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arXiv:1803.00331 · Physical Review A

Clauser-Horne-Shimony-Holt Bell inequality test in an optomechanical device

Juuso Manninen, Muhammad Asjad, Risto Ojajärvi, Petri Kuusela, Francesco Massel

Published Oct 15, 2018• 17 citations
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Abstract

We propose here a scheme based on the measurement of quadrature phase coherence that is aimed at testing the Clauser-Horne-Shimony-Holt Bell inequality in an optomechanical setting. Our setup is constituted by two optical cavities dispersively coupled to a common mechanical resonator. We show that it is possible to generate Einstein-Podolsky-Rosen--like correlations between the quadratures of the output fields of the two cavities and, depending on the system parameters, to observe the violation of the Clauser-Horne-Shimony-Holt inequality.

DOI
10.1103/physreva.98.043831

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We propose here a scheme based on the measurement of quadrature phase coherence that is aimed at testing the Clauser-Horne-Shimony-Holt Bell inequality in an optomechanical setting. Our setup is constituted by two optical cavities dispersively coupled to a common mechanical resonator. We show that it is possible to generate Einstein-Podolsky-Rosen--like correlations between the quadratures of the output fields of the two cavities and, depending on the system parameters, to observe the violation of the Clauser-Horne-Shimony-Holt inequality.
An inequality is deduced from Einstein's locality and a supplementary assumption. This inequality defines an experiment that can actually be performed with present technology to test local realism. Quantum mechanics violates this inequality a factor of 1.5. In contrast, quantum mechanics violates previous inequalities [for example, those of J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, Phys. Rev. Lett. 23, 880 (1969); S. J. Freedman and I. F. Clauser ibid. 28, 938 (1972); and J. F. Clauser and M. A. Horne, Phys. Rev. D 10, 526 (1974)] by a factor of 2.\sqrt{2}.2​. Thus the magnitude of violation of the inequality derived in this paper is approximately 20.7% larger than the magnitude of violation of previous inequalities. This result can be particularly important for the experimental test of locality.
We present here a classical optics device based on an imaging architecture as an analogy of a quantum system where the violation of the Bell inequality can be evidenced. Quantum states are encoded using an electromagnetic wave modulated in amplitude and phase. Unitary operations involved in the measurement of the observables are simulated with the use of a coherent optical processor. The images obtained in the output of the process contain all the information about the possible outcomes of the joint measurement. By measuring the intensity distribution in the image plane we evaluate the mean values of the simulated observables. The obtained experimental results show how some correlations of Clauser-Horne-Shimony-Holt-type exceed the upper bound imposed by the local realism hypothesis as a consequence of the joint effect of entanglement and two-particle interference.
A correlation inequality is derived from local realism and a supplementary assumption. Unlike Clauser-Horne (CH) inequality [or Clauser-Horne-Shimony-Holt (CHSH) inequality] which is violated by quantum mechanics by a factor of 2\sqrt 22​, this inequality is violated by a factor of 1.5. Thus the magnitude of violation of this inequality is approximately 20.7% larger than the magnitude of violation of previous inequalities. Moreover, unlike CH (or CHSH) inequality which requires the measurement of five detection probabilities, the present inequality requires the measurement of only two detection probabilities. This inequality can therefore be used to test locality more simply than CH or CHSH inequality.
We propose and theoretically simulate an experiment for demonstrating a motional-state Bell inequality violation for pairs of momentum-entangled atoms produced in Bose-Einstein condensate collisions. The proposal is based on realizing an atom-optics analog of the Rarity-Tapster optical scheme: it uses laser-induced Bragg pulses to implement two-particle interferometry on the underlying Bell state for two pairs of atomic scattering modes with equal but opposite momenta. The collision dynamics and the sequence of Bragg pulses are simulated using the stochastic Bogoliubov approach in the positive-PPP representation. We predict values of the Clauser-Horne-Shimony-Holt (CHSH) parameter up to $S\ensuremath{\simeq}2.5$ for experimentally realistic parameter regimes, showing a strong violation of the CSHS-Bell inequality bounded classically by $S\ensuremath{\le}2$.
We investigate quantum nonlocality of a single-photon entangled state under feasible measurement techniques consisting of on-off and homodyne detections along with unitary operations of displacement and squeezing. We test for a potential violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality, in which each of the bipartite party has a freedom to choose between two measurement settings, with each measurement yielding a binary outcome. We find that single-photon quantum nonlocality can be detected when two or less of the four total measurements are carried out by homodyne detection. The largest violation of the CHSH inequality is obtained when all four measurements are squeezed-and-displaced on-off detections. We test the robustness of violations against imperfections in on-off detectors and single-photon sources, finding that the squeezed-and-displaced measurement schemes perform better than the displacement-only measurement schemes.