Spatiotemporal coherence of non-equilibrium multimode photon condensates

Abstract

We report on the observation of quantum coherence of Bose-Einstein condensed photons in an optically pumped, dye-filled microcavity. We find that coherence is long-range in space and time above condensation threshold, but short-range below threshold, compatible with thermalequilibrium theory. Far above threshold, the condensate is no longer at thermal equilibrium and is fragmented over non-degenerate, spatially overlapping modes. A microscopic theory including cavity loss, molecular structure and relaxation shows that this multimode condensation is similar to multimode lasing induced by imperfect gain clamping. BEC means that interferometry is one of the most urgent measurements to be made with a condensate [4,5]. Where thermal equilibrium is not completely reached, coherence is the defining characteristic of non-BEC quantum condensation, e.g for semiconductor exciton-polaritons [6-9] and organic polaritons [10,11]. In nonideal Bose gases, such as ultracold atoms, interactions tend to reduce but not destroy the coherence [12][13][14].The long range coherence behaviour of two-dimensional (2D) microcavity condensates is currently an open question. The coherence of interacting, equilibrium 2D Bose gases decays with a power law at large distances. The exponent is no greater than 1/4, which is reached at the threshold for the Berezinskii-Kosterlitz-Thouless transition [15]. It is known that the equation of motion for the local phase of a non-equilibrium drivendissipative 2D condensate is in the universality class of the Kardar-Parisi-Zhang (KPZ) equation [16], and nonpower-law decays are possible. Since the long-range coherence only shows non-equilibrium behaviour for systems which are very large compared to interaction length scales (such as the healing length), it has proven difficult to observe the true long-range behaviour, mainly due to unavoidable pumping inhomogeneities [17].Photon condensates in dye-filled microcavities are weakly interacting [18][19][20][21], inhomogeneous [22, 23], dissipative Bose gases close to thermal equilibrium at room temperature [24][25][26][27][28]. It is worth noting that the physical system has some similarities to a dye laser, with the decisive difference being that lasing is necessarily a non-equilibrium effect whereas photons can also undergo BEC in thermal equilibrium. Consequently BEC implies macroscopic occupation of the ground state independently of the loss and gain properties, whereas a laser is characterised by a large occupation of exactly the mode that has the most gain [29].Unique among physical realisations of BEC, in dye-microcavity photon BEC the particles thermalise only with a bath and not directly among themselves. This implies that the establishment of phase coherence in the OPEN ACCESS RECEIVED

Spontaneous Symmetry Breaking and Phase Coherence of a Photon Bose-Einstein Condensate Coupled to a Reservoir

“…For condensates of polaritons, mixed states of matter and light, polarization symmetry breaking was reported [7,8], while polariton arrays have shown phase locking [9]. Further, spatial coherence has been reported for equilibrium photon condensates [10], and also in a nonequilibrium regime [11]. Both atomic and polariton condensates are usually assumed to emit a single wave train of constant amplitude [1,12].…”

Bose-Einstein condensation of photons from the thermodynamic limit to small photon numbers

“…They were able to show that the multimode condensation seen in Ref. [37] was due to imperfect clamping of the molecular excited-state population in regions adjacent to the central condensate light mode which leaves the possibility of positive gain for other modes.…”

Tunable Open‐Access Microcavities for Solid‐State Quantum Photonics and Polaritonics

“…The small mode volume of the system allows self‐diffusion that quickly circulates photobleached dye molecules out of the cavity mode, in which the authors demonstrated CW operation of a dye laser without externally driven recirculation, with single mode tunability over a bandwidth of 20 nm. In parallel with dye‐based microlasers, dye molecules incorporated in cavities were also investigated for photon condensations, wherein the photons can reach thermal equilibrium through frequent energy exchanges with the thermal bath of dye–solvent vibrations . Walker et al.…”

“…In parallel with dye-based microlasers, dye molecules incorporated in cavities were also investigated for photon condensations, wherein the photons can reach thermal equilibrium through frequent energy exchanges with the thermal bath of dye-solvent vibrations. [128][129][130][131][132] Walker et al reported nonequilibrium BEC of a very small number (7 ± 2) of photons in the chip-based open-access microcavity incorporating dye molecules. [133] The concave mirror, with a RoC of 400 µm fabricated by FIB milling, was specifically designed to form a photonic potential of 2D harmonic oscillator that enabled the observation of a multimode condensate regime of photons that exhibit strong intermode correlations.…”