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

TL;DR

This paper theoretically shows that in dissipative multimode systems with U(1) symmetry, certain total quantum correlation functions are conserved over time, demonstrated through numerical simulations of specific models.

Contribution

It introduces a conserved total correlation function in multimode systems with U(1) symmetry under linear dissipation, supported by numerical examples.

Findings

Total correlation function conservation in U(1) symmetric systems

Numerical validation with coupled cavity and Jaynes-Cummings models

Conservation holds under linear dissipation processes

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.