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arXiv:1809.08772 · Physical Review Letters

Noncritical Slowing Down of Photonic Condensation

Benjamin T. Walker, Henry J. Hesten, Himadri Shekhar Dhar, Robert A. Nyman, Florian Mintert

Published Nov 13, 2019• 17 citations
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Abstract

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.

DOI
10.1103/physrevlett.123.203602

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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.
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.
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.
While equilibrium phase transitions are easily described by order parameters and free-energy landscapes, for their non-stationary counterparts these quantities are usually ill-defined. Here, we probe transient non-equilibrium dynamics of an optically pumped, dye-filled microcavity. We quench the system to a far-from-equilibrium state and find delayed condensation close to a critical excitation energy, a transient equivalent of critical slowing down. Besides number fluctuations near the critical excitation energy, we show that transient phase transitions exhibit timing jitter in the condensate formation. This jitter is a manifestation of the randomness associated with spontaneous emission, showing that condensation is a stochastic, rather than deterministic process. Despite the non-equilibrium character of this phase transition, we construct an effective free-energy landscape that describes the formation jitter and allows, in principle, its generalization to a wider class of processes.
Abstract While equilibrium phase transitions are easily described by order parameters and free-energy landscapes, for their non-stationary counterparts these quantities are usually ill-defined. Here, we probe transient non-equilibrium dynamics of an optically pumped, dye-filled microcavity. We quench the system to a far-from-equilibrium state and find delayed condensation close to a critical excitation energy, a transient equivalent of critical slowing down. Besides number fluctuations near the critical excitation energy, we show that transient phase transitions exhibit timing jitter in the condensate formation. This jitter is a manifestation of the randomness associated with spontaneous emission, showing that condensation is a stochastic, rather than deterministic process. Despite the non-equilibrium character of this phase transition, we construct an effective free-energy landscape that describes the formation jitter and allows, in principle, its generalization to a wider class of processes.
Photons in a dye filled microcavity have been proven to form Bose-Einstein condensates both theoretically and experimentally. The system may also be placed in a fundamentally non- equilibrium state where multiple modes are condensed. This thesis theoretically examines some of the deviations from traditional Bose-Einstein condensate models which have been observed and which may be expected in future experiments. Unusual and potentially unseen condensed states are predicted, along with the unexpected non-critical slowing down of system evolution when in these states. A rigorous derivation of a master equation from a microscopic Hamiltonian is given in chapter two. This is used to study the multimode phases of the condensate in chapter three along with transitions between them. The temporal evolution of the condensate in various phases and close to phase boundaries is presented in chapter four. Dramatic improvements in the simulation of photonic condensates are also discussed in chapter four. These improvements also offer a conceptual shift in the theoretical description of photonic condensates which allows new insights to be made. The fifth chapter establishes a foundation of coupled rate equations which may be used to model the higher order coherences of photons and molecules in future work. Finally the transport of photons across non-standard cavities is modelled, providing guidance for future experiments and possible applications of photonic condensates.
Systems close to a phase transition turn weak perturbations into large responses. At equilibrium, this amplification is closely linked to criticality: fluctuations grow, dynamics slow, and a common soft mode controls the response. Whether this correspondence survives in driven-dissipative quantum systems, sustained by continuous pumping and loss away from thermal equilibrium, remains an open question. Here we show experimentally that it does. In a room-temperature semiconductor photon Bose-Einstein condensate, the critical slowing of spontaneous intensity fluctuations and the amplification of weak pump perturbations are measured independently. Both peak at the same condensate population, nˉc=1250\bar{n}_c = 1250nˉc​=1250, where the dimensionless slowing factor and susceptibility reach the same value, nˉc/2=625\bar{n}_c/2 = 625nˉc​/2=625. A single weakly damped collective photon-reservoir mode governs both effects. This fluctuation-response correspondence in a finite open quantum gas establishes critical susceptibility as a measurable dynamical signature of condensation, with peak gain set by system size.