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IOP Conference Series Materials Science and Engineering

Modelling photon condensation in a fluorescent dye filled optical microcavity

Renju Rajan, P. Ramesh Babu, Krishnamoorthy Senthilnathan

Published Nov 1, 2017• 0 citations
Publisher

Abstract

In this paper, a mathematical model for photon condensation in an optical microcavity is considered based on Gross-Pitaevskii equation. The interaction of photons with fluorescent dye molecules in an optical microcavity resembles electron-ion interaction in a periodic lattice. The system is modelled analogous to Kronig-Penney model for electrons in a one-dimensional periodic lattice. The laser used as the light source gives rise to nonlinearity due to the deformation of electron orbits in the fluorescent dye. To accommodate the optical Kerr effect which arises due to this nonlinear interaction, the resultant Schrödinger equation is modified, which assumes the form of Gross-Pitaevskii equation. The model is validated using equation of state, whose virial coefficients can be evaluated from grand canonical ensemble scheme taking into account the interaction between photons and fluorescent dye molecules.

DOI
10.1088/1757-899x/263/2/022005

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In this paper, a mathematical model for photon condensation in an optical microcavity is considered based on Gross-Pitaevskii equation. The interaction of photons with fluorescent dye molecules in an optical microcavity resembles electron-ion interaction in a periodic lattice. The system is modelled analogous to Kronig-Penney model for electrons in a one-dimensional periodic lattice. The laser used as the light source gives rise to nonlinearity due to the deformation of electron orbits in the fluorescent dye. To accommodate the optical Kerr effect which arises due to this nonlinear interaction, the resultant Schrödinger equation is modified, which assumes the form of Gross-Pitaevskii equation. The model is validated using equation of state, whose virial coefficients can be evaluated from grand canonical ensemble scheme taking into account the interaction between photons and fluorescent dye molecules.
We derive the equation of motion for a Bose-Einstein condensate of photons in a dye-microcavity system, starting from Maxwell's equations. Our theory takes into account mirror shape, Kerr-type intensity-dependent refractive index and incoherent pumping and loss. The resulting equation is remarkably similar to the Gross-Pitaevskii equation for exciton-polariton condensates, despite the different microscopic origins. We calculate the incoherent photoluminescence spectrum of the photon condensate, which shows the Bogoliubov-type excitations around the mean field at thermal equilibrium. Both open- and closed-system models are presented to account for, respectively dissipation and inhomogeneities. Considering realistic parameters and experimental resolution, we estimate that by observing the angle-resolved spectrum of incoherent photoluminescence it is possible to resolve dimensionless interaction parameters of order ${10}^{\ensuremath{-}5}$, two orders of magnitude below current estimates. Thus we expect that this technique will lead to accurate measurements of the interactions in photon condensates.
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.
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 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.
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.
Bose–Einstein condensation is a state of matter known to be responsible for peculiar properties exhibited by superfluid Helium-4 and superconductors. Bose–Einstein condensate (BEC) in its pure form is realizable with alkali atoms under ultra-cold temperatures. In this paper, we review the experimental scheme that demonstrates the atomic Bose–Einstein condensate. We also elaborate on the theoretical framework for atomic Bose–Einstein condensation, which includes statistical mechanics and the Gross–Pitaevskii equation. As an extension, we discuss Bose–Einstein condensation of photons realized in a fluorescent dye filled optical microcavity. We analyze this phenomenon based on the generalized Planck’s law in statistical mechanics. Further, a comparison is made between photon condensate and laser. We describe how photon condensate may be a possible alternative for lasers since it does not require an energy consuming population inversion process.