On Measurement of the Second-order Coherence of Light-matter BECs with a Single Detector

The second-order autocorrelation function, g (2) (0), measured in the Hanbury Brown–Twiss scheme is the strong indicator separating the thermal (incoherent) from the coherent state of light emitted by lasers or photon or polariton condensates. Consequently, g (2) (0) can be used to determine if the Bose–Einstein condensate forms in the system. The fast dynamics of non-equilibrium light-matter Bose–Einstein condensate make implementing the Hanbury Brown–Twiss scheme challenging and expensive. A good time resolution requires single-photon detectors operating at cryogenic temperatures. An alternative approach to measuring g (2) (0), taken in many experiments, is to rely on the scheme with a single detector and measure the intensity fluctuations to directly obtain g (2) (0). In this paper, we show that the Hanbury Brown–Twiss scheme and the single detector scheme are not equivalent in the general case because we cannot directly use the intensity fluctuations measured in the single detector scheme to obtain g (2) (0) of light emitted by a multi-mode system. Nevertheless, we develop a method allowing for the reconstruction of g (2) (0) from the measurements in the single detector scheme for a multi-mode system with fast thermalization and illustrate it for a special case of non-equilibrium light-matter Bose–Einstein condensate.