Semiclassical bifurcations and quantum trajectories: a case study of the open Bose-Hubbard dimer

TL;DR

This paper investigates the relationship between semiclassical bifurcations and quantum trajectories in an open Bose-Hubbard dimer, revealing that semiclassical models can predict quantum behavior even at small photon numbers.

Contribution

It demonstrates that semiclassical bifurcation diagrams accurately reflect quantum trajectory statistics in an open Bose-Hubbard dimer, bridging classical and quantum descriptions.

Findings

Semiclassical bifurcation diagrams match quantum trajectory statistics.

Quantum signatures of bifurcations are observable at small photon numbers.

Symmetry-breaking transitions relate to bifurcation phenomena.

Abstract

We consider the open two-site Bose-Hubbard dimer, a well-known quantum mechanical model that has been realised recently for photons in two coupled photonic crystal nanocavities. The system is described by a Lindblad master equation which, for large numbers of photons, gives rise to a limiting semiclassical model in the form of a four-dimensional vector field. From the situation where both sites trap the same amount of photons under symmetric pumping, one encounters a transition that involves symmetry breaking, the creation of periodic oscillations and multistability as the pump strength is increased. We show that the associated one-parameter bifurcation diagram of the semiclassical model captures the essence of statistical properties of computed quantum trajectories as the pump strength is increased. Even for small numbers of photons, the fingerprint of the semiclassical bifurcations can be recognised reliably in observables of quantum trajectories.