Cavity Quantum Electrodynamics of Continuously Monitored Bose-Condensed Atoms

Mark Lee,Janne Ruostekoski

doi:10.3390/atoms3030450

Abstract

We study cavity quantum electrodynamics of Bose-condensed atoms that are subjected to continuous monitoring of the light leaking out of the cavity. Due to a given detection record of each stochastic realization, individual runs spontaneously break the symmetry of the spatial profile of the atom cloud and this symmetry can be restored by considering ensemble averages over many realizations. We show that the cavity optomechanical excitations of the condensate can be engineered to target specific collective modes. This is achieved by exploiting the spatial structure and symmetries of the collective modes and light fields. The cavity fields can be utilized both for strong driving of the collective modes and for their measurement. In the weak excitation limit the condensate–cavity system may be employed as a sensitive phonon detector which operates by counting photons outside the cavity that have been selectively scattered by desired phonons.

Highlights

Cavity quantum electrodynamics is a paradigm model of quantum optics [1]
In the weak excitation limit, the selective coupling of the collective modes by the tailored Bose–Einstein condensates (BECs)–cavity system may be employed as a sensitive phonon detector
The coupling of a BEC to the cavity light mode and the continuous measurement of light leaking out of the cavity generate a mechanical response on the atoms

Summary

Introduction

Cavity quantum electrodynamics (cQED) is a paradigm model of quantum optics [1]. In typical realizations a single atom interacts strongly with a single quantized light field. The full quantum treatment of the measurement backaction may be incorporated in stochastic master equations and stochastic quantum trajectories of state vectors (quantum Monte Carlo wave functions) [11,12,13] These approaches can produce a faithful representation of a possible measurement record for an individual experimental run, where the dynamics is conditioned on the stochastic measurement outcomes. For very large systems quantum trajectory simulations are not possible and there is a quest to develop approximate computationally efficient approaches The motive for such developments is, e.g., the observation of the measurement backaction of the cavity output on the dynamics of the atoms in ultracold atom experiments [4,5]. The technique could potentially open the gate for a sensitive single phonon detector of BEC excitations that could measure statistical properties of the phonons, act as an accurate BEC thermometer, and prepare complex quantum states of phonons

Hamiltonian Formalism and Open System Dynamics

Phase-Space and Stochastic Descriptions

Cavity Optomechanical System

Selective Phonon Excitations and Their Measurements

Phonon Detection

Concluding Remarks