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arXiv:1705.02173 · Physical Review Letters

Decondensation in Nonequilibrium Photonic Condensates: When Less Is More

Henry J. Hesten, Robert A. Nyman, Florian Mintert

Published Jan 23, 2018• 41 citations
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Abstract

We investigate the steady state of a system of photons in a pumped dye-filled microcavity. By varying pump and thermalization the system can be tuned between Bose-Einstein condensation, multimode condensation, and lasing. We present a rich nonequilibrium phase diagram which exhibits transitions between these phases, including decondensation of individual modes under conditions that would typically favor condensation.

DOI
10.1103/physrevlett.120.040601

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We investigate the steady state of a system of photons in a pumped dye-filled microcavity. By varying pump and thermalization the system can be tuned between Bose-Einstein condensation, multimode condensation, and lasing. We present a rich nonequilibrium phase diagram which exhibits transitions between these phases, including decondensation of individual modes under conditions that would typically favor condensation.
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.
Photon condensation in semiconductor microcavities is a transformative technique for engineering quantum states of light at room temperature by tailoring strong but incoherent light-matter interactions. While continuous-wave and electrical pumping offer exceptional prospects for miniaturized quantum photonic technologies, harnessing these requires conceptual advances in understanding nonequilibrium light-matter dynamics in semiconductors. We resolve this challenge through an \textit{ab initio} quantum kinetic theory capturing how Coulomb interactions of optically excited carriers and phonon scattering mediate photon thermalization and condensation in semiconductors. Our microscopic model shows that at high carrier densities, thermalization is dominated by carrier-carrier Coulomb scattering, in clear contrast to the rovibrational relaxation that governs dye-based photon condensates. The theory predicts a rich nonequilibrium phase diagram with thermal, Bose-condensed, multimode, and lasing phases, quantitatively in agreement with recent experiments. Crucially, we identify how cavity detuning controls transitions between equilibrium and gain-dominated regimes, enabling tailored design of coherent light sources. This work thus provides the foundation for semiconductor-based quantum photonic devices operating beyond conventional laser paradigms.
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 report a time-resolved study of the thermalization dynamics and the lasing to photon Bose-Einstein condensation crossover by in situ monitoring the photon kinetics in a dye microcavity. When the equilibration of the light to the dye temperature by absorption and reemission is faster than photon loss in the cavity, the optical spectrum becomes Bose-Einstein distributed and photons accumulate at low-energy states, forming a Bose-Einstein condensate. The thermalization of the photon gas and its evolution from nonequilibrium initial distributions to condensation is monitored in real time. In contrast, if photons leave the cavity before they thermalize, the system operates as a laser.
Bose-Einstein condensation (BEC) is the transition to a macroscopic occupation of the ground state of a system of bosonic particles. In 1995 the first experimental realization of BEC was achieved by condensing a dilute atomic gas [1,2]. It was long thought only massive particles could undergo BEC. However, in 2010 it was shown that photon BEC was achieved in an optical dye-filled microcavity [3]. In 2015, we became the second group to successfully repeat these experiments.\n\nBEC is a phase transition and thus it occurs at thermal equilibrium. To achieve a thermal photon gas the cavity is filled with a fluorescent dye solution. The dye molecules thermalize the photons by means of repeated absorption-emission cycles. We optically pump the cavity. With the pump we determine the number of photons absorbed by the dye, consequently defining a nonvanishing chemical potential. This ensures a conserved photon number. The photons are trapped by the harmonic potential induced by the concave cavity mirrors. Due to the cutoff energy determined by the cavity length, the trapped photons have a dispersion similar to that of a massive particle in a quantum harmonic oscillator. The cavity length is tuned such that the free spectral range is larger than the bandwidth of the dye. Therefore, only one longitudinal mode fits inside the cavity, making the photon gas effectively two-dimensional. We end up with a thermalized two-dimensional photon gas that has the eigenenergies of a quantum harmonic oscillator. The Bose-Einstein distribution function predicts a critical photon number. Pumping the thermal photon gas beyond this critical number will lead to photon BEC.\n\nWe measure the spectral- and spatial distributions of our two-dimensional photon gas. In both distributions we observe photon BEC. Results show the characteristics of a phase transition: the appearance of a sharp peak on top of the thermal cloud that coincides with a converging chemical potential to zero. Both the spectral- and spatial distribution are in agreement with the theoretical distribution of photons with an effective mass in a quantum harmonic oscillator. Expansion of the condensate has been measured. This could indicate nonlinear optical effects such as thermal lensing or repulsive photon-photon interactions.
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){g}^{(2)}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.