Quantum optical measurements in ultracold gases: macroscopic Bose-Einstein condensates

TL;DR

This paper develops an analytical approach to study quantum optical measurements in ultracold Bose-Einstein condensates within optical lattices, highlighting entanglement and measurement effects on many-body atomic states.

Contribution

It simplifies the complex quantum Monte Carlo simulation for macroscopic BECs into an analytical model applicable to various lattice fillings.

Findings

Analytical solution for atomic dynamics in BECs under optical measurement

Analysis of multipartite entanglement purity in atomic states

Applicable to both low and high filling factor lattices

Abstract

We consider an ultracold quantum degenerate gas in an optical lattice inside a cavity. This system represents a simple but key model for "quantum optics with quantum gases," where a quantum description of both light and atomic motion is equally important. Due to the dynamical entanglement of atomic motion and light, the measurement of light affects the many-body atomic state as well. The conditional atomic dynamics can be described using the Quantum Monte Carlo Wave Function Simulation method. In this paper, we emphasize how this usually complicated numerical procedure can be reduced to an analytical solution after some assumptions and approximations valid for macroscopic Bose-Einstein condensates (BEC) with large atom numbers. The theory can be applied for lattices with both low filling factors (e.g. one atom per lattice site in average) and very high filling factors (e.g. a BEC in a double-well potential). The purity of the resulting multipartite entangled atomic state is analyzed.