Critical Theory for the Breakdown of Photon Blockade

TL;DR

This paper analyzes the breakdown of photon blockade as a second order phase transition in a Jaynes--Cummings system, revealing critical behavior and symmetry breaking, with implications for experimental observation.

Contribution

It introduces a theoretical framework connecting photon blockade breakdown to a PT-symmetry breaking phase transition, including critical scaling and a universal toy model.

Findings

Photon blockade breaks down at a critical drive strength.

Steady state observables exhibit power-law divergence near criticality.

The proposed toy model captures universal properties of the phase transition.

Abstract

Photon blockade is the result of the interplay between the quantized nature of light and strong optical nonlinearities, whereby strong photon-photon repulsion prevents a quantum optical system from absorbing multiple photons. We theoretically study a single atom coupled to the light field, described by the resonantly driven Jaynes--Cummings model, in which case the photon blockade breaks down in a second order phase transition at a critical drive strength. We show that this transition is associated to the spontaneous breaking of an anti-unitary PT-symmetry. Within a semiclassical approximation we calculate the expectation values of observables in the steady state. We then move beyond the semiclassical approximation and approach the critical point from the disordered (blockaded) phase by reducing the Lindblad quantum master equation to a classical rate equation that we solve. The width of the steady-state distribution in Fock space is found to diverge as we approach the critical point with a simple power-law, allowing us to calculate the critical scaling of steady state observables without invoking mean-field theory. We propose a simple physical toy model for biased diffusion in the space of occupation numbers, which captures the universal properties of the steady state. We list several experimental platforms where this phenomenon may be observed.