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Journal of Optics

Partial nonseparability of spin-orbit modes

V. S. Lamego, D. G. Braga, L S Oliveira, W. F. Balthazar, J. A. O. Huguenin

Published Jan 16, 2023• 3 citations
Publisher

Abstract

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.

DOI
10.1088/2040-8986/acb36c

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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.
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 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.
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.
We introduce a proposal to prepare spin-obit maximally discordant mixed states by a linear optical circuit, with quantum bits (qubits) encoded in the polarization and transverse mode degrees of freedom of photons. In particular, we discuss how to prepare nonbalanced spin-orbit entangled states, applying this technique to obtain maximally discordant mixed states. We present a simulation of the optical circuit by using the Jones matrix formalism. We performed a study of entanglement, classical, and quantum correlations. The results show excellent agreement with the underlying theory and open an alternative experimental approach for addressing quantum correlations in optical setups.
Single photons emerging from Pancharatnam-Berry phase optical elements (q plates) exhibit entanglement in the degrees of freedom of spin and orbital angular momentum. We put forward an experimental scheme for probing the spin-orbit correlations of single photons. It is found that the Clauser-Horne-Shimony-Holt parameter S for the single-photon spin-orbit entangled state could be as high as 2√2, evidently violating the Bell-like inequality and thus invalidating the noncontextual hidden variable theories.
We demonstrate electromagnetic quantum states of single photons and of correlated photon pairs exhibiting ``hybrid'' entanglement between spin and orbital angular momentum. These states are obtained from entangled photon pairs emitted by spontaneous parametric down conversion by employing a qqq plate for coupling the spin and orbital degrees of freedom of a photon. Entanglement and contextual quantum behavior (that is also nonlocal, in the case of photon pairs) is demonstrated by the reported violation of the Clauser-Horne-Shimony-Holt inequality. In addition, a classical analog of the hybrid spin-orbit photonic entanglement is reported and discussed.