# Quantum noise in a transversely pumped cavity Bose--Hubbard model

## TL;DR

This paper studies how quantum measurement noise affects the dynamics of a Bose-Hubbard model in an optical cavity, revealing phase-dependent noise effects on superfluid, supersolid, Mott, and charge-density-wave states.

## Contribution

It introduces a hybrid model combining Bose-Hubbard and Heisenberg-Langevin equations to analyze quantum noise effects in cavity-coupled atomic lattices.

## Key findings

- Quantum noise causes excess depletion in superfluid and supersolid phases.
- Incompressible phases exhibit chemical potential fluctuations due to quantum noise.
- Analytical expressions for ground state departure time and quasiparticle broadening are derived.

## Abstract

We investigate the quantum measurement noise effects on the dynamics of an atomic Bose lattice gas inside an optical resonator. We describe the dynamics by means of a hybrid model consisting of a Bose--Hubbard Hamiltonian for the atoms and a Heisenberg--Langevin equation for the lossy cavity field mode. We assume that the atoms are prepared initially in the ground state of the lattice Hamiltonian and then start to interact with the cavity mode. We show that the cavity field fluctuations originating from the dissipative outcoupling of photons from the resonator lead to vastly different effects in the different possible ground state phases, i.e., the superfluid, the supersolid, the Mott- and the charge-density-wave phases. In the former two phases with the presence of a superfluid wavefunction, the quantum measurement noise appears as a driving term leading to excess noise depletion of the ground state. The time scale for the system to leave the ground scale is determined analytically. For the latter two incompressible phases, the quantum noise results in the fluctuation of the chemical potential. We derive an analytical expression for the corresponding broadening of the quasiparticle resonances.