# Optomechanical Toy Model for Gravitationally Induced Decoherence: Exact Solution

## TL;DR

This paper provides an exact solution to a toy optomechanical model demonstrating how gravitational effects can induce decoherence, highlighting the role of vacuum fluctuations and bath frequency ratios.

## Contribution

It introduces an exactly solvable model for gravitationally induced decoherence with analytical results, connecting optomechanical systems to quantum gravitational effects.

## Key findings

- Decoherence occurs due to vacuum fluctuations at zero temperature.
- Decoherence persists with finite baths unless bath frequencies are rationally related.
- The model offers insights into gravitational decoherence mechanisms.

## Abstract

I present the exact solution of a toy model for gravitationally induced decoherence. The toy model has Hamiltonian resembling optomechanical systems. It is an oscillator system coupled through its energy to an oscillator heat bath. I find the decoherence effect of vacuum fluctuations at zero temperature. Also for a finite bath I show that the decoherence is in general present and the system does not return to its initial coherence unless the fundamental frequencies of the bath have rational ratios.