Probing a Dissipative Phase Transition via Dynamical Optical Hysteresis

Abstract

We experimentally explore the dynamic optical hysteresis of a semiconductor microcavity as a function of the sweep time. The hysteresis area exhibits a double power law decay due to the shot noise of the driving laser, which triggers switching between metastable states. Upon increasing the average photon number and approaching the thermodynamic limit, the double power law evolves into a single power law. This algebraic behavior characterizes a dissipative phase transition. Our findings are in good agreement with theoretical predictions, and the present experimental approach is promising for the exploration of critical phenomena in photonic lattices.Optical bistability -the existence of two stable states with different photon numbers for the same driving conditions -is a general feature of driven nonlinear systems described within the mean-field approximation (MFA) [1]. Beyond the MFA, a quantum treatment predicts that the steady-state of a nonlinear cavity is unique at any driving condition [2]. The origin of this apparent contradiction was noted by Bonifacio and Lugiato [3], and by Drummond and Walls [4]: quantum fluctuations (the lost feature in the MFA) trigger switching between states and the exact solution corresponds to a weighted average over the two metastable states. Experiments in the 80's with two-mode lasers evidenced extremely long switching times [5], which were predicted to diverge for weak fluctuations and/or large photon numbers [6]. Already in these early works, this dramatic slowing down of the system dynamics was linked to a first order phase transition [5][6][7].The physics of nonlinear resonators is receiving renewed interest in connection to predictions of quantum many-body phases [8][9][10][11][12][13], critical phenomena [5,[12][13][14][16][17][18], and dissipative phase transitions [4]. Impressive progress is being made in building lattices of nonlinear resonators, such as photonic crystal cavities [20,21], waveguides [22], superconducting microwave resonators [23,24], or optomechanical resonators [25,26]. In this context, semiconductor microcavities operating in the exciton-photon strong coupling regime provide a versatile platform where photon hopping and the pumping geometry can be controlled [27]. Lattices of different dimensionalities can be engineered [28,29], and the hybrid light-matter nature of their elementary excitations, namely cavity polaritons, provide a strong and tunable Kerr nonlinearity via the exciton component [1,[30][31][32].Recently, it was predicted that even in a single resonator, critical exponents could be retrieved from dynamical hysteresis measurements [17]. More precisely, when the driving power is swept at a finite speed across a bistability, the area of the hysteresis cycle is expected to close following a double power-law as a function of the sweep time [5, 6]. The long-time decay arises from quantum fluctuations, and presents a universal −1 exponent [5]. In the thermodynamic limit wherein the photon number in the bistability tends to infinity and fluctua...

Two coupled nonlinear cavities in a driven-dissipative environment

“…For the closed system, the physics of double well has been studied in great detail [21][22][23][24][25][26], giving rise to phenomena such as the Josephson effect, matter wave interference and self-trapped and symmetry breaking states, among others. For open systems, studies of two coupled cavities have appeared in several contexts in both theory [27][28][29][30][31][32][33][34][35] and experiment [17,18,36,37]. For an enddriven cavity, studies focused on the topics of unconventional photon blockade [31][32][33] and multi-stability [17], among others.…”

Superradiant to subradiant phase transition in the open system Dicke model: dark state cascades

“…In the range investigated in this work ( g k~) the clear distinction between cooperative resonance fluorescence and optical bistability breaks down, thus combining these distinct fields of quantum optics. Besides the steady state, density matrix states with very long lifetimes can exist in these systems, which lead to the observation of bistabilities in experiments with finite measurement time [40]. In some limits these lifetimes go to infinity, resulting in a second steady state.…”

Spontaneous Beliaev-Landau scattering out of equilibrium

“…2b, the experimental signal from Beliaev-Landau processes is enhanced with a larger nonlinearity. Although experimentally challenging, a stronger nonlinearity can in principle be achieved by reducing the size of the microcavities or by increasing the excitonic fraction of polaritons [53]. Another more speculative possibility is to use the platform of superconducting circuits, where high nonlinearities are naturally achieved [54].…”