Bell inequality test with entanglement between an atom and a coherent state in a cavity

TL;DR

This paper investigates Bell inequality tests involving entanglement between a cavity field in a coherent state and a two-level atom, exploring measurement techniques, detection efficiencies, and decoherence effects to demonstrate quantum nonlocality.

Contribution

It introduces methods for Bell tests using photon on/off and parity measurements, achieving high Bell violations and analyzing practical conditions for loophole-free experiments.

Findings

Photon on/off detection requires at least 50% efficiency.

Parity measurements can reach Cirel'son's bound.

Decoherence effects are analyzed for realistic experimental conditions.

Abstract

We study Bell inequality tests with entanglement between a coherent-state field in a cavity and a two-level atom. In order to detect the cavity field for such a test, photon on/off measurements and photon number parity measurements, respectively, are investigated. When photon on/off measurements are used, at least 50% of detec- tion efficiency is required to demonstrate violation of the Bell inequality. Photon number parity measurements for the cavity field can be effectively performed using ancillary atoms and an atomic detector, which leads to large degrees of Bell violations up to Cirel'son's bound. We also analyze decoherence effects in both field and atomic modes and discuss conditions required to perform a Bell inequality test free from the locality loophole.