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arXiv:1311.6634 · Physical Review Letters

Observation of Grand-Canonical Number Statistics in a Photon Bose-Einstein Condensate

Julian Schmitt, Tobias Damm, David Dung, Frank Vewinger, Jan Klaers, Martin Weitz

Published Jan 21, 2014• 126 citations
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Abstract

We report measurements of particle number correlations and fluctuations of a photon Bose-Einstein condensate in a dye microcavity using a Hanbury Brown-Twiss experiment. The photon gas is coupled to a reservoir of molecular excitations, which serve as both heat bath and particle reservoir to realize grand-canonical conditions. For large reservoirs, we observe strong number fluctuations of the order of the total particle number extending deep into the condensed phase. Our results demonstrate that Bose-Einstein condensation under grand-canonical ensemble conditions does not imply second-order coherence.

DOI
10.1103/physrevlett.112.030401

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We report measurements of particle number correlations and fluctuations of a photon Bose-Einstein condensate in a dye microcavity using a Hanbury Brown-Twiss experiment. The photon gas is coupled to a reservoir of molecular excitations, which serve as both heat bath and particle reservoir to realize grand-canonical conditions. For large reservoirs, we observe strong number fluctuations of the order of the total particle number extending deep into the condensed phase. Our results demonstrate that Bose-Einstein condensation under grand-canonical ensemble conditions does not imply second-order coherence.
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 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 examine the phase evolution of a Bose-Einstein condensate of photons generated in a dye microcavity by temporal interference with a phase reference. The photoexcitable dye molecules constitute a reservoir of variable size for the condensate particles, allowing for grand canonical statistics with photon bunching, as in a lamp-type source. We directly observe phase jumps of the condensate associated with the large statistical number fluctuations and find a separation of correlation time scales. For large systems, our data reveal phase coherence and a spontaneously broken symmetry, despite the statistical fluctuations.
Abstract The Tutorial reports recent experimental advances in studies of the dynamics as well as the number and phase correlations of a Bose–Einstein condensed photon gas confined in a high-finesse dye-filled microcavity. Repeated absorption–emission-processes of photons on dye molecules here establish a thermal coupling of the photonic quantum gas to both a heat bath and a particle reservoir comprised of dye molecules. In this way, for the first time Bose–Einstein condensation under grand-canonical statistical ensemble conditions becomes experimentally accessible. The work presented in this Tutorial was one of the four shortlisted finalists of the 2017 DPG SAMOP dissertation prize.
Photons are mutually nearly noninteracting particles, so thermalized photon ensembles are commonly obtained not from direct particle-particle-interactions but rather from contact with matter, which can constitute a reservoir for the photon gas. We develop a theory model for photons in a material-filled (e.g. liquid dye) optical microcavity, with the aim to study the fluctuation properties using a free-energy description for noninteracting photons coupled to a reservoir of material electronic excitations. To begin with, we use a single mode description for the condensate. For a small relative size of the material reservoir, corresponding to the canonical regime, condensate number fluctuations are small, and the derived free energy landscape takes the usual Mexican-hat shaped form such that spontaneous symmetry breaking occurs. In contrast, for a large relative size of the reservoir, corresponding to the grand canonical regime, fluctuations become as large as the average particle number. We show that the resulting free energy landscape acquires a bowl-shaped form, with a single minimum at the origin. Thus, a macroscopic occupation of the ground state (i.e., Bose-Einstein condensation) in the absence of spontaneous symmetry breaking is expected. We also provide a model for the treatment of a photon gas trapped in a box-shaped potential with spatially distributed coupling to a reservoir. The model predicts, for example, a statistically fluctuating pattern of islands with long-range coherence, resembling transient microcondensates.
Bose-Einstein condensation in the grand canonical ensemble admits a formulation in terms of a phase-density decomposition of the condensate mode operator ψ^0\hatψ_{\bf 0}ψ^​0​. In the presence of macroscopic condensate number fluctuations this representation presents nontrivial implications. In particular, we show that, for the ideal gas, under the assumption of a well-defined phase and a fluctuating condensate density, the square modulus of the anomalous average ⟨ψ^0⟩\langle \hatψ_{\bf 0}\rangle⟨ψ^​0​⟩ can provide only a fraction of the whole condensate density ρ0ρ_{\bf 0}ρ0​ and for the grand canonical statistics of the ideal Bose gas one obtains the value ∣⟨ψ^0⟩∣2=(π/4)ρ0|\langle {\hat ψ}_{\bf 0}\rangle|^2 =(π/4) ρ_{\bf 0}∣⟨ψ^​0​⟩∣2=(π/4)ρ0​. The remaining part is supplemented by the (macroscopic) fluctuations of ψ^0\hatψ_{\bf 0}ψ^​0​, which become a distinctive feature of the BEC in this setting. This provides a transparent physical picture of a condensate of photons with a well-defined phase but large number fluctuations, as observed in dye-filled microcavity photon experiments. We also propose a way to access the square modulus of the anomalous average to test theoretical predictions.