Stability via symmetry breaking in interacting driven systems

Conventional wisdom dictates that incoherent, Markovian pumping of a photonic or bosonic lattice cannot be stabilized with Hamiltonian non-linearities, because the infinite pump bandwidth is agnostic to the internal system energy levels. However, we present an extremely general mechanism to circumvent this common problem [1]; when the Hamiltonian non-linearity effectively breaks symmetries of the underlying quadratic model at high photon density, it can restabilize the dynamics by forcing stable and unstable modes to hybridize.

We analyze two concrete examples, showing that this is of practical as well as fundamental relevance. The first is a new kind of PT laser, where Hermitian Hamiltonian interactions can move the dynamics between the 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. In the limit of weak interactions, this generates a new mechanism for topological lasing. When interactions are strong, we show that our mechanism can also stabilize non-classical quantum many-body states, like a single photon Fock state in a topological edge mode.

[1] A. Pocklington and A.A. Clerk, arXiv:2307.16743