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arXiv:1709.03533 · Physical Review A

Continuous-variable entanglement of two bright coherent states that never interacted

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

Published Nov 8, 2017• 21 citations
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Abstract

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.

DOI
10.1103/physreva.96.053822

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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 ${\ensuremath{\chi}}^{(2)}$ 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.
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.
We theoretically show that continuous-variable genuine quadripartite entanglement can be generated by intracavity cascaded nonlinear optical interactions. The process consists of a parametric down-conversion, a sum-frequency generation of pump and signal and a sum-frequency generation of pump and idler. The characteristics of the quadripartite entanglement among the signal, the idler, and two sum-frequency modes are analyzed by applying a sufficient inseparability criterion for multipartite continuous-variable entanglement proposed by Van Loock and Furusawa. The threshold properties of the system are also discussed.
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.
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.
Abstract Multipartite entanglement is the crucial requirement for quantum information processing, quantum computation, quantum communication and quantum sensing. Therefore, the generation and characterization of such entanglement are primary goals in quantum technologies. Here we theoretically study the multipartite continuous-variable quadrature entanglement generated by three symmetric cascaded nonlinear optical systems. Such cascaded systems allow us to study the bipartite, tripartite and quadripartite entanglement. We use different continuous-variable entanglement criteria to characterize the entanglement. We observe that only a few bipartite combinations show the entanglement out of all possible combinations, while most tripartite combinations are entangled. Interestingly such a system depicts a full quadripartite entanglement. Moreover, we show that, unlike the quadrature sum-variance entanglement criterion, the negative partial transpose criterion can show the entanglement in most cases. The present comprehensive analysis of the generation and characterization of the continuous-variable entanglement with cascaded systems would pave the way to realizing a complex quantum network.