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arXiv:2307.11123 · Optics Letters

Violating Bell inequality using weak coherent states

M. Mahdavifar, S. M. Hashemi Rafsanjani

Published Nov 1, 2021• 7 citations
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Abstract

We present an experimental investigation of two-photon interference using a continuous-wave laser. We demonstrate the violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality using the phase-randomized weak coherent states from a continuous-wave laser. Our implementation serves as an approach to reveal the quantum nature of a state that is considered to be a classical state.

DOI
10.1364/ol.441499

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We present an experimental investigation of two-photon interference using a continuous-wave laser. We demonstrate the violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality using the phase-randomized weak coherent states from a continuous-wave laser. Our implementation serves as an approach to reveal the quantum nature of a state that is considered to be a classical state.
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A violation of Bell's inequalities using quantum entanglement indicates the nonlocality of two particles such as photons and electrons. We observe a violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality, a particular Bell's inequality, in polarization-entangled photon pairs in the 1550 nm band. For photon pair generation based on spontaneous parametric down conversion, a fiber-optic two-photon interferometer with two periodically poled lithium niobate waveguides is adopted. The obtained S value of the CHSH inequality is 2.44 ±0.02 without subtraction of accidental coincidences, yielding a violation by ∼22 standard deviations in an hour. Two-photon interference with a visibility of 0.885 is also observed. If those coincidences are subtracted, the visibility becomes almost unity.
Witnessing continuous-variable Bell nonlocality is a challenging endeavor, but Bell himself showed how one might demonstrate this nonlocality. Although Bell nearly showed a violation using the Clauser-Horne-Shimony-Holt (CHSH) inequality with sign-binned position-momentum statistics of entangled pairs of particles measured at different times, his demonstration is subject to approximations not realizable in a laboratory setting. Moreover, he does not give a quantitative estimation of the maximum achievable violation for the wave function he considers. In this article, we show how his strategy can be reimagined using the transverse positions and momenta of entangled photon pairs measured at different propagation distances, and we find that the maximum achievable violation for the state he considers is actually very small relative to the upper limit of 222\sqrt{2}22​. Although Bell's wave function does not produce a large violation of the CHSH inequality, other states may yet do so.
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.