Chiral Light--Matter Interaction Beyond the Rotating-Wave Approximation

I introduce and analyse chiral light--matter interaction in the ultrastrong coupling limit where the rotating-wave approximation cannot be made. Within this limit, a two-level system (TLS) with a circularly polarized transition dipole interacts with a copolarized mode through rotating-wave terms. However, the counter-rotating terms allow the TLS to couple to a counter-polarized mode with the same coupling strength, i.e., one that is completely decoupled within the rotating-wave approximation. Although such a Hamiltonian is not particle number conserving, the conservation of angular momentum generates a $U(1)$ symmetry which allows constructing an ansatz. The eigenstates and dynamics of this novel model are computed for single-cavity interactions and for a many-mode system. The form of the ansatz provides significant analytic insight into the physics of the ground state and the dynamics, e.g., it indicates that the ground states are two-mode squeezed. This work has significant implications for engineering light--matter interaction and novel quantum many-body dynamics beyond the rotating-wave approximation.