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Physical Review A

Entanglement of a two-mode field in a collective three-level atomic system

Zhao-Hong Tang, Gao‐xiang Li

Published Dec 1, 2011• 10 citations
Publisher

Abstract

The entanglement properties of two-mode field from a laser-driven collective three-level atomic system are investigated by taking into account the spontaneously generated coherence. Under some conditions, it is found that the entanglement between the two cavity modes can be significantly enhanced by the collectivity of the atoms compared to the case of independent atoms when the relative phase $\ensuremath{\Delta}\ensuremath{\varphi}=\ensuremath{\pi}$. Moreover, the spontaneously generated coherence can also greatly enhance the entanglement in comparison to the case without this coherence.

DOI
10.1103/physreva.84.063801

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The entanglement properties of two-mode field from a laser-driven collective three-level atomic system are investigated by taking into account the spontaneously generated coherence. Under some conditions, it is found that the entanglement between the two cavity modes can be significantly enhanced by the collectivity of the atoms compared to the case of independent atoms when the relative phase \ensuremathΔ\ensuremathφ=\ensuremathπ\ensuremath{\Delta}\ensuremath{\varphi}=\ensuremath{\pi}\ensuremathΔ\ensuremathφ=\ensuremathπ. Moreover, the spontaneously generated coherence can also greatly enhance the entanglement in comparison to the case without this coherence.
The effect of a dark state on the entanglement properties of the two-mode field from a laser-driven Λ-type three-level atomic system is investigated by taking into account the spontaneously generated coherence (SGC). When the dark state is present, it is found that the entanglement between the two cavity modes can be significantly enhanced compared to the case without the dark state. When the value of SGC is maximal, the dark state population depending on the initial values of the system can affect the entanglement dramatically. Moreover, the effects of a squeezed parameter and Rabi frequency on entanglement evolution are also presented in the presence of a dark state.
We investigate the generation of two-mode-entangled light from a laser-driven three-level $\mathbsf{V}$-type atom inside a cavity by taking into account spontaneously generated quantum interference between two atomic decay channels. We show that under some conditions, the system can reduce to a nondegenerate parametric amplifier which is responsible for the entanglement between the two cavity modes. Compared to the case without the quantum interference, it is found that the entanglement of the cavity field can be significantly enhanced by the interference when the relative phase of the two pumping lasers $\ensuremath{\delta}\ensuremath{\phi}=\ensuremath{\pi}$.
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.
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.