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Journal of Physics B Atomic Molecular and Optical Physics

Entanglement of three-mode light via six-wave mixing in a four-level Y-type atomic system

Wenxing Shi, Xiangming Hu, Jingyan Li, Fei Wang

Published Jul 20, 2010• 11 citations
Publisher

Abstract

In this paper, we show that it is possible to achieve continuous-variable entanglement of three optical fields in a four-level Y-type atomic system. The three fields are amplified through the Rabi resonances of the different driven transitions. Two fields from the V configuration are in one quantum beat and in the mixing parametric interactions with the third field from the lower transition. This yields entanglement between the pair of beat modes and the third field. The best achievable state in the output approaches the Einstein–Podolsky–Rosen entangled state.

DOI
10.1088/0953-4075/43/15/155506

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In this paper, we show that it is possible to achieve continuous-variable entanglement of three optical fields in a four-level Y-type atomic system. The three fields are amplified through the Rabi resonances of the different driven transitions. Two fields from the V configuration are in one quantum beat and in the mixing parametric interactions with the third field from the lower transition. This yields entanglement between the pair of beat modes and the third field. The best achievable state in the output approaches the Einstein–Podolsky–Rosen entangled state.
We explore the quantum entanglement between two collective fields via atomic coherence effects. For three-level atoms in V\mathsf{V}V configuration driven by two applied fields on two-photon resonance, one coherent superposition of the excited states is not excited, which is the counterpart of coherent population trapping. The coherence-induced depopulation makes two cavity fields in each collection combine into a quantum-beat, i.e., equivalently, the difference mode of the two components decouples from the driven atoms. The two sum modes, when they are arranged in the four-wave mixinglike interactions, can be prepared in Einstein-Podolsky-Rosen entangled state. Correspondingly, any two individual fields from different collective modes are entangled with each other. Furthermore, the effects of thermal reservoir and laser linewidths are discussed, and a generalization is given to the case in which each quantum beat involves more than two modes.
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.
The entanglement properties of two mode fields generated from four-wave mixing are discussed in the system of an ensemble of VVV-type three-level atoms embedded in a two-mode cavity, in which the atomic transitions from the two excited states to the ground state are driven by one strong and one relative weak laser field, respectively. The nondegenerate four-wave mixing process occurs in the strong laser-driven transition, which is also coupled by the two cavity modes. With the help of the auxiliary atomic transition driven by the weak laser field and adjusting the frequency difference of the two modes, highly squeezed and entangled light with high intensity can be generated.
In this paper, we investigate the generation of polychromatic quadripartite entanglement of continuous variables from a three-level $\ensuremath{\Lambda}$-type atomic system inside an optical quadruply resonant cavity. The atoms are driven by external lasers and simultaneously coupled to four cavity modes by means of multiply concurrent four-wave mixing interactions. The general master equation of the cavity field is derived explicitly. By solving the Gaussian-type master equation and using the negative-partial-transpose criterion for bipartite entanglement, we show that the genuine quadripartite entanglement of the field can be generated over a wide range of parameters. The entanglement properties of the four-mode field are discussed in detail. We find that the optimal quadripartite entanglement can be obtained when the cavity modes are tuned to be resonant with the Rabi sidebands of the driven atoms.
We analyze quantum correlations in four-wave mixing in three-level $\ensuremath{\Lambda}$ and V atomic systems 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 two channels that the entanglement is greatly enhanced and the best achievable state approaches the original Einstein-Podolsky-Rosen 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.