Coherence is a defining feature of quantum condensates. These condensates are inherently multimode phenomena and in the macroscopic limit it becomes extremely difficult to resolve populations of individual modes and the coherence between them. In this work we demonstrate non-equilibrium Bose-Einstein condensation (BEC) of photons in a sculpted dye-filled microcavity, where threshold is found for 8 ± 2 photons. With this nanocondensate we are able to measure occupancies and coherences of individual energy levels of the bosonic field. Coherence of individual modes generally increases with increasing photon number, but at the breakdown of thermal equilibrium we observe multimode-condensation phase transitions wherein coherence unexpectedly decreases with increasing population, suggesting that the photons show strong inter-mode phase or number correlations despite the absence of a direct nonlinearity. Experiments are well-matched to a detailed non-equilibrium model. We find that microlaser and Bose-Einstein statistics each describe complementary parts of our data and are limits of our model in appropriate regimes, which informs the debate on the differences between the two [1, 2].

The aging lesbian, gay, bisexual, and transgender (LGBT) community continues to grow considerably while often being faced with unique and unmet needs separate from younger LGBT cohorts or their non-LGBT counterparts. This article explores some of the differences in attitudes among generational cohort groups regarding coming out decisions; sexual risk and safety; the impact of evolving policies within systems and society; as well as the demonstrated strengths and resiliencies of the aging LGBT community. Implications and suggestions for education, training, and best practices among this expansive and diverse population are considered as well as continued research in the field of LGBT aging.

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.

Photons can come to thermal equilibrium at room temperature by scattering multiple times from a fluorescent dye. By confining the light and dye in a microcavity, a minimum energy is set and the photons can then show Bose-Einstein condensation. We present here the physical principles underlying photon thermalization and condensation, and review the literature on the subject. We then explore the 'small' regime where very few photons are needed for condensation. We compare thermal equilibrium results to a rate-equation model of microlasers, which includes spontaneous emission into the cavity, and we note that small systems result in ambiguity in the definition of threshold. FOREWORDThis article is written in memory of Danny Segal, who was a colleague of one of us (Rob Nyman) in the Quantum Optics and Laser Science group at Imperial College for many years. The topic of this article touches on the subject of dye lasers, the stuff of nightmares for any AMO physicist of his generation, but a stronger connection to Danny is that he was very supportive of my application for the fellowship that pushed my career forward, and funded this research. One of Danny's quirks was a strong dislike of flying. As a consequence, I had the pleasure of joining him on a 24 hour, four-train journey from London to Italy to a conference. That's a lot of time for story telling and forging memories for life. Danny was one of the good guys, and I sorely miss his good humour and advice.This article presents a gentle introduction to thermalization and Bose-Einstein condensation (BEC) of photons in dye-filled microcavities, followed by a review of the state of the art. We then note the similarity to microlasers, particularly when there are very few photons involved. We compare a simple non-equilibrium model for microlasers with an even simpler thermal equilibrium model for BEC and show that the models coincide for similar values of a 'smallness' parameter.

While equilibrium phase transitions are well described by a free-energy landscape, there are few tools to describe general features of their non-equilibrium counterparts. On the other hand, near-equilibrium free-energies are easily accessible but their full geometry is only explored in nonequilibrium conditions, e.g. after a quench. In the particular case of a non-stationary system, however, the concepts of an order parameter and free energy become ill-defined, and a comprehensive understanding of non-stationary (transient) phase transitions is still lacking. Here, we probe transient non-equilibrium dynamics of an optically pumped, dye-filled microcavity which exhibits near-equilibrium Bose-Einstein condensation under steady-state conditions. By rapidly exciting a large number of dye molecules, we quench the system to a far-from-equilibrium state and, close to a critical excitation energy, find delayed condensation, interpreted as a transient equivalent of critical slowing down. We introduce the two-time, non-stationary, second-order correlation function, g (2) (t1, t2), as a powerful experimental tool for probing the statistical properties of the transient relaxation dynamics. In addition to number fluctuations near the critical excitation energy, we show that transient phase transitions exhibit a different form of diverging fluctuations, namely timing jitter in the growth of the order parameter. This jitter is seeded by the randomness associated with spontaneous emission, with its effect being amplified near the critical point. The experimental results are accurately described by a microscopic model of light-matter interactions. The general character of our observations is then discussed based on the geometry of effective free-energy landscapes. We thus identify universal features, such as the formation timing jitter, for a larger set of systems undergoing transient phase transitions. Our results carry immediate implications to diverse systems, including micro-and nano-lasers and growth of colloidal nanoparticles.

Photonic condensates are complex systems exhibiting phase transitions due to the interaction with their molecular environment. Given the macroscopic number of molecules that form a reservoir of excitations, numerical simulations are expensive, even for systems with few cavity modes. We present a systematic construction of molecular excitation profiles with a clear hierarchical ordering, such that only modes in the lowest order in the hierarchy directly affect the cavity photon dynamics. In addition to a substantial gain in computational efficiency for simulations of photon dynamics, the explicit spatial shape of the mode profiles offers a clear physical insight into the competition among the cavity modes for access to molecular excitations.

In this work, we use focused ion beam (FIB) milling to generate custom mirror shapes for quantum simulation in optical microcavities. In the paraxial limit, light in multimode optical microcavities follows an equation of motion which is equivalent to Schrödinger’s equation, with the surface topography of the mirrors playing the role of the potential energy landscape. FIB milling allows us to engineer a wide variety of trapping potentials for microcavity light, through exquisite control over the mirror topography, including 2D box, 1D waveguide, and Mexican hat potentials. The 2D box potentials are sufficiently flat over tens of microns, that the optical modes of the cavity, found by solving Schrödinger’s equation on the measured cavity topography, are standing-wave modes of the box, rather than localised to deviations. The predicted scattering loss due to surface roughness measured using atomic force microscopy is found to be 177 parts per million, which corresponds to a cavity finesse of 2.2 × 104 once other losses have been taken into account. Spectra from dye-filled microcavities formed using these features show thermalised light in flat 2D potentials close to dye resonance, and spectrally-resolved cavity modes at the predicted frequencies for elliptical potentials. These results also represent a first step towards realising superfluid light and quantum simulation in arbitrary-shaped optical microcavities using FIB milling.

We investigate the response of a photonic gas interacting with a reservoir of pumped dye molecules to quenches in the pump power. In addition to the expected dramatic critical slowing down of the equilibration time around phase transitions, we find extremely slow equilibration even far away from phase transitions. This noncritical slowing down can be accounted for quantitatively by fierce competition among cavity modes for access to the molecular environment, and we provide a quantitative explanation for this noncritical slowing down.