Quantum optics of lossy metasurfaces: Propagating the photon-moment matrix by the semiclassical Liouvillian

In this paper we map the quantum optical scattering of a linear dissipative metasurface to an equivalent Liouvillian dynamics with respect to the effective Hamiltonian of the metasurface propagating in fictitious time. By using a lossy bianisotropic metasurface as a generic example, our formulation allows a complete specification of the generalized eigenspace of the Liouvillian superoperator starting from either a diagonalizable or defective classical scattering matrix of the metasurface. With a further factorization of the Liouvillian superoperator, we demonstrate the input-output relationship on the photon density matrix can be obtained by propagating the photon-moment matrix using a complete basis of the semiclassical Liouvillian superoperator. Our investigations will be useful for characterizing quantum scattering of generally bianisotropic metasurfaces, paving the way for investigating and designing passive parity-time symmetric and non-Hermitian metasurfaces for quantum information processing applications.

Automated summary

In this paper, we describe the quantum optical scattering of a linear dissipative metasurface using an equivalent Liouvillian dynamics. We demonstrate that the input-output relationship on the photon density matrix can be obtained by propagating the photon-moment matrix using a complete basis of the semiclassical Liouvillian superoperator. Our findings are important for characterizing quantum scattering of generally bianisotropic metasurfaces and for designing passive parity-time symmetric and non-Hermitian metasurfaces for quantum information processing applications.