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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Spatially Separated Generalized Two-Mode Squeezed Vacuum States in Lossy Coupled Resonator Optical Waveguides

Hossein Seifoory, L. G. Helt, John E. Sipe, Marc M. Dignam

Published Jun 1, 2019• 1 citation

Abstract

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.

DOI: 10.1109/cleoe-eqec.2019.8872724

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Continuous-variable (CV) entanglement is a valuable resource in the field of quantum information. One source of CV entanglement is the correlations between the position and momentum of photons in a two-mode squeezed state of light. In this paper, we theoretically study the generation of squeezed states, via spontaneous parametric down conversion, inside a two-mode lossy cavity that is pumped with a classical optical pulse. The dynamics of the density operator in the cavity is modeled using the Lindblad master equation, and we show that the solution to this model is the density operator for a two-mode squeezed thermal state, with a time-dependent squeezing amplitude and average thermal photon number for each mode. We derive an expression for the minimum correlation variance inside the cavity that depends crucially on the difference in the losses between the two modes. We apply our analytic solution to the important example of a microring resonator that is pumped with a Gaussian pulse. The expressions that we derive will help researchers optimize CV entanglement in lossy cavities.

We present an integrated source of counterpropagating entangled states based on a coupled resonator optical waveguide that is pumped by a classical pulsed source incident from above the waveguide. We investigate theoretically the generation and propagation of continuous-variable entangled states in this coupled-cavity system in the presence of intrinsic loss. Using a tight-binding approximation, we derive analytic time-dependent expressions for the number of photons in each cavity, as well as for the correlation variance between the photons in different pairs of cavities, to evaluate the degree of quantum entanglement. We also derive simple approximate expressions for these quantities that can be used to guide the design of such systems, and discuss how pumping configurations and physical properties of the system affect the photon statistics and the degree of quantum correlation.

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