Dissipative Pairing Interactions: Quantum Instabilities, Topological Light, and Volume-Law Entanglement

It is well known that coherent bosonic pairing interactions (as described by a fully Hermitian Hamiltonian) can lead to dynamical instabilities, with the paradigmatic example being a degenerate parametric amplifier. Here, we instead study the physics of dissipative pairing interactions in a fully quantum setting. We show that in isolation, these dissipative (or non-Hermitian) interactions are dynamically stable. However, by combining a stable dissipative pairing interaction with a stable multi-mode hopping Hamiltonian, one can create a novel and potentially useful class of bosonic instabilities [1]. These pairing-induced instabilities exhibit extraordinary properties: the steady state solution remains completely pure up to the instability threshold, and there is a pronounced sensitivity to wavefunction localization. This provides a simple yet powerful method for selectively populating and entangling edge modes of topological photonic lattices, using only a single, localized, engineered reservoir; this is considerably simpler than standard methods which require complicated, non-local driving. We outline how our technique can be physically realized in a number of experimental platforms, including superconducting circuits.

[1] A. Pocklington, Y.-X. Wang, and A. A. Clerk, arXiv:2210.09252