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arXiv:1703.03675 · Journal of the Optical Society of America B

Entanglement detection via atomic deflection

C. E. Máximo, Romain Bachelard, G. D. de Moraes Neto, M. H. Y. Moussa

Published Nov 6, 2017• 4 citations

Abstract

We report on criteria to detect entanglement between the light modes of two crossed optical cavities by analyzing the transverse deflection patterns of an atomic beam. The photon exchange between the modes and atoms occurs around the overlapping nodes of associated standing waves, which generates the two-dimensional (2D) version of the Optical Stern–Gerlach (OSG) effect. In this optical cross-cavity setup, we show that the discrete signatures of the field states, left in the momentum distribution of the deflected atoms, may reveal entanglement for a certain class of two-mode states. For a single photon, we present the possibility of quantifying entanglement by the rotation of the momentum distribution. For a larger number of photons, we demonstrate that quantum interference precludes the population of specific momentum states revealing maximum entanglement between the light modes.

DOI: 10.1364/josab.34.002452

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We report on criteria to detect entanglement between the light modes of two crossed optical cavities by analyzing the transverse deflection patterns of an atomic beam. The photon exchange between the modes and atoms occurs around the overlapping nodes of associated standing waves, which generates the two-dimensional (2D) version of the Optical Stern–Gerlach (OSG) effect. In this optical cross-cavity setup, we show that the discrete signatures of the field states, left in the momentum distribution of the deflected atoms, may reveal entanglement for a certain class of two-mode states. For a single photon, we present the possibility of quantifying entanglement by the rotation of the momentum distribution. For a larger number of photons, we demonstrate that quantum interference precludes the population of specific momentum states revealing maximum entanglement between the light modes.

We investigate deflections, spatial entanglement, and localization of an atomic beam due to its interaction with two modes of a standing electromagnetic field in an optical cavity. It is demonstrated that the deflection properties of an atom passing through two crossed standing light waves are crucially modified when photon-number correlated states of light are used instead of independent waves. Depending on the atom-light interaction scheme, various periodic two-dimensional patterns in a subwavelength regime are reported.

The paper presents a scheme to detect entanglement arising from the quantum nature of gravity between a spin qubit and photons, using Stokes parameters. One of the crucial tests of the general theory of relativity is the bending of light due to the curvature. Recently, a quantum counterpart of this experiment to test the quantum nature of the gravitational interaction has been proposed, in which the spin-2, massless graviton yields entanglement between matter and a photon sector. Hence, it provides one of the most crucial experimental signatures for testing the quantum nature of gravity in a lab, since only spin-2-induced entanglement can yield the correct deflection of light due to matter. Here, we propose a positive partial-transpose (PPT) witness criterion for witnessing such an entanglement. We scan the entangled states in this context by studying the overlap of the final state, which is proportional to the entanglement phase. We exploit the Stokes observables to measure the photon state and the spins in the matter sector, thereby constructing a witness for the quantum nature of gravity in this setup. To quantify this entanglement, we will couple the photon to a local oscillator, whose phase need to be controlled to probe the orthogonal components of the macroscopic interference in the laser beam. We have shown that for a non-maximally entangled state mediated by the quantum nature of gravity, the witness attains a maximal negativity of

-0.052

. Our findings indicate that this witness effectively detects entanglement within the range

0.71 \leq |γ| < 1

, where

γ

is the overlap between the two coherent states of the photon, providing a clear signature of quantum correlations.

It is shown that the deflection of an atom de Broglie wave at two adjacent cavities containing non-resonant weak fields can yield a highly entangled quantum state of the atom–field system in which discernible atomic beams are entangled to internal states of the atom and to two-mode photon-number states of the fields. Two-mode anticorrelated entangled photon-number states characterized by the total photon number can be prepared by the detection of the atom in given directions of the propagation.