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Photonics North (PN)

Continuous-variable entangled states in a lossy CROW

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

Published May 1, 2019• 0 citations
Publisher

Abstract

We theoretically model the counterpropagating entangled states generated in vertically-pumped, lossy, coupled resonator optical waveguides and use the model to investigate the effects of the loss on the propagation of the entangled states for different pump parameters.
DOI
10.1109/pn.2019.8819586

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We present a general theoretical approach to model an integrated source of counterpropagating continuous-variable entangled states in lossy waveguides pumped by a classical pulsed source incident from above the waveguide. We use a backward Heisenberg approach to model the generation of the entangled state and then solve the adjoint master equation to model the propagation of the state in the lossy waveguide. We employ a numerical method to implement the Schmidt decomposition method for the biphoton wave function rather than pursuing analytical methods. This approach allows us to model a wide variety of waveguide systems and pump configurations. We apply our model to the nonlinear generation and propagation of continuous-variable entangled states in a coupled resonator optical waveguide under a variety of different pump conditions and derive the optimal pumping conditions for our system.
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.
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.
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.