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Journal of Physics B Atomic Molecular and Optical Physics

Quadripartite square graph-state entanglement via atomic coherent effects in two-photon resonant systems

Xiangming Hu, Liang Zhang, Xuehua Zhang, Lingfeng Kong

Published Sep 6, 2010• 2 citations
Publisher

Abstract

We show that it is possible to generate a quadripartite square graph-state entanglement in two-photon resonant systems. Every vertex of the square represents an optical field and every side stands for the entanglement of the two vertices. Four optical fields of different frequencies are coupled to coherently driven three-level ladder atoms. Through such a system, quantum beats and two-photon resonant interactions combine to cause the collective-mode parametric interactions. This results in the collective-mode entanglement, which corresponds to the square graph-state entanglement of the four individual fields.

DOI
10.1088/0953-4075/43/18/185502

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We show that it is possible to generate a quadripartite square graph-state entanglement in two-photon resonant systems. Every vertex of the square represents an optical field and every side stands for the entanglement of the two vertices. Four optical fields of different frequencies are coupled to coherently driven three-level ladder atoms. Through such a system, quantum beats and two-photon resonant interactions combine to cause the collective-mode parametric interactions. This results in the collective-mode entanglement, which corresponds to the square graph-state entanglement of the four individual fields.
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.
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.
It has been known that two-mode entangled light can possibly be generated by employing near-resonant interaction with an ensemble of two-level atoms. The responsible mechanism is the absorption of two photons from the strong driving field and the emission of two new photons into the cavity field. Here, we generalize such a mechanism to three separated atomic ensembles and establish cascade interactions for four nondegenerate fields. It is shown that the quadripartite cluster and Greenberger–Horne–Zeilinger entangled states occur for continuous variables. The advantage of the present scheme for the multipartite entanglement lies in that the coupling strengths are much larger due to the near resonances than for far-off-resonance-based parametric processes.
We present a theoretical scheme for the generation of four quantized modes in a three-level double-$\ensuremath{\Lambda}$ atomic system driven by two counterpropagating far-detuned pump beams and find the entanglement between the four modes. By using the second-order perturbation method and the phase-matching condition for the four-wave mixing processes, the effective Hamiltonian is derived, which clearly illustrates the generation of four light beams and their entanglement. The dependence of the four-mode entanglement on interaction time, pump detuning, strength of interaction force, and the ratio of Rabi frequency of two pump beams is analyzed with inseparability. The result presented here provides a method for the experimental generation of multipartite entanglement in an atomic system.
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.
Abstract Graph states are a broad family of entangled quantum states, each defined by a graph composed of edges representing the correlations between subsystems. Such states constitute versatile resources for quantum computation and quantum-enhanced measurement. Their generation and engineering require a high level of control over entanglement. Here we report on the generation of continuous-variable graph states of atomic spin ensembles, which form the nodes of the graph. We program the entanglement structure encoded in the graph edges by combining global photon-mediated interactions in an optical cavity with local spin rotations. By tuning the entanglement between two subsystems, we either localize correlations within each subsystem or enable Einstein–Podolsky–Rosen steering—a strong form of entanglement that enables the extraction of precise information from one subsystem through measurements on the other. We further engineer a four-mode square graph state, highlighting the flexibility of our approach. Our method is scalable to larger and more complex graphs, laying groundwork for measurement-based quantum computation and advanced protocols in quantum metrology.