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Journal of Physics B Atomic Molecular and Optical Physics

Three-mode entanglement and amplification in correlated spontaneous emission lasers

Wen-xing Shi, Xiangming Hu, Fei Wang

Published Jul 31, 2009• 11 citations
Publisher

Abstract

We propose a scheme for establishing three-coloured correlated spontaneous emission lasers and generating tripartite continuous-variable entanglement. The interaction of three cavity fields is formed by beating two of them in a two-channel Raman or two-photon transition and by correlating the two-mode beat and the third cavity field in the successive transitions. Using the sufficient inseparability criterion proposed by van Loock and Furusawa, we show that the three cavity fields are entangled when the numbers of photons are large and the saturation is weak. The upper limits of the photon numbers for the entanglement are dependent on the frequencies and amplitudes of the external coherent fields.

DOI
10.1088/0953-4075/42/16/165506

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We propose a scheme for establishing three-coloured correlated spontaneous emission lasers and generating tripartite continuous-variable entanglement. The interaction of three cavity fields is formed by beating two of them in a two-channel Raman or two-photon transition and by correlating the two-mode beat and the third cavity field in the successive transitions. Using the sufficient inseparability criterion proposed by van Loock and Furusawa, we show that the three cavity fields are entangled when the numbers of photons are large and the saturation is weak. The upper limits of the photon numbers for the entanglement are dependent on the frequencies and amplitudes of the external coherent fields.
The generation of enhanced three-mode continuously variable (CV) entanglement via difference-frequency amplification in an optical cavity above the threshold is investigated. The quantum entanglement characteristics among the pump, signal, and idler beams are demonstrated by applying a sufficient inseparability criterion for CV entanglement proposed by van Loock and Furusawa. Bright three-mode CV entanglement with different frequencies can be generated in this simple system when the optical cavity operates above its threshold, and the best three-mode CV entanglement can be obtained when the pump threshold parameter is modulated at about σ = 1.3.
We examine the quantum correlations at steady state in a three-mode quantum-beat laser that operates well above threshold. The analysis is presented by employing the dressed-atom combination-mode picture, in which only one combination mode of three cavity fields is coupled to the active medium, while the other two combination modes are decoupled. For suitable operating conditions, the coupled mode has the intensity fluctuations below the shot noise, while the two decoupled modes retain in their vacuum states. This determines that all of the original modes exhibit sub-Poissonian statistics. When the system operates well above threshold, the van Loock-Furusawa inequality is satisfied, concluding that the genuine tripartite entanglement among three sub-Poissonian fields is established. Physically, the responsible mechanism is the combined effect of atomic coherence controlled correlated-spontaneous emission and intrinsic feedback.
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.
Analysis of the externally induced quantum features of the cavity radiation of the two-photon correlated emission laser is presented. It turns out that the pumping process induces atomic coherence accountable for observing entanglement in the cavity radiation as well as the nonclassical photon number correlation despite the arising vacuum fluctuations. Even though a significant continuous variable entanglement is obtained near threshold in the strong driving limit, increasing the amplitude of the driving radiation more than required for a fixed value of the linear gain coefficient is found to degrade the degree of entanglement. The two-mode squeezing of the superimposed radiation, entanglement of the cavity radiation and mean number of photon pairs increase with the rate at which the atoms are injected into the cavity, but the nonclassical photon number correlation decreases. Moreover, the mean photon number corresponding to the transition from the upper energy level to the intermediate is found to be greater than the transition from the intermediate to the lower. With conceivable practical challenges, it is in principle possible to generate an intense continuous variable entanglement and quantify it via photon count measurements.