation between the degrees of second-order coherence for the photon condensate and the polarized photon condensate is obtained. The photon Bose-Einstein condensate can be used as a new source of nonclassical light.
We introduce a model describing the competition of interactions between NNN two-level systems (TLSs) against decoherence. We apply it to analyze dye molecules in an optical microcavity, where molecular vibrations provide a local source for decoherence. The most interesting case is when decoherence strongly affects each individual TLS, e.g., via broadening of emission lines as well as vibrational satellites; however, its influence is strongly suppressed for large NNN due to the interactions between TLSs. In this interaction-dominated regime we find unique signatures in the emission spectrum, including strong O(N)O(\sqrt{N})O(N​) level shifts, as well as 1/N1/N1/N suppression of both the decoherence width and the vibrational satellites. These effects are most pronounced in the unexplored regime near 5050%50 polarization of the TLSs.
A theory of Bose-Einstein condensation of light in a dye-filled optical microcavity is presented. The theory is based on the hierarchical maximum entropy principle and allows one to investigate the fluctuating behavior of the photon gas in the microcavity for all numbers of photons, dye molecules, and excitations at all temperatures, including the whole critical region. The master equation describing the interaction between photons and dye molecules in the microcavity is derived and the equivalence between the hierarchical maximum entropy principle and the master equation approach is shown. The cases of a fixed mean total photon number and a fixed total excitation number are considered, and a much sharper, nonparabolic onset of a macroscopic Bose-Einstein condensation of light in the latter case is demonstrated. The theory does not use the grand canonical approximation, takes into account the photon polarization degeneracy, and exactly describes the microscopic, mesoscopic, and macroscopic Bose-Einstein condensation of light. Under certain conditions, it predicts sub-Poissonian statistics of the photon condensate and the polarized photon condensate, and a universal relation takes place between the degrees of second-order coherence for these condensates. In the macroscopic case, there appear a sharp jump in the degrees of second-order coherence, a sharp jump and kink in the reduced standard deviations of the fluctuating numbers of photons in the polarized and whole condensates, and a sharp peak, a cusp, of the Mandel parameter for the whole condensate in the critical region. The possibility of nonclassical light generation in the microcavity with the photon Bose-Einstein condensate is predicted.