Conservation of Quantum Correlations in Multimode Systems with $U(1)$ Symmetry

Abstract

We present a theoretical investigation of the properties of quantum correlation functions in a dissipative multimode system. We define a total mth order equal-time correlation function, summed over all modes, which is shown to be conserved if the Hamiltonian possesses U(1) symmetry, provided any dissipation processes are linear in the system operators. As examples, we demonstrate this conservation using numerical simulations of a coupled cavity system and the Jaynes-Cummings model.

5 pages, 2 figures

References in corpus (7)

• Exciton Polaritons in a Two-Dimensional Lieb Lattice with Spin-Orbit Coupling
• Spatial Coherence of a Polariton Condensate
• Strong coupling theory for the Jaynes-Cummings-Hubbard model
• Dissipatively Coupled Waveguide Networks for Coherent Diffusive Photonics
• Klein tunneling in driven-dissipative photonic graphene
• Stochastic Differential Equations for Quantum Dynamics of Spin-Boson Networks
• Normal and anti-normal ordered expressions for annihilation and creation operators

Cited by in corpus (1)

• Quantum optics of nonlinear systems in cascade