Theoretical realization and application of parity-time-symmetric oscillators in a quantum regime

In the existing parity-time (PT) symmetry with the balanced gain and loss, the gain is derived from semiclassical but not full quantum theories, which significantly restricts the applications of PT symmetry in quantum fields. In this work, we propose and analyze a theoretical scheme to realize full quantum oscillator PT symmetry. The quantum gain is provided by a dissipation optical cavity with a blue-detuned laser field. After adiabatically eliminating the cavity modes, we give an effective master equation, which is a complete quantum description compared with the non-Hermitian Hamiltonian, to reveal the quantum behaviors of such a gain oscillator. This kind of PT symmetry can eliminate the dissipation effect in the quantum regime. As an example, we apply PT symmetric oscillators to enhance optomechanically induced transparency.