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Physical Review A

Polarization properties of macroscopic Bell states

T. Sh. Iskhakov, I. N. Agafonov, Maria V. Chekhova, Georgy O. Rytikov, Gerd Leuchs

Published Oct 6, 2011• 19 citations
Publisher

Abstract

The four two-photon polarization Bell states are one of the main instruments in the toolbox of quantum optics and quantum information. In our experiment we produce their multiphoton counterparts, macroscopic Bell states. These are relevant to applications in quantum technologies because they provide efficient interactions with material quantum objects and with each other via nonlinear interactions. Furthermore, we study the polarization properties of these states using the concept of second-order degree of polarization and its higher-order generalization.

DOI
10.1103/physreva.84.045804

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The four two-photon polarization Bell states are one of the main instruments in the toolbox of quantum optics and quantum information. In our experiment we produce their multiphoton counterparts, macroscopic Bell states. These are relevant to applications in quantum technologies because they provide efficient interactions with material quantum objects and with each other via nonlinear interactions. Furthermore, we study the polarization properties of these states using the concept of second-order degree of polarization and its higher-order generalization.
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In this work we focus our attention on the correlation properties of a new class of bright nonclassical states of light, which are called the macroscopic Bell states [1,2]. These states are of interest in quantum optics due to their rarely combined two properties: brightness and quantumness. Recently we have investigated the polarization properties of these states, namely we have shown that the macroscopic singlet state is absolutely unpolarized and free of polarization noise [2], while the triplet states reveal the effect of hidden polarization [3]. Now we experimentally prove that both singlet and triplet macroscopic Bell states are entangled.
Two photon states entangled in polarization and momentum, hyper-entangled, have been generated by using linear optics and a single Type I nonlinear crystal. These states have been completely characterized and their nonlocal behaviour have been verified by independent Bell's inequalities tests performed in the two degrees of freedom of entanglement and by an "all versus nothing" test of local realism. The manipulation of these states may represent a useful control in quantum state engineering and Bell state measurements and, more in general, in Quantum Information applications.
Advanced photonic quantum technologies—from quantum key distribution to quantum computing—require on-chip sources of entangled photons that are both efficient and readily scalable. This theoretical study demonstrates the generation of polarization-entangled Bell states in structurally simple waveguides by exploiting the intrinsic properties of nonlinear crystals. Elaborate phase-matching strategies that commonly involve the spatial modulation of a waveguide’s linear or nonlinear optical properties are thereby circumvented. This study begins with the derivation of general criteria for the second-order susceptibility tensor that enable the generation of cross-polarized photon pairs via spontaneous parametric down-conversion in single-material waveguides. Based on these criteria, all birefringent, non-centrosymmetric crystal classes are then categorized regarding their suitability. Finally, using coupled mode theory, a numerical analysis is performed of cuboid waveguides made from two materials that are highly relevant to integrated photonics: lithium niobate, a well-established platform, and barium titanate, an emerging alternative. Barium titanate is found to consistently outperform lithium niobate by providing a higher nonlinear efficiency and high concurrence over a significantly broader spectral range. These findings outline a practical route towards highly efficient, fabrication-friendly, and scalable sources of polarization-entangled photons for integrated quantum photonic circuits.