Phase transitions and quench dynamics in driven-dissipative condensates

Abstract

Exciton-polaritons are composite quasi-particles, thought of as being half-matter and half-light: they have a low effective mass, enabling them to form a Bose-Einstein condensate at room temperature, but are inherently unstable quasi-particles, with the observed coherence arising as a result of the interplay between driving and decay. An important open question tackled in this thesis, is the extent to which the driven-dissipative nature of these “fluids of light” makes them different to the usual “equilibrium” condensates. Exciton-polariton condensates are of particular interest both for fundamental studies and for potential applications in quantum technologies. In this thesis, we focus on the investigation of static and dynamic properties of such systems, specifically addressing the nature of the phase transition and the dynamics during and after a quench. After confirming the validity of our model (a stochastic nonlinear equation for the lower-polariton branch) for experimentally-relevant parameters, we perform a detailed characterisation of the steady-state system, obtaining results in broad agreement with the Berezinskii-Kosterlitz- Thouless phase transition characterising the transition from a disordered to an ordered state in two-dimensional equilibrium systems. Our analysis enables us to identify the critical external pumping rate at which the phase transition occurs, critical for our next study. Firstly, by instantaneously quenching the system across the transition,we discuss dynamical scaling of defects and characteristic length of the system: this enables us to evaluate the dynamical critical exponent characterising the growth of long-range order. Our results reveal that universal critical properties of driven-dissipative polariton systems are consistent with those expected for the equilibrium Berezinskii-Kosterlitz Thouless transition, ruling out other proposed scenarios (“conservative superfluid”, “Kardar-Parisi-Zhang” predictions). Finally, analysing finite-duration quench dynamics across the phase transition, we explicitly verify universal behaviour in the formof the Kibble-Zurek mechanism, a universal scaling law relating the number of spontaneously-generated defects (vortices) to the quench duration.