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arXiv:1108.1027 · Physical Review A

Loophole-free Bell test with one atom and less than one photon on average

Nicolas Sangouard, Jean-Daniel Bancal, Nicolas Gisin, Wenjamin Rosenfeld, Pavel Sekatski, M. Weber, Harald Weinfurter

Published Nov 28, 2011• 26 citations
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Abstract

We consider the entanglement between two internal states of a single atom and two photon number states describing either the vacuum or a single photon and thus containing, on average, less than one photon. We show that this intriguing entanglement can be characterized through substantial violations of a Bell inequality by performing homodyne detections on the optical mode. We present the experimental challenges that need to be overcome to pave the way toward a loophole-free Bell test.

DOI
10.1103/physreva.84.052122

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We propose a feasible optical setup allowing for a loophole‐free Bell test with efficient homodyne detection. A non‐Gaussian entangled state is generated from a two‐mode squeezed vacuum by subtracting a single photon from each mode, using beam splitters and standard low‐efficiency single‐photon detectors. A Bell violation exceeding 1% is achievable with 6 dB of squeezing, a photodetector efficiency around 10%, and an homodyne efficiency around 95%. A feasibility analysis, based upon the recent generation of single‐mode non‐Gaussian states via photon subtraction, suggests that this method opens a promising avenue towards a complete experimental Bell test.
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We provide a detailed analysis of the recently proposed setup for a loophole-free test of Bell inequality violation using conditionally generated non-Gaussian states of light and balanced homodyning. In the proposed scheme, a two-mode squeezed vacuum state is de-Gaussified by subtracting a single photon from each mode with the use of an unbalanced beam splitter and a standard low-efficiency single-photon detector. We thoroughly discuss the tolerance of the achievable Bell violation in the various experimentally relevant parameters such as the detector efficiencies, the electronic noise, the mixedness of the initial Gaussian state, and the probability of false triggers. We also consider several alternative schemes involving squeezed states, linear optical elements, conditional photon subtraction, and homodyne detection.