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International Journal of Quantum Information

EFFICIENT POLARIZATION ENTANGLEMENT GENERATION FROM SPATIALLY CORRELATED PHOTONS

Bin Gu, CHUAN-QI LI, Yulin Chen

Published May 29, 2009• 0 citations
Publisher

Abstract

We present an efficient protocol for polarization entanglement generation from spatially correlated photons in spontaneous parametric down-conversion. Compare with the protocol proposed by Shimuzu et al. (Phys. Rev. A77 032338), only one polarizing beam splitter is used in this protocol, which makes it simpler and more convenient in a practical application. By increasing the number of the slits, we provide a way for generation of a hyperentangled state in both the spatial and polarization degrees of freedom.

DOI
10.1142/s021974990900550x

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We present an efficient protocol for polarization entanglement generation from spatially correlated photons in spontaneous parametric down-conversion. Compare with the protocol proposed by Shimuzu et al. (Phys. Rev. A77 032338), only one polarizing beam splitter is used in this protocol, which makes it simpler and more convenient in a practical application. By increasing the number of the slits, we provide a way for generation of a hyperentangled state in both the spatial and polarization degrees of freedom.
Nowadays, the nonlinear optical process of spontaneous parametric down-conversion is considered as the canonical approach for creating entangled-photon pairs. We consider three pairs of entangled photons emitted by the parametric down-conversion source, and introduce a setup for evolving these photons based on linear optics, which is composed of several polarizing beam splitters, beam splitters, and half wave plates. By using the parametric down-conversion source and the setup, we carefully design an efficient scheme for preparing six-photon hyperentangled states in both the polarization and the spatial degrees of freedom. Because we use almost all possible behaviors of the three pairs of entangled photons, the present scheme is efficient for creating six-photon hyperentangled states. Next, in the regime of weak nonlinearity we design a quantum nondemolition detection to distinguish the two cases of photons in two special spatial modes. It is worth pointing out that our scheme is much easier to realize, since the strength of the nonlinearities in the process of quantum nondemolition detection can be restricted to the scalable orders of magnitude in practicality.
A growing number of experiments make use of multiple pairs of photons generated in the process of spontaneous parametric down-conversion. We show that entanglement in unwanted degrees of freedom can adversely affect the results of these experiments. We also discuss techniques to reduce or eliminate spectral and spatial entanglement, and we present results from two-photon polarization-entangled source with almost no entanglement in these degrees of freedom. Finally, we present two methods for the generation of four-photon polarization-entangled states. In one of these methods, four-photon can be generated without the need for intermediate two-photon entanglement.
Two-photon states generated from spontaneous parametric down-conversion (SPDC) can display entanglement in all degrees of freedom (DoFs) of light, including spatial, temporal, and polarization. The coupling between different DoFs of a two-photon state has been shown to display rich structures that enable novel and robust information processing schemes. While existing literature has studied these couplings by post-selecting the SPDC field, a comprehensive understanding of the inherent spatial-polarization coupling produced in the SPDC process is still lacking. This work produces a full spatial map of the polarization entanglement generated across the entire SPDC field, which contains an entire class of near-maximally polarization-entangled states with an average concurrence of 0.8303 +/- 0.0004. The spatial-polarization coupling manifests as radially or linearly varying polarization-entangled states, whose wavefunctions are dependent on the transverse momenta of the down-converted photons and the pump beam, respectively. Our study lays important groundwork for further exploiting the coupling between entanglement in different DoFs for future quantum technologies
Nowadays,the generation of multiphoton entangled states is almost realized by combining the coupled entangled photons emitted from spontaneous parametric down-conversion (SPDC) with the first-order term.In this case,one may focus mainly on the first-order term,and then avoid multipair emission events by restricting experimental parameters.On the other hand,for the higher-order terms in SPDC source,these emitted entangled photons have interesting features.For example,they are entangled maximally not only in photon number for the spatial modes,but also in polarization degree of freedom.In general,two photons,which are entangled in two or more degrees of freedom,are called hyperentangled pair of photons or hyperentangled state.We present a scheme to generate the four-photon hyperentangled state based on four indistinguishable photons emitted from SPDC source with the second-order term.Consider two SPDC sources with equal probability of emission of photons in respective spatial modes.With the passive linear optical devices,i.e., beam splitters,half wave plates,polarizing beam splitters,etc.,under the condition of registering a specified four-photon coincidence,we can obtain the four-photon hyperentangled state in which the photons are entangled in both polarization and spatial-mode degrees of freedom.Here,of course,for an arbitrary fourfold coincidence detection,one obtains a canonical four-photon Greenberger-Horne-Zeilinger (GHZ) state.Then we show the results of fourfold coincidence detections and the corresponding probabilities for the four-photon GHZ states,where the generation of the four-photon hyperentangled state is included as long as we are not to distinguish the two detectors located at the same locations. As a result,our scheme has two notable features.When we only consider the second-order emission,since it is not needed for us to distinguish between the two SPDC sources,the present scheme is simple and feasible.Also,based on the postselection with fourfold coincidence detection,our scheme is suitable for the normal first-order emission where we restrict the four photons emitted from the same source.In this sense,our scheme is efficient.In a word,we describe a method to generate the four-photon hyperentangled state with the second-order emission in SPDC source,which may contribute to the exploration of multipair entanglement with higher-order emissions from the SPDC source.