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Physical Review A

Polychromatic quadripartite entanglement from concurrent four-wave mixing in a three-level atomic system

Huatang Tan, Gao‐xiang Li

Published Sep 22, 2010• 14 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.82.032322

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In this paper, we investigate the generation of polychromatic quadripartite entanglement of continuous variables from a three-level \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ-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 investigate the generation of multicolor quadripartite entangled beams of light with continuous variables via optomechanical coupling in an optical cavity. It is found that the genuine quadripartite entanglement can be achieved among the Stokes and anti-Stokes sidebands of two driven cavity fields. This entanglement still exists for the environment temperature up to about 50K50\phantom{\rule{4pt}{0ex}}\text{K}50K. We also show that the obtained genuine quadripartite entanglement actually results from concurrent four-wave-mixing processes in the system, which can, in principle, be generalized to obtain a genuine 2N2N2N-partite entangled state of light from a generic NNN-mode cavity optomechanical system.
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.
We propose an experimentally feasible scheme to produce bright quadricolor continuous-variable (CV) entanglement by a four-wave mixing process (FWM) with four-level atoms inside the optical ring cavities operating above threshold. The Stokes and anti-Stokes beams are generated via the pump beam (tuned close to one atomic transition) and the coupling beam (tuned to the resonance of another atomic transition), respectively. The quadruply resonant and narrowed linewidth of the cavity fields with different frequencies are achieved and quadricolor CV entanglement among the four cavity fields is demonstrated according to the criterion proposed by van Loock and Furusawa [Phys. Rev. A 67, 052315 (2003)]. This scheme provides a way to generate bright quadricolor CV entanglement and will be significant for applications in quantum information processing and quantum networks.
In this paper, we study theoretically bipartite and tripartite continuous variable entanglement as well as normal-mode splitting in a single-atom cavity optomechanical system with intensity-dependent coupling. The system under consideration is formed by a Fabry-P\'erot cavity with a thin vibrating end mirror and a two-level atom in the Gaussian standing wave of the cavity mode. We first derive the general form of the Hamiltonian describing the tripartite intensity-dependent atom-field-mirror coupling due to the presence of the cavity mode structure. We then restrict our treatment to the first vibrational sideband of the mechanical resonator and derive a tripartite atom-field-mirror Hamiltonian. We show that when the optical cavity is intensely driven, one can generate bipartite entanglement between any pair in the tripartite system and that, due to entanglement sharing, atom-mirror entanglement is efficiently generated at the expense of optical-mechanical and optical-atom entanglement. We also find that in such a system, when the Lamb-Dicke parameter is large enough, one can simultaneously observe the normal mode splitting into three modes.
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 investigate the generation and the evolution of continuous-variable (CV) entanglement from a laser-driven four-state atom inside a doubly resonant cavity under Raman excitation. Two transitions in the four-state atom independently interact with the two cavity modes, while two other transitions are driven by coupling laser fields. By including the atomic relaxation as well as cavity losses, we show that the CV entanglement with large mean number of photons can be generated in our scheme. We also show that the intensity of the coupling laser fields can influence effectively the entanglement period of the cavity field. Different from the conventional resonant excitation scheme where zero one-photon detuning are required, it is found that the intensity and period of entanglement between the two cavity modes as well as the total mean photon number of the cavity field can be adjusted by properly modulating the frequency detuning.