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Physica Scripta

Four-mode entangled states in coupled nonlinear optical processes and teleportation of two-mode entangled CV state

A. S. Chirkin, M. Yu. Saygin

Published Jul 1, 2009• 15 citations
Publisher

Abstract

We consider the forming of a four-mode entangled state for continuous variables (CV) in coupled optical parametric processes. The processes comprise one down-conversion process and two up-conversion ones. Such interactions can simultaneously be realized in a single aperiodical nonlinear photonic crystal. To reveal the entanglement between continuous variables at generated frequencies, the different criteria of the separability have been applied. We also consider teleportation of two-mode entangled CV state using the created four-mode state. It is shown that in the proposed scheme the fidelity of entangled CV teleportation can be almost perfect.

DOI
10.1088/0031-8949/2009/t135/014029

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We introduce and theoretically investigate a scheme for teleportation of two-frequency entangled optical images in which the quantum channel is formed by four-frequency multimode states, generated in a single nonlinear photonic crystal by coupled parametric interactions. We study in detail the performance of the scheme. Namely, we evaluate its fidelity and the spatial-frequency spectra of the quadrature components characterizing the deterioration of the entanglement in the initial images due to the teleportation process. We analyze the influence of the spatial bandwidth of entanglement on the fidelity of teleportation. We investigate the performance of the scheme both in the near and the far diffraction field. Our analysis suggests that bandwidth matching of the quantum channel field with that of the images is generally necessary for high-quality teleportation. We show that entangled images are more fragile and more difficult to teleport than their coherent counterparts.
Continuous-variable multipartite entanglement is a key resource for quantum technologies. This paper considers the multipartite entanglement generated in separated spatial modes of the same light beam by three different parametric sources: a standard ${\ensuremath{\chi}}^{(2)}$ medium pumped by two pumps, a single-pump nonlinear photonic crystal, and a doubly pumped nonlinear photonic crystal. These sources have in common the coexistence of several concurrent nonlinear processes in the same medium, which allows the generation of nonstandard three- and four-mode couplings. We test the genuine nature of the multipartite entangled states thereby generated in a common framework, using criteria based both on proper bounds for the variances of nonlocal observables and on the positive partial transpose criterion. The relative simplicity of these states allows a (hopefully) useful comparison of the different inseparability tests.
We study parametric interactions in a new type of nonlinear photonic structure, which is realized in the volume between a pair of nonlinear crystals. In this kind of structure, which we call binary, multiple nonlinear optical processes can be implemented simultaneously, owing to multiple phase-matching conditions, fulfilled separately in the constituent crystals. The coupling between the nonlinear processes by means of modes sharing similar frequency is attained by the spatially broadband nature of the parametric fields. We investigate the spatial properties of the fields generated in the binary structure constructed from periodically poled crystals for the two examples: (1) single parametric downconversion and (2) coupled parametric downconversion and upconversion processes. The efficacy of the fields’ generation in these examples is analyzed through comparison with the cases of a traditional single periodically poled crystal and an aperiodic photonic structure, respectively. For this, we have devised a method that allowed us to solve the field equations numerically without resorting to statistically modeling the input vacuum states. It has been shown that the relative shift between the periodic crystal lattices has a crucial effect on the generated spatial field spectrum and overall efficiency. In addition, the influence of the intercrystal distance on these characteristics has been studied. Therefore, our study suggests that one can construct optical elements with sophisticated nonlinear properties from simpler elements without significant sacrifice of efficacy.
We theoretically show that six-partite continuous-variable entanglement can be generated by nonlinear optical processes conducted in a designed photonic crystal-like periodically poled lithium niobat (PPLN). The processes consist of a nonlinear parametric down-conversion and four sum-frequency processes. The characteristics of the six-partite entanglement among the six beams are analyzed both above and below the threshold by applying a sufficient inseparability criterion for multipartite continuous-variable entanglement. We investigated our proposal for a specific case of a PPLN optical superlattice with fixed light and material properties.