Non-stationary statistics and formation jitter in transient photon condensation

Abstract

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.

Sub-picosecond thermalization dynamics in condensation of strongly coupled lattice plasmons

“…It has been shown both experimentally and theoretically that, in the weak coupling regime, recurrent absorption and emission processes of light with molecules whose vibrational manifold is coupled to an external bath lead to thermalization and condensation with a BE(-type) distribution. This occurs both for continuous wave 19,33,36,53 and pulsed 28,54,55 pumping. The vibrational manifold serves as the energy loss channel to move the photon population towards lower energies, and thermal population of the vibrational states provides the temperature for the BE distribution.…”

“Amplified Spontaneous Emission” in Micro- and Nanolasers

“…The observation of the condensation of photons in interaction with a resonant medium in a cavity [39], and of its different statistical and non-stationary properties [40,41], has prompted the investigation of its occurrence even in other systems [42,43], hinting to a phenomenon more general than what initially considered (even without considering polariton and excitons which lie outside the realm of this discussion). A generalized thermodynamical treatment of Kirchoff's law [44] enables the description of subsystems with different temperatures-thus out of equilibrium-bridging the gap between the traditional thermal point of view and more modern devices.…”

Transport and localization of light inside a dye-filled microcavity

“…To better understand transport it is necessary to unravel the role of different dynamical processes, and over the past decade, two-dimensional photon gases inside dye-filled microcavities have become useful systems for studying both equilibrium and nonequlibrium physics [18][19][20][21][22][23][24]. The photon gas can thermalize via repeated absorption and reemission of photons by the dye molecules, ultimately leading to the formation of a near-equilibrium Bose-Einstein condensate (BEC) [18][19][20].…”

“…Recent experiments using dye-filled microcavities have demonstrated exciting new physics in both these regimes. For instance, exploiting thermalization to create spatially bifurcated coherent quantum states [39], or the study of photon statistics and formation jitter in transient condensation [24], and fuzzy phases of photonic condensates [40].…”