Stability via symmetry breaking in interacting driven systems

TL;DR

This paper introduces a general mechanism where Hamiltonian interactions break symmetries in driven systems, enabling stable phases without relying on nonlinear losses or finite pump bandwidths, demonstrated through two concrete examples.

Contribution

It presents a novel symmetry-breaking mechanism via Hamiltonian interactions to achieve stability in driven photonic systems, expanding beyond traditional dissipation-based methods.

Findings

Hamiltonian interactions can induce stability by breaking symmetries in linearized dynamics.

Demonstrated a new $ ext{PT}$ laser where interactions switch between phases to stabilize.

Showed topological effects like Fock state stabilization and topological lasing.

Abstract

Photonic and bosonic systems subject to incoherent, wide-bandwidth driving cannot typically reach stable finite-density phases using only non-dissipative Hamiltonian nonlinearities; one instead needs nonlinear losses, or a finite pump bandwidth. We describe here a very general mechanism for circumventing this common limit, whereby Hamiltonian interactions can cut-off heating from a Markovian pump, by effectively breaking a symmetry of the unstable, linearized dynamics. We analyze two concrete examples of this mechanism. The first is a new kind of $\mathcal{PT}$ laser, where Hermitian Hamiltonian interactions can move the dynamics between the $\mathcal{PT}$ broken and unbroken phases and thus induce stability. The second uses onsite Kerr or Hubbard type interactions to break the chiral symmetry in a topological photonic lattice, inducing exotic phenomena from topological lasing to the stabilization of Fock states in a topologically protected edge mode.