The quadratically driven nonlinear photonic lattice and its dissipative phase transition: from quantum to classical

Phase transitions (PT) appear in many flavors. In a Classical PT it results from a competition between energy and entropy, whereas in a quantum PT at zero temperature it results from the competition between non-commuting terms in the Hamiltonian. A quantum PT at finite temperature either vanishes or exhibits a continuous crossover to a classical PT [1]. The fate of a quantum PT at finite dissipation is much less understood.
A paradigmic example of a driven-dissipative system are lattices consisting of nonlinear optical cavities. By driving this system with a two-photon laser, the system retains a Z₂-symmetry, that can be spontaneously broken [2].

Here, I show how, using quantum trajectories with a Gaussian ansatz [3], we are able to explore a much larger parameter regime than before. In lattices up to 12x12 cavities we observe a transition from quantum to classical critical behavior, consistent with the interpretation of losses acting as temperature.
This work has been performed in collaboration with Riccardo Rota, Vincenzo Savona and Michiel Wouters.

[1] S. Sachdev-Quantum Phase Transitions
[2] V. Savona, PRA 96, 033826 (2017)
[3] Wouter Verstraelen and Michiel Wouters, Appl. Sci. 8(9), 1427 (2018)