Localization transition in presence of cavity backaction

TL;DR

This paper investigates how cavity backaction can induce a localization transition in an atom trapped in an optical lattice, revealing a controllable transition influenced by cavity nonlinearity and resonances.

Contribution

It introduces a model linking cavity backaction to localization phenomena, deriving a phase diagram, and analyzing the transition's dependence on cavity parameters.

Findings

Cavity backaction can induce localization similar to Aubry-André transition.

The transition is controlled by cavity nonlinearity strength.

Lyapunov exponent shows resonance-like behavior at optomechanical resonances.

Abstract

We study the localization transition of an atom confined by an external optical lattice in a high-finesse cavity. The atom-cavity coupling yields an effective secondary lattice potential, whose wavelength is incommensurate with the periodicity of the optical lattice. The cavity lattice can induce localization of the atomic wave function analogously to the Aubry-Andr\'e localization transition. Starting from the master equation for the cavity and the atom we perform a mapping of the system dynamics to a Hubbard Hamiltonian, which can be reduced to the Harper's Hamiltonian in appropriate limits. We evaluate the phase diagram for the atom ground state and show that the transition between extended and localized wavefunction is controlled by the strength of the cavity nonlinearity, which determines the size of the localized region and the behaviour of the Lyapunov exponent. The Lyapunov exponent, in particular, exhibits resonance-like behaviour in correspondence with the optomechanical resonances. Finally we discuss the experimental feasibility of these predictions.