# Time evolution of coupled multimode and multiresonator optomechanical systems

## TL;DR

This paper derives analytical solutions for the time evolution of complex multimode optomechanical systems, enabling detailed analysis of quantum coherence, mixedness, and the effects of nonlinear interactions versus linear approximations.

## Contribution

It provides the first analytical expressions for the full time evolution of coupled multimode optomechanical systems with arbitrary interactions, including nonlinear effects.

## Key findings

- Analytical expressions for system evolution and expectation values.
- Identification of regimes with significant nonlinear effects.
- Comparison showing differences between nonlinear and linearized models.

## Abstract

We study the time evolution of bosonic systems where multiple driven bosonic modes of light interact with multiple mechanical resonators through arbitrary, time-dependent, optomechanical-like interactions. We find the analytical expression for the full time evolution of the system and compute the expectation value of relevant quantities of interest. Among the most interesting ones, we are able to compute the first-order quantum bipartite coherence between pairs of subsystems, and the analytical expression for the mixedness induced by the nonlinear interaction in the reduced state of the mechanical oscillators. Finally, we also compare our results with a linearised version of the system, and we find a regime where there are qualitative and quantitative differences in the behavior of some measurable quantities. Our results can therefore be used to describe the full time-evolution of the system, to characterise its nonlinear character and explore the validity of the linearisation approach.