Light thermalized at room temperature in an optically pumped, dye-filled microcavity resembles a model system of noninteracting Bose-Einstein condensation in the presence of dissipation. We have experimentally investigated some of the steady-state properties of this unusual state of light and found features which do not match the available theoretical descriptions. We have seen that the critical pump power for condensation depends on the pump beam geometry, being lower for smaller pump beams. Far below threshold, both intracavity photon number and thermalized photon cloud size depend on pump beam size, with optimal coupling when the pump beam matches the thermalized cloud size. We also note that the critical pump power for condensation depends on the cavity cutoff wavelength and longitudinal mode number, which suggests that energy-dependent thermalization and loss mechanisms are important.The decision to categorize an experimentally observed phenomenon as Bose-Einstein condensation (BEC) goes hand in hand with the consensus microscopic description. For exam ple, the popular definition of BEC by Penrose and Onsager [ 1 ] of extensive or macroscopic occupancy by identical bosons of a single quantum state was chosen to extend the original idea of Bose and Einstein to interacting particles, implicitly assuming homogeneity, in their case superfluid helium.In general, BEC at thermal equilibrium arises because the Bose-Einstein distribution diverges when the chemical potential approaches the energy of the ground state (from below). In dissipative, nonequilibrium condensation of exciton polaritons in semiconductors (e.g., [2-4]) or of polaritons in organic molecules [5,6], the system may be effectively homogeneous, so the Penrose and Onsager definition of BEC applies, but thermal equilibrium is not always strongly established. In these cases, BEC is widely accepted when thermal equilibrium is experimentally demonstrated to be a good description, and a macroscopic population is observed in the lowest-energy state, despite the strong interactions.Photons thermalized in a dye-filled microcavity probably have the weakest interactions of any system to have exhibited BEC, including atoms near Feshbach resonances [7,8]. In this intrinsically inhomogeneous system, thermal equilibrium and macroscopic occupancy of the ground state are the usual criteria for BEC, and both have been observed despite the dissipation [9,10], so BEC is assigned without major controversy [11]. Interactions are so weak, that questions have been asked about the mechanism by which the condensate forms [12], There has been considerable recent activity developing microscopic models of this physical system, but most of the models, e.g., by Kruchkov [13], assume that near-thermal-equilibrium conditions hold.'Correspondence should be addressed to r.nyman@imperial.ac.uk Published by the American Physical Society under the terms o f theCreative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the pu...

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

We have observed momentum-and position-resolved spectra and images of the photoluminescence from thermalised and condensed dye-microcavity photons. The spectra yield the dispersion relation and the potential energy landscape for the photons. From this dispersion relation, we find that the effective mass is that of a free photon not a polariton. We place an upper bound on the dimensionless two-dimensional interaction strength ofg 10 −3 , which is compatible with existing estimates. Both photon-photon and photon-molecule interactions are weak. The temperature is found to be independent of momentum, but dependent on pump spot size, indicating that the system is ergodic but not perfectly at thermal equilibrium. Condensation always happens first in the mode with lowest potential and lowest kinetic energy, although at very high pump powers multimode condensation occurs into other modes.

No abstract