Non-stationary statistics and formation jitter in transient photon condensation

Observation of nonlinear response and Onsager regression in a photon Bose-Einstein condensate

The quantum regression theorem states that the correlations of a system at two different times are governed by the same equations of motion as the single-time averages. This provides a powerful framework for the investigation of the intrinsic microscopic behaviour of physical systems by studying their macroscopic response to a controlled external perturbation. Here we experimentally demonstrate that the two-time particle number correlations in a photon Bose-Einstein condensate inside a dye-filled microcavity exhibit the same dynamics as the response of the condensate to a sudden perturbation of the dye molecule bath. This confirms the regression theorem for a quantum gas, and, moreover, demonstrates it in an unconventional form where the perturbation acts on the bath and only the condensate response is monitored. For strong perturbations, we observe nonlinear relaxation dynamics which our microscopic theory relates to the equilibrium fluctuations, thereby extending the regression theorem beyond the regime of linear response.

Breakdown of Temporal Coherence in Photon Condensates

The temporal coherence of an ideal Bose gas increases as the system approaches the Bose-Einstein condensation threshold from below, with coherence time diverging at the critical point. However, counterexamples have been observed for condensates of photons formed in an externally pumped, dye-filled microcavity, wherein the coherence time decreases rapidly for increasing particle number above threshold. This Letter establishes intermode correlations as the central explanation for the experimentally observed dramatic decrease in the coherence time beyond critical pump power.

Engineering Photon Statistics in a Spinor Polariton Condensate

We implement full polarization tomography on photon correlations in a spinor exciton-polariton condensate. Our measurements reveal condensate pseudospin mean-field dynamics spanning from stochastic switching between linear polarization components, limit cycles, and stable fixed points, and their intrinsic relation to the condensate photon statistics. We optically harness the cavity birefringence, polariton interactions, and the optical orientation of an incoherent exciton reservoir to engineer photon statistics with precise control. Our results demonstrate a smooth transition from a highly coherent to a super-thermal state of the condensate polarization components.

Learning the Fuzzy Phases of Small Photonic Condensates

Phase transitions, being the ultimate manifestation of collective behavior, are typically features of many-particle systems only. Here, we describe the experimental observation of collective behavior in small photonic condensates made up of only a few photons. Moreover, a wide range of both equilibrium and nonequilibrium regimes, including Bose-Einstein condensation or laserlike emission are identified. However, the small photon number and the presence of large relative fluctuations places major difficulties in identifying different phases and phase transitions. We overcome this limitation by employing unsupervised learning and fuzzy clustering algorithms to systematically construct the fuzzy phase diagram of our small photonic condensate. Our results thus demonstrate the rich and complex phase structure of even small collections of photons, making them an ideal platform to investigate equilibrium and nonequilibrium physics at the few particle level.

Observation of a non-Hermitian phase transition in an optical quantum gas

Quantum gases of light, such as photon or polariton condensates in optical microcavities, are collective quantum systems enabling a tailoring of dissipation from, for example, cavity loss. This characteristic makes them a tool to study dissipative phases, an emerging subject in quantum many-body physics. We experimentally demonstrate a non-Hermitian phase transition of a photon Bose-Einstein condensate to a dissipative phase characterized by a biexponential decay of the condensate's second-order coherence. The phase transition occurs because of the emergence of an exceptional point in the quantum gas. Although Bose-Einstein condensation is usually connected to lasing by a smooth crossover, the observed phase transition separates the biexponential phase from both lasing and an intermediate, oscillatory condensate regime. Our approach can be used to study a wide class of dissipative quantum phases in topological or lattice systems.