Signatures of a dissipative phase transition in photon correlation measurements

Abstract

, which leads to long-lived deviations from the steady state as the system is driven towards the transition. Here, we show that photon correlation measurements can be used to characterize the corresponding critical slowing down of non-equilibrium dynamics. We focus on the extensively studied phenomenon of optical bistability in GaAs cavity polaritons 10,11 , which can be described as a first-order dissipative phase transition [12][13][14] . Increasing the excitation strength towards the bistable range results in an increasing photon-bunching signal along with a decay time that is prolonged by more than nine orders of magnitude as compared with that of single polaritons. In the limit of strong polariton interactions leading to pronounced quantum fluctuations, the mean-field bistability threshold is washed out. Nevertheless, the functional form with which the Liouvillian gap closes as the thermodynamic limit is approached provides a signature of the emerging dissipative phase transition. Our results establish photon correlation measurements as an invaluable tool for studying dynamical properties of dissipative phase transitions without requiring phase-sensitive interferometric measurements.Bistability, the coexistence of two stable states with different photon number under the same driving conditions, is a general signature of driven-dissipative nonlinear systems, and is commonly observed in a broad range of experimental realizations 10,11,[15][16][17] . This phenomenon can be well understood by treating the system in a mean-field description, that is, replacing the system's creation and annihilation operators by their corresponding expectation values. Neglecting quantum fluctuations in this way leads to diverging lifetimes of the two (otherwise metastable) states and results in hysteretic behaviour when the excitation power is ramped. A full quantum treatment, on the other hand, predicts a unique steady state with no indication of the underlying bistability 12,18 . These two pictures can be reconciled by investigating quantum non-equilibrium dynamics, described by a Liouvillian superoperator. In analogy with the spectrum of a Hamiltonian, the real part of the Liouvillian eigenvalues corresponds to the decay rate of the respective eigenmodes. The steady state of the driven-dissipative evolution is the eigenmode of the Liouvillian with zero eigenvalue. In the bistable regime, the Liouvillian excitation gap, or the asymptotic decay rate of its first excited state, vanishes in the thermodynamic limit (where the number of system excitations/particles N → ∞ ), corresponding to a diverging lifetime of a second eigenmode. The latter can exceed all intrinsic timescales by many orders of magnitude and is the reason for the successful description of bistability experiments by meanfield theory 19 . In general, a vanishing Liouvillian excitation gap signals a dissipative phase transition (DPT) 9,13,14,20,21 . Here, we demonstrate that the asymptotic decay rate of the Liouvillian can be determined by measuring photon correlati...

Tunable Open‐Access Microcavities for Solid‐State Quantum Photonics and Polaritonics

“…The orange, green, red, and purple colors correspond to the detuning Δ/γ = 0.2, 0.4, 0.8, and 1.0. Reproduced with permission . Copyright 2018, Springer Nature.…”

“…This can be done by loading the open‐access microcavity setup in a metal vacuum tube filled with low‐pressure helium (He) gas, with controlling electronic wires and optical fibers connected out through vacuum‐sealed ports. The vacuum tube is then inserted into a liquid He dewar, forming a bath cryostat that cools the whole system to ≈5K ( Figure a,b) . For k‐space imaging, extra lenses are loaded inside the vacuum tube to make a fully confocal optical system, as sketched in Figure b .…”

“…a) Fiber‐based open‐access microcavity in transmission configuration. Reproduced with permission . Copyright 2018, Springer Nature.…”

“…In order to distinguish the emission of cavity polaritons from the backscattered pump laser, the best solution is to structure the setup in transmission configuration as discussed in previous sections (Figure a,c). The realization of such transmission setup at liquid helium temperature is reported in a number of works from both fiber‐ and chip‐based cavities …”

“…The dissipative and quantum features of polaritons at the optical bistability region was investigated by Fink et al. in a fiber‐based open‐access microcavity, where the photon correlation measurement is demonstrated as an effective tool for studying the dynamics of dissipative phase transitions . At the bistability region ( Figure a), the intermittent light bursts due to the jump from low to high intensity states give rise to strong super‐Poissonian photon statistics, resulting in highly bunched polariton states exhibiting a second‐order correlation function g (2) (0) more than 2 .…”