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arXiv:1805.07959 · Physical Review A

Minimum resources for versatile continuous-variable entanglement in integrated nonlinear waveguides

David Barral, Kamel Bencheikh, Virginia D’Auria, Sébastien Tanzilli, Nadia Belabas, Juan Ariel Levenson

Published Aug 29, 2018• 11 citations
arXivHTMLPDF

Abstract

In a recent paper [Barral et al., Phys. Rev. A 96, 053822 (2017)], we proposed a strategy to generate bipartite and quadripartite continuous-variable entanglement of bright quantum states based on degenerate down-conversion in a pair of evanescently coupled nonlinear ${\ensuremath{\chi}}^{(2)}$ waveguides. Here, we show that the resources needed for obtaining these features can be optimized by exploiting the regime of second harmonic generation: the combination of depletion and coupling among pump beams indeed supplies all necessary wavelengths and appropriate phase mismatch along propagation. Our device thus entangles the two fundamental classical input fields without the participation of any harmonic ancilla. Depending on the propagation distance, the generated harmonics are entangled in bright or vacuum modes. We also evidence two-color bipartite and quadripartite entanglement over the interacting modes. The proposed device represents a boost in continuous-variable integrated quantum optics since it enables a broad range of quantum effects in a very simple scheme, which optimizes the resources and can be easily realized with current technology.

DOI
10.1103/physreva.98.023857

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In a recent paper [Barral et al., Phys. Rev. A 96, 053822 (2017)], we proposed a strategy to generate bipartite and quadripartite continuous-variable entanglement of bright quantum states based on degenerate down-conversion in a pair of evanescently coupled nonlinear \ensuremathχ(2){\ensuremath{\chi}}^{(2)}\ensuremathχ(2) waveguides. Here, we show that the resources needed for obtaining these features can be optimized by exploiting the regime of second harmonic generation: the combination of depletion and coupling among pump beams indeed supplies all necessary wavelengths and appropriate phase mismatch along propagation. Our device thus entangles the two fundamental classical input fields without the participation of any harmonic ancilla. Depending on the propagation distance, the generated harmonics are entangled in bright or vacuum modes. We also evidence two-color bipartite and quadripartite entanglement over the interacting modes. The proposed device represents a boost in continuous-variable integrated quantum optics since it enables a broad range of quantum effects in a very simple scheme, which optimizes the resources and can be easily realized with current technology.
We study continuous-variable entanglement of bright quantum states in a pair of evanescently coupled nonlinear ${\ensuremath{\chi}}^{(2)}$ waveguides operating in the regime of degenerate down conversion. We consider the case where only the energy of the nonlinearly generated fields is exchanged between the waveguides while the pump fields stay independently guided in each original waveguide. We show that this device, when operated in the depletion regime, entangles the two noninteracting bright pump modes due to a nonlinear cascade effect. It is also shown that two-color quadripartite entanglement can be produced when certain system parameters are appropriately set. This device works in the traveling-wave configuration, such that the generated quantum light shows a broad spectrum. The proposed device can be easily realized with current technology and therefore stands as a good candidate for a source of bipartite or multipartite entangled states for the emerging field of optical continuous-variable quantum information processing.
We show that arrays of ${\ensuremath{\chi}}^{(2)}$ nonlinear waveguides in the second-harmonic generation regime are a promising source of continuous-variable entanglement. We indeed demonstrate analytically that optical arrays with an odd number of waveguides injected with the zero-eigenvalue fundamental supermode entangle this fundamental supermode with a collective harmonic field. Moreover, the fundamental individual modes are multipartite entangled and their entanglement grows with propagation length. The device is scalable, robust to losses, does not rely on specific values of nonlinearity and coupling, and is easily realized with current technology. It thus stands as an unprecedented candidate for generation of multipartite continuous-variable entanglement for optical quantum information processing.
In this Brief Report, we investigate the generation of bright quadripartite entanglement of continuous variables in an experimentally realizable system involving second-order harmonic generation with competing nondegenerate optical parametric downconversion. By using the well-known van Loock--Furusawa criterion for continuous variable correlations, we find that the genuine quadripartite entanglement can be generated in the system over a wide range of controllable parameters. Besides this, it is shown that the bipartite entanglement between any two field modes can be achievable. In addition, the dependence of the quantum correlations on the pump parameter is also discussed.
Encoding continuous-variable quantum information in the optical domain has recently enabled the generation of large entangled states, yet robust implementation remains a challenge. Here, we present a straightforward protocol for generating multipartite entanglement based on spontaneous parametric down-conversion in a circular array of quadratic nonlinear waveguides. We provide a rigorous theoretical framework, including comprehensive derivations of the propagation equations and the identification of regimes where analytical solutions are possible. Crucially, our approach identifies the pump and detection configurations required to sustain and measure multipartite full inseparability across arbitrary propagation distances and for any number of waveguides N=4nN=4 nN=4n. This regime, elusive to standard numerical methods, represents a key requirement for scalable quantum protocols. Our scheme is inherently robust as it relies on phase-matched propagation eigenmodes, making it resilient against variations in sample length, coupling, and nonlinearity.
An experimentally feasible intracavity coupler scheme is proposed to generate bright quadripartite continuous-variable (CV) entanglement by the coupled second-harmonic generation processes. By solving the steady-state equations and calculating the correlation spectra of the four output beams, we show that the four output beams are all entangled with each other according to the sufficient inseparability criterion for multipartite CV entanglement. By utilizing the upconversion process, the generated four entanglement fields have macroscopic intensities as soon as the input fields are turned on.
We study a class of nonlinear waveguide arrays in which the waveguides are endowed with ${\ensuremath{\chi}}^{(2)}$ nonlinearity and coupled through the evanescent overlap of the guided modes. We investigate the viability of such an array as a platform for generating both bipartite and tripartite continuous-variable entanglement. We explicitly address the effect of realistic losses on the entanglement produced, discuss the possible types of nonlinear materials that could be used, and suggest solutions for the possible phase matching issues in the waveguides. The simultaneous generation and manipulation of the light on a single waveguide chip circumvents the usual bandwidth problems associated with the use of external bulky optical elements and makes this avenue promising for further investigation.