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arXiv:2005.07240 · Physical Review A

Quantum state engineering in arrays of nonlinear waveguides

David Barral, Mattia Walschaers, Kamel Bencheikh, Valentina Parigi, Juan Ariel Levenson, Nicolas Treps, Nadia Belabas

Published Oct 13, 2020• 23 citations
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Abstract

In the current quest for efficient and experimentally feasible platforms for implementation of multimode squeezing and entanglement in the continuous variable regime, we underpin and complement our results on the generation of versatile multimode entanglement and cluster states in nonlinear waveguide arrays presented by Barral et al., arXiv:1912.11154 [Phys. Rev. Appl. (to be published)]. We present detailed derivations of the equations that describe the propagation of light through this system, and then we focus on parameter regimes where these equations can be solved analytically. These analytical solutions build an intuition for the wide landscape of quantum states that are accessible through the activation of pumping, coupling, and measurement schemes. Furthermore, we showcase the acquired insights by using one of the identified analytical solutions to exhibit the generation, optimization, and scalability of spatial linear cluster states.

DOI
10.1103/physreva.102.043706

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In the current quest for efficient and experimentally feasible platforms for implementation of multimode squeezing and entanglement in the continuous variable regime, we underpin and complement our results on the generation of versatile multimode entanglement and cluster states in nonlinear waveguide arrays presented by Barral et al., arXiv:1912.11154 [Phys. Rev. Appl. (to be published)]. We present detailed derivations of the equations that describe the propagation of light through this system, and then we focus on parameter regimes where these equations can be solved analytically. These analytical solutions build an intuition for the wide landscape of quantum states that are accessible through the activation of pumping, coupling, and measurement schemes. Furthermore, we showcase the acquired insights by using one of the identified analytical solutions to exhibit the generation, optimization, and scalability of spatial linear cluster states.
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Continuous-variable encoding of quantum information in the optical domain has recently yielded large temporal and spectral entangled states instrumental for quantum computing and quantum communication.We introduce a protocol for the generation of spatial multipartite entanglement based on phase-matching of a propagation eigenmode in a monolithic photonic device: the array of quadratic nonlinear waveguides.We theoretically demonstrate in the spontaneous parametric downconversion regime the generation of large multipartite entangled states useful for multimode quantum networks.Our protocol is remarkably simple and robust as it does not rely on specific values of coupling, nonlinearity, or length of the sample.
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.
The arrays of nonlinear waveguides are a powerful integrated photonics platform for studying and manipulating quantum states of light. Also, they are a valuable resource for various quantum technologies. In this work, we employed a supermode approach to obtain an analytic solution to the evolution of degenerate biphoton states in arrays of nonlinear waveguides. The solution accounts for arrays of an arbitrary number of waveguides and coupling profiles. In addition, it provides an explicit analytic expression without the need of computationally-expensive steps. Actually, it only relies on the calculation of the eigenvalues and eigenvectors of the coupling matrix. In general, this needs to be performed numerically, but there are relevant instances in which analytic expressions are available. Thus, in certain cases, the procedure proposed here does not require the use of any numerical method. We analyze the general properties of the solution and show some application examples. Particularly, simple solutions that can be obtained by special symmetric injection profiles, the results for small arrays, and the properties of the propagation when only the center waveguide is pumped in a symmetric odd array. In addition, we present a proof-of-principle example on how to use the analytic solution to tackle inversion problems. That is, obtaining the initial conditions required to achieve a desired quantum state -- which is a valuable technological application. A relevant aspect of the method presented here is its scalability for large arrays due to the lack of resource-intensive steps -- both for the direct and inverse problems.
Entangled multi-mode squeezed states of light have a wide variety of applications in quantum information systems, particularly in the generation of non-Gaussian states of light, which are central to continuous-variable quantum computing. Although theoretical approaches exist to model the nonlinear generation of one- and two-mode entangled states of light in ring resonator systems, these approaches are difficult to implement in modeling more complicated many-cavity systems. In this work, we present an efficient and accurate theoretical approach to modeling the generation and propagation of quantum states of light in lossy coupled-cavity systems containing a two- or three-mode nonlinear resonant structure. Our approach is general and computationally viable even in systems with hundreds of modes. We apply our method to the design and modeling of a multimode photonic crystal coupled-cavity system for the generation of entangled squeezed states of light on-chip. The system consists of a three-mode resonant structure coupled to three coupled-resonator optical waveguides (CROWs) in a square lattice silicon photonic crystal slab. The computational speed of the method allows us to efficiently optimize the system such that the signal and idler light in the two output CROWs remains entangled even after propagating tens of cavities down the CROWs.
Multimode entanglement is an essential resource for quantum information in continuous-variable systems. Light-based quantum technologies will arguably not be built upon table-top bulk setups, but will presumably rather resort to integrated optics. Sequential bulk opticslike proposals based on cascaded integrated interferometers are not scalable with the current state-of-the-art low-loss materials used for continuous variables. We analyze the multimode continuous-variable entanglement capabilities of a compact currently available integrated bulk-optics analog: the array of nonlinear waveguides. We theoretically demonstrate that this simple and compact structure, together with a reconfigurable input pump distribution and multimode coherent detection of the output modes, is a versatile entanglement synthesizer in the spatial domain. We exhibit this versatility through analytical and numerically optimized multimode squeezing, entanglement, and cluster-state generation in different encodings. Our results re-establish spatial encoding as a contender in the game of continuous-variable quantum information processing.