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Witness of Macroscopic Entanglement in Classical Statistical Optical Fields

Xiao-Feng Qian, Bethany Little, John C. Howell, Joseph H. Eberly

Published Jan 1, 2015• 0 citations
Publisher

Abstract

We examine correlations between polarization and amplitude degrees of freedom for classical statistical optical fields with Bell-analysis experiments. Strong violations of the Clauser-Horne-Shimony-Holt inequality are observed. These constitute a new witness of classical macroscopic entanglement.
DOI
10.1364/cleo_qels.2015.ftu1a.2

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Abstract We report experiments in which the Bell parameter S that enters the Clauser–Horne–Shimony–Holt inequality: ∣ S ∣ ≤ 2 , attains values ∣ S ∣ > 2 . In our experiments, we used two spatially separated optical beams, the electric fields of which were correlated to one another. The amount of correlation was quantified by the spectral degree of coherence η ( α , β ) . This quantity measures the correlation between fields that exist at two distant locations and whose respective polarizations are given in terms of angles α and β , which can be set independently from one another. Such a correlation qualifies for the construction of the Bell parameter S . By changing the amount of field correlation, we could cover a range that goes from ∣ S ∣ < 2 to ∣ S ∣ > 2 . Our experimental findings should provide useful material for the ongoing, theoretical discussions about the quantum–classical border.
An entangled state of a two-particle system is a quantum state that cannot be separated-it cannot be written as the product of states of the individual particles.One way to tell if a system is entangled is to use it to violate a Bell inequality (such as the Clauser-Horne-Shimony-Holt, CHSH, inequality), because entanglement is necessary to violate these inequalities.However, there are other, more efficient measurements that determine whether or not a system is entangled; an operator that corresponds to such a measurement is referred to as an entanglement witness.We present the theory of witness operators, and an undergraduate experiment that measures an entanglement witness for the joint polarization state of two photons.We are able to produce states for which the expectation value of the witness operator is entangled by more than 160 standard deviations.
We demonstrate hybrid entanglement of photon pairs via the experimental violation of a Bell inequality with two different degrees of freedom (DOF), namely, the path (linear momentum) of one photon and the polarization of the other photon. Hybrid entangled photon pairs are created by spontaneous parametric down conversion and coherent polarization to path conversion for one photon. For that photon, path superposition is analyzed, and polarization superposition for its twin photon. The correlations between these two measurements give an SSS parameter of $S=2.653\ifmmode\pm\else\textpm\fi{}0.027$ in a Clauser-Horne-Shimony-Holt inequality and thus violate local realism for two different DOF by more than 24 standard deviations. This experimentally supports the idea that entanglement is a fundamental concept which is indifferent to the specific physical realization of Hilbert space.
An entangled state of a two-particle system is a quantum state that cannot be separated, meaning it cannot be written as the product of states of the individual particles. One way to tell if a system is entangled is to use it to violate a Bell inequality (such as the Clauser-Horne-Shimony-Holt, CHSH, inequality), because entanglement is necessary for such a violation. However, there are other, easier-to-perform measurements that determine whether or not a system is entangled. An operator that corresponds to such a measurement is referred to as an entanglement witness. Here, we present the theory of witness operators and an undergraduate experiment that measures entanglement witnesses for the joint polarization state of two photons. We are able to produce states for which the expectation value of a witness operator is entangled by more than 300 standard deviations. In order to further examine the performance of these witness operators, we present a simple way to generate states that closely approximate Werner states, which have a controllable degree of entanglement.