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arXiv:0708.2963 · Physical Review A

Tripartite entanglement and threshold properties of coupled intracavity down-conversion and sum-frequency generation

C. Pennarun, Ashton S. Bradley, M. K. Olsen

Published Dec 14, 2007• 47 citations
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Abstract

The process of cascaded down-conversion and sum-frequency generation inside an optical cavity has been predicted to be a potential source of three-mode continuous-variable entanglement. When the cavity is pumped by two fields, the threshold properties have been analyzed, showing that these are more complicated than in well-known processes such as optical parametric oscillation. When there is only a single pumping field, the entanglement properties have been calculated using a linearized fluctuation analysis, but without any consideration of the threshold properties or critical operating points of the system. In this work we extend this analysis to demonstrate that the singly pumped system demonstrates a rich range of threshold behavior when quantization of the pump field is taken into account and that asymmetric polychromatic entanglement is available over a wide range of operational parameters.

DOI
10.1103/physreva.76.063812

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The process of cascaded down-conversion and sum-frequency generation inside an optical cavity has been predicted to be a potential source of three-mode continuous-variable entanglement. When the cavity is pumped by two fields, the threshold properties have been analyzed, showing that these are more complicated than in well-known processes such as optical parametric oscillation. When there is only a single pumping field, the entanglement properties have been calculated using a linearized fluctuation analysis, but without any consideration of the threshold properties or critical operating points of the system. In this work we extend this analysis to demonstrate that the singly pumped system demonstrates a rich range of threshold behavior when quantization of the pump field is taken into account and that asymmetric polychromatic entanglement is available over a wide range of operational parameters.
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It is theoretically shown that tripartite entanglement with different wavelengths can be generated by cascaded nonlinear interaction in an optical parametric oscillator cavity with parametric down conversion and sum-frequency generation. A sufficient inseparability criterion for continuous-variable tripartite entanglement proposed by van Loock and Furusawa was used to evaluate the degree of the quadrature-phase amplitude correlations between the three modes. The dependences of correlation on the cavity parameters and pump intensity are discussed.
We analyze an optical parametric oscillator (OPO) in which cascaded down-conversion occurs inside a cavity resonant for all modes but the initial pump. Due to the resonant cascade design, the OPO presents two ${\ensuremath{\chi}}^{(2)}$-level oscillation thresholds that are therefore much lower than for a ${\ensuremath{\chi}}^{(3)}$ OPO. This is promising for reaching the regime of an effective third-order nonlinearity well above both thresholds. Such a ${\ensuremath{\chi}}^{(2)}$ cascaded device also has potential applications in frequency conversion to far-infrared regimes. But, most importantly, it can generate novel multipartite quantum correlations in the output radiation, which represent a step beyond squeezed or entangled light. The output can be highly non-Gaussian and therefore not describable by any semiclassical model. In this paper, we derive quantum stochastic equations in the positive-PPP representation and undertake an analysis of steady-state and dynamical properties of this system.
We calculate the quantum correlations existing among the three output fields (pump, signal, and idler) of a triply resonant nondegenerate optical parametric oscillator operating above threshold. By applying the standard criteria [P. van Loock and A. Furusawa, Phys. Rev. A 67, 052315 (2003)], we show that strong tripartite continuous-variable entanglement is present in this well-known and simple system. Furthermore, since the entanglement is generated directly from a nonlinear process, the three entangled fields can have very different frequencies, opening the way for multicolored quantum information networks.
We analyze an optical parametric oscillator (OPO) in which cascaded down-conversion occurs inside a cavity resonant for all modes but the initial pump. Due to the resonant cascade design, the OPO present two χ^2 level oscillation thresholds that are therefore remarkably lower than for a χ^3 OPO. This is promising for reaching the regime of an effective third-order nonlinearity well above both thresholds. Such a χ^2 cascaded device also has potential applications in frequency conversion to far infra-red regimes. But, most importantly, it can generate novel multi-partite quantum correlations in the output radiation, which represent a step beyond squeezed or entangled light. The output can be highly non-Gaussian, and therefore not describable by any semi-classical model.
We explore in detail the possibility of intracavity generation of continuous-variable (CV) entangled states of light beams under mode phase-locked conditions. We show that such quantum states can be generated in a self-phase-locked nondegenerate optical parametric oscillator (NOPO) based on type II phase-matched down-conversion combined with a linear mixer of two orthogonally polarized modes of the subharmonics in a cavity. A quantum theory of this device, recently realized in the experiment, is developed for both subthreshold and above-threshold operational regimes. We show that the system providing high-level phase coherence between two generated modes, unlike the ordinary NOPO, also exhibits different types of quantum correlations between photon numbers and phases of these modes. We quantify the CV entanglement as two-mode squeezing and show that the maximal degree of the integral two-mode squeezing (which is 5050%50 relative to the level of vacuum fluctuations) is achieved at the pump field intensity close to the generation threshold of a self-phase-locked NOPO, provided that the constant of linear coupling between the two polarizations is much less than the mode detunings. The peculiarities of CV entanglement for the case of unitary, nondissipative dynamics of the system under consideration are also cleared up.