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arXiv:2009.00094 · Physical Review A

Transport and localization of light inside a dye-filled microcavity

Himadri Shekhar Dhar, João D. Rodrigues, Benjamin T. Walker, Rupert F. Oulton, Robert A. Nyman, Florian Mintert

Published Nov 25, 2020• 5 citations

Abstract

The driven-dissipative nature of light-matter interaction inside a multimode, dye-filled microcavity makes it an ideal system to study nonequilibrium phenomena, such as transport. In this work, we investigate how light is efficiently transported inside such a microcavity, mediated by incoherent absorption and emission processes. In particular, we show that there exist two distinct regimes of transport, viz. conductive and localized, arising from the complex interplay between the thermalizing effect of the dye molecules and the nonequilibrium influence of driving and loss. The propagation of light in the conductive regime occurs when several localized cavity modes undergo dynamical phase transitions to a condensed, or lasing, state. Furthermore, we observe that, while such transport is robust for weak disorder in the cavity potential, strong disorder can lead to localization of light even under good thermalizing conditions. Importantly, the exhibited transport and localization of light is a manifestation of the nonequilibrium dynamics rather than any coherent interference in the system.

DOI: 10.1103/physreva.102.053517

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The driven-dissipative nature of light-matter interaction inside a multimode, dye-filled microcavity makes it an ideal system to study nonequilibrium phenomena, such as transport. In this work, we investigate how light is efficiently transported inside such a microcavity, mediated by incoherent absorption and emission processes. In particular, we show that there exist two distinct regimes of transport, viz. conductive and localized, arising from the complex interplay between the thermalizing effect of the dye molecules and the nonequilibrium influence of driving and loss. The propagation of light in the conductive regime occurs when several localized cavity modes undergo dynamical phase transitions to a condensed, or lasing, state. Furthermore, we observe that, while such transport is robust for weak disorder in the cavity potential, strong disorder can lead to localization of light even under good thermalizing conditions. Importantly, the exhibited transport and localization of light is a manifestation of the nonequilibrium dynamics rather than any coherent interference in the system.

We develop a nonequilibrium model of condensation and lasing of photons in a dye filled microcavity. We examine in detail the nature of the thermalization process induced by absorption and emission of photons by the dye molecules, and investigate when the photons are able to reach a thermal equilibrium Bose-Einstein distribution. At low temperatures, or large cavity losses, the absorption and emission rates are too small to allow the photons to reach thermal equilibrium and the behavior becomes more like that of a conventional laser.

We consider a homogeneously pumped photon gas coupled to a dye medium and investigate how its steady state is affected when varying the pump power, the photon cavity lifetime, and the cutoff frequency. We study how the interplay between pumping, loss, and dye-induced thermalization influences the selection of the cavity modes that acquire large occupation. Depending on the parameter regime, the latter can be related either to lasing of (typically multiple) modes or to equilibrium-like photon condensation in the ground mode. We calculate and explain the phase diagram of the system, with a particular emphasis on the role played by mode competition that occurs in the regime of weak cavity loss.

We examine in detail the mechanisms behind thermalization and Bose-Einstein condensation (BEC) of a gas of photons in a dye-filled microcavity. We derive a microscopic quantum model, based on that of a standard laser, and show how this model can reproduce the behavior of recent experiments. Using the rate-equation approximation of this model, we show how a thermal distribution of photons arises. We go on to describe how the nonequilibrium effects in our model can cause thermalization to break down as one moves away from the experimental parameter values. In particular, we examine the effects of changing cavity length, and of altering the vibrational spectrum of the dye molecules. We are able to identify two measures which quantify whether the system is in thermal equilibrium. Using these, we plot ``phase diagrams'' distinguishing BEC and standard lasing regimes. Going beyond the rate-equation approximation, our quantum model allows us to investigate both the second-order coherence

{g}^{(2)}

and the linewidth of the emission from the cavity. We show how the linewidth collapses as the system transitions to a Bose condensed state, and compare the results to the Schawlow-Townes linewidth.

We have observed momentum- and position-resolved spectra and images of the photoluminescence from thermalized and condensed dye-microcavity photons. The spectra yield the dispersion relation and the potential energy landscape for the photons. From this dispersion relation, below condensation threshold, we find that the effective mass is that of a bare cavity photon, not a polariton. Above threshold, we place an upper bound on the dimensionless two-dimensional interaction strength of $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{g}\ensuremath{\lesssim}{10}^{\ensuremath{-}3}$, 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.

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