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arXiv:2504.20254

Multimode Entangled Squeezed Light Generation and Propagation in a Coupled-Cavity Photonic Crystal

Dylan van Eeden, Marc M. Dignam

Published Apr 28, 2025• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.2504.20254

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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.
We investigate theoretically the temporal evolution of a squeezed state in lossy coupled-cavity systems. We present a general formalism based upon the tight-binding approximation and apply this to a two-cavity system as well as to a coupled-resonator optical waveguide in a photonic crystal. We derive analytical expressions for the number of photons and the quadrature noise in each cavity as a function of time when the initial excited state is a squeezed state in one of the cavities. We also analytically evaluate the time-dependent cross correlation between the photons in different cavities to evaluate the degree of quantum entanglement. We demonstrate that loss in such coupled-cavity systems cannot be treated using simple exponential factors. Finally, we also derive approximate analytic expressions for the maximum photon number, maximum squeezing, and maximum entanglement for cavities far from the initially excited cavity in a lossless coupled-resonator optical waveguide.
For large-scale, multi-partite photonic quantum information system, stable on-demand single photon sources are particularly important building blocks. A scheme to implement the source is to multiplex many heralded single photon sources of identical photon pair generators. To achieve this, we must increase the integration density of the photon pair generators. Slow light enhanced nonlinearity in Si photonic waveguides has proven useful for reducing the device size. So far, we demonstrated that coupled-resonator optical waveguides (CROWs) based on photonic crystal (PhC) nanocavities exhibited the largest nonlinear constant γ (/W/m) in Si-core waveguides thanks to the slow light enhancement and a strong spatial field confinement achieved by PhC nanocavities. Using the PhC-cavity-based CROW, we demonstrate efficient correlated photon pair generation.
Gaussian quantum states of light have many applications in quantum technologies. Two of the most widely used Gaussian quantum states of light are the single- and two-mode squeezed states. In this thesis, we propose the generation of a hybrid of these two states, which has both properties of single- and two-mode squeezed states. We then extend our method to the generation of multimode squeezed states which posses N-partite entanglement. Our states are defined using Gaussian frequency modes, and our method relies on a nonlinear-optical process called spontaneous parametric downconversion. We shape the joint spectral amplitude of the generated light in two ways, by spectrally engineering the light incident on the crystal and by the engineering of the nonlinear crystal to have desired properties. We first use our method to generate tuneable hybrid squeezed states and then extend it to multimode squeezed states. We then investigate design considerations for the nonlinear crystal and study the effect of fabrication errors. The tuneable hybrid and multimode squeezed states are localized in both frequency and time, making them ideal for a variety of quantum information protocols. We expect that the states will be used to generalize many quantum information protocols to their multimode counterparts, such as, multi-parameter quantum metrology, multi-channel quantum imaging and multi-partite teleportation. Our work will therefore broaden the applicability of optics for the development of quantum technologies.
Two-mode squeezed states have potential applications in quantum teleportation, quantum computation, and quantum information. Spontaneous parametric down conversion (SPDC) is one of the processes that can be used to generate two-mode squeezed optical states, both in bulk and integrated systems. In this work, we theoretically model SPDC in a vertically-pumped, lossy, coupled-resonator optical waveguide (CROW), shown in Fig. 1(a), to generate counterpropagating continuous variable (CV) entangled states. For a CROW in which the cavities are identical, using the nearest neighbour TB approximation, the CROW mode dispersion is given by ω̃Fk≈ ω̃F[1+ β̃1cos(kD)] ≡ ωFk-iγFk,, where ω̃Fis the individual-cavity complex mode frequency, β̃1is the complex coupling parameter, D is the periodicity of the CROW, and k is the Bloch vector. We consider the case of a pump that is Gaussian in time and space, with spatial and temporal full width at half maxima of ΔrFMHM= 2 √{l n2}/σ+and ΔtFMHM= 2 √{l n2}/τ/(σ_D), respectively, where σ+and σ_ are the k-space width parameters (see below), and τ = Re {1 / (ω̃Fβ̃1)} is the minimum time for the light to propagate one period.