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Acta Physica Sinica

Entanglement property of two-mode cavity field in a nondegenerate four-wave mixing system

物理学报

Published Jan 1, 2007• 0 citations
Publisher

Abstract

摘要 利用非简并四波混频体系制备出稳定的连续变量的纠缠态，研究了纠缠随时间的演化情况.同时，得到双模光场的特征函数.经分析可知，在强抽运光的作用下此体系相当于一个光学参量放大器；在满足一定的条件下，能够制备出稳定的连续变量的量子纠缠态，并且纠缠的程度与双光子抽运光强度、合作参量及失谐频率有关. 关键词: 连续变量 / 三能级 / 高斯态 / 参量放大器 Abstract We apply nondegenerate four-wave mixing processes to the generation of stable continuous variable entangled light and study the time evolution of continuous variable entangled light. We analytically get the characteristic function of the two-mode field and find that the system is an optical parametric amplifier. We also show that the two-mode cavity field exhibits stable continuous variable entanglement under certain conditions. The degree of entanglement depends upon the two-photon intensity I2，the cooperativity parameter C and the side-mode detuning Δ′. Keywords: continuous variable / three-level model / Gaussian state / parametric amplifier 作者及机构信息 邓文武, 郑 俊, 谭华堂, 李高翔 基金项目: 国家自然科学基金(批准号：60478049，10674052)和湖北省自然科学基金(批准号：2006ABB015)资助的课题. Authors and contacts 参考文献 施引文献

DOI
10.7498/aps.56.6970

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摘要 利用非简并四波混频体系制备出稳定的连续变量的纠缠态，研究了纠缠随时间的演化情况.同时，得到双模光场的特征函数.经分析可知，在强抽运光的作用下此体系相当于一个光学参量放大器；在满足一定的条件下，能够制备出稳定的连续变量的量子纠缠态，并且纠缠的程度与双光子抽运光强度、合作参量及失谐频率有关. 关键词: 连续变量 / 三能级 / 高斯态 / 参量放大器 Abstract We apply nondegenerate four-wave mixing processes to the generation of stable continuous variable entangled light and study the time evolution of continuous variable entangled light. We analytically get the characteristic function of the two-mode field and find that the system is an optical parametric amplifier. We also show that the two-mode cavity field exhibits stable continuous variable entanglement under certain conditions. The degree of entanglement depends upon the two-photon intensity I2，the cooperativity parameter C and the side-mode detuning Δ′. Keywords: continuous variable / three-level model / Gaussian state / parametric amplifier 作者及机构信息 邓文武, 郑 俊, 谭华堂, 李高翔 基金项目: 国家自然科学基金(批准号：60478049，10674052)和湖北省自然科学基金(批准号：2006ABB015)资助的课题. Authors and contacts 参考文献 施引文献
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.
We discuss the generation and evolution of entangled light in a correlated spontaneous emission laser. The master equation for the two-mode field in a cavity is derived and solved analytically. The time-dependent characteristic function in the Wigner representation for the two-mode field is obtained. It shows that the two-mode field in the cavity evolves in a two-mode Gaussian state. The entanglement degree of the two-mode field in the cavity increases initially, then decreases, and finally vanishes as the field evolves from an initial vacuum. The period of the entanglement is extended as the intensity of the driving field is increased. It is found that the entanglement still exists even when the two-mode squeezing disappears. During the entanglement period, the intensity of the field is amplified. The entanglement for the initial field being a two-mode squeezed vacuum and the entanglement of the output field are also discussed.
We explore in detail the possibility of intracavity generation of continuous-variable (CV) entangled states of light beams under mode phase-locked conditions. We show that such quantum states can be generated in a self-phase-locked nondegenerate optical parametric oscillator (NOPO) based on type II phase-matched down-conversion combined with a linear mixer of two orthogonally polarized modes of the subharmonics in a cavity. A quantum theory of this device, recently realized in the experiment, is developed for both subthreshold and above-threshold operational regimes. We show that the system providing high-level phase coherence between two generated modes, unlike the ordinary NOPO, also exhibits different types of quantum correlations between photon numbers and phases of these modes. We quantify the CV entanglement as two-mode squeezing and show that the maximal degree of the integral two-mode squeezing (which is 5050%50 relative to the level of vacuum fluctuations) is achieved at the pump field intensity close to the generation threshold of a self-phase-locked NOPO, provided that the constant of linear coupling between the two polarizations is much less than the mode detunings. The peculiarities of CV entanglement for the case of unitary, nondissipative dynamics of the system under consideration are also cleared up.
Continuous-variable (CV) entanglement is a valuable resource in the field of quantum information. One source of CV entanglement is the correlations between the position and momentum of photons in a two-mode squeezed state of light. In this paper, we theoretically study the generation of squeezed states, via spontaneous parametric down conversion, inside a two-mode lossy cavity that is pumped with a classical optical pulse. The dynamics of the density operator in the cavity is modeled using the Lindblad master equation, and we show that the solution to this model is the density operator for a two-mode squeezed thermal state, with a time-dependent squeezing amplitude and average thermal photon number for each mode. We derive an expression for the minimum correlation variance inside the cavity that depends crucially on the difference in the losses between the two modes. We apply our analytic solution to the important example of a microring resonator that is pumped with a Gaussian pulse. The expressions that we derive will help researchers optimize CV entanglement in lossy cavities.