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Physical Review A

Tripartite entanglement in quantum-beat lasers

Xiaoxia Li, Xiangming Hu

Published Aug 19, 2009• 28 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.80.023815

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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.
We show that a quantum-beat system with incoherent pump or coherent driving produces an entangled sub-shot-noise laser that operates well above threshold. The numerical results and physical analyses are presented using the combination modes of the lasing fields. The relative mode is decoupled from the active medium and thus remains in its vacuum state, while the sum mode operates well above threshold and has sub-shot-noise. The quantum beat and the sum mode intensity noise reduction combine to yield entanglement between two bright beams and sub-Poissonian photon statistics of the respective beams.
We present a collection of our recent schemes that have been proposed for continuous variable entanglement. Included in this collection are two types of optical systems. One is the four-wave mixing in resonantly or near-resonantly driven atomic systems. The numerical results and physical analyses are presented by using dressed atomic states and squeeze transformed cavity modes. Two dissipation channels are identified, through which the dressed atoms simultaneously absorb in the excitations from the pair of squeeze transformed modes. It is in the presence of such two channels that the entanglement is greatly enhanced and the best achievable state is the original Einstein-Podolsky-Rosen (EPR) entangled state. This scheme is applicable in the optical regime where atomic spontaneous emission has to be taken into account, unlike the two-step atomic reservoir engineering scheme, which is limited to the microwave regime. The other kind of systems is the quantum-beat laser with incoherent pump or coherent driving. Such a laser, when it operates well above threshold, produces entangled light. The numerical results and physical analyses are presented by using the collective modes of the lasing fields. The relative mode is decoupled from the active medium and thus remains in its vacuum state, while the sum mode operates well above threshold and displays sub-shot noise. The quantum-beat and the sum mode intensity noise reduction combine to yield entanglement between two bright beams and sub-Poissonian photon statistics of respective beams.
Using the `dressed-atom-dressed-mode' approach and separating the decoupled atomic state, we investigate the statistical properties of a quantum-beat laser without inversion. While the fluctuations of the relative amplitude and phase are retained at their vacuum noise levels, the intensity fluctuations in the sum mode are reduced below the shot noise limit with an optimum Mandel parameter when the laser is operated well above threshold. In particular, we show that the decoupled atomic state significantly relaxes the parameter requirement for squeezing. The physical cause is also explained.
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.