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

We present a theoretical investigation of the properties of quantum correlation functions in a multimode system. We define a total m th order equal-time correlation function, summed over all modes, which is shown to be conserved if the Hamiltonian possesses U(1) symmetry. It is also conserved in the presence of dissipation, provided the loss rate is the same for all modes of the system. As examples, we demonstrate this conservation using numerical simulations of a coupled cavity system and the Jaynes-Cummings model.