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arXiv:0911.2440 · Physical Review A

Bell-like inequality for the spin-orbit separability of a laser beam

C. V. S. Borges, Malena O. Hor-Meyll, J. A. O. Huguenin, Antonio Zelaquett Khoury

Published Sep 28, 2010• 212 citations
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Abstract

In analogy with Bell's inequality for two-qubit quantum states, we propose an inequality criterion for the nonseparability of the spin-orbit degrees of freedom of a laser beam. A definition of separable and nonseparable spin-orbit modes is used in consonance with the one presented in Phys. Rev. Lett. 99, 160401 (2007). As the usual Bell's inequality can be violated for entangled two-qubit quantum states, we show both theoretically and experimentally that the proposed spin-orbit inequality criterion can be violated for nonseparable modes. The inequality is discussed in both the classical and quantum domains.

DOI
10.1103/physreva.82.033833

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In analogy with Bell's inequality for two-qubit quantum states, we propose an inequality criterion for the nonseparability of the spin-orbit degrees of freedom of a laser beam. A definition of separable and nonseparable spin-orbit modes is used in consonance with the one presented in Phys. Rev. Lett. 99, 160401 (2007). As the usual Bell's inequality can be violated for entangled two-qubit quantum states, we show both theoretically and experimentally that the proposed spin-orbit inequality criterion can be violated for nonseparable modes. The inequality is discussed in both the classical and quantum domains.
In analogy with Bell’s inequality for two-qubit quantum states we propose an inequality criterion for the non-separability of the spin-orbit degrees of freedom of a laser beam. A definition of separable and non-separable spin-orbit modes is used in consonance with the one presented in Phys. Rev. Lett. 99, 160401 (2007). As the usual Bell’s inequality can be violated for entangled two-qubit quantum states, we show both theoretically and experimentally that the proposed spin-orbit inequality criterion can be violated for non-separable modes. The inequality is discussed both in the classical and quantum domains.
Abstract Structured light plays an essential role in several quantum information protocols by using the degrees of freedom of light to encode qubits. For exploring different correlations, especially in mixed states, such as discord, it is necessary to prepare partially entangled states. In this work, we present a theoretical and experimental study of a partial nonseparable spin-orbit modes. By exploring classical-quantum analogy, we perform the measurement of the concurrence of partially separable modes directly from projective measurement of polarization. The results show a clear agreement with predictions of quantum theory for partially entangled states. We also perform a study of Clauser, Horn, Shimony, and Holt (CHSH) inequality and show that partial violation is observed in entire agreement with the expected by quantum theory. For the maximally nonseparable mode, we achieve a violation of S = 2.73 ± 0.03 , one of the higher ones observed for spin-orbit modes based on our best knowledge.
We experimentally observed the violation of Kujula--Dzhafarov noncontextuality inequalities by nonseparable spin-orbit laser modes. Qubits are encoded on polarization and transverse modes of an intense laser beam. A spin-orbit nonseparable mode was produced by means of a radial polarization converter (SSS plate). Our results show that the quantum contextuality can be emulated by nonseparable spin-orbit modes in an intense laser beam. Additionally, an improvement in the nonseparable mode preparation allowed us to observe a greater violation of the Clauser--Horne--Shimony--Holt inequality for such system. The results are in very good agreement with the theoretical predictions of quantum mechanics.
Abstract We show that the general quantum state of synthetically spin–orbit coupled ultra cold bosonic atoms, whose condensate was experimentally created recently by Lin et al (2011 Nature 471 , 83), shows entanglement between motional degrees of freedom (momentum) and internal degrees of freedom (hyperfine spin). We demonstrate the violation of Bell-like inequality (CHSH) for such states that provide a unique opportunity to verify fundamental principles like quantum contextuality for commutating observables which are not spatially separated. We analyze in detail the Rabi oscillation executed by such an atom-laser system and how this influences quantities like entanglement entropy, the violation of Bell-like inequality, etc. We also discuss the implications of our result in testing quantum contextuality and Bell’s Inequality violation by macroscopic quantum object like Bose–Einstein condensate of ultra cold atoms.
We report the experimental violation of Leggett-type inequalities for a hybrid entangled state of spin and orbital angular momentum of a single photon. These inequalities give a physical criterion to verify the possible validity of a class of hidden-variable theories, originally named ``crypto nonlocal,'' that are not excluded by the violation of Bell-type inequalities. In our case, the tested theories assume the existence of hidden variables associated with independent degrees of freedom of the same particle, while admitting the possibility of an influence between the two measurements, i.e., the so-called contextuality of observables. We observe a violation of the Leggett inequalities for a range of experimental inputs, with a maximum violation of seven standard deviations, thus ruling out this class of hidden-variable models with a high level of confidence.
In this paper we investigate the quantum noise properties of polarization vortices in connection with an intensity-based Clauser-Horne-Shimony-Holt (CHSH) inequality for their spin-orbit separability. We evaluate the inequality for different input quantum states and the corresponding intensity fluctuations. The roles played by coherence and photon number squeezing provide a suitable framework for characterizing pure state spin-orbit entanglement. Structural inseparability of the spin-orbit mode requires coherence, an issue concerning either classical or quantum descriptions. In both cases, it can be witnessed by violation of this intensity-based CHSH inequality. However, in the quantum domain, entanglement requires both coherence and reduced photon number fluctuations.