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在双电磁感应透明区中通过交叉相位调制产生纠缠相干态

Generation of entangled coherent states via cross phase modulation in a double electromagnetically induced transparency regime

M. Paternostro, M. S. Kim, B. S. Ham

备注：
15 pages, 9 figures; extensively revised version; added Section V
发表信息：
Phys. Rev. A 67, 023811 (2003)
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摘要：

纠缠相干态的产生是利用相干态进行量子信息处理的重要组成部分。最近，已经提出了许多方案来实现这一任务。为了产生行波纠缠相干态，交叉相位调制，优化的光学克尔效应增强在电磁诱导透明（EIT）制度的稠密介质中，似乎是非常有前途的。在这种情况下，我们提出了一个完全量化的模型，最近提出的双EIT计划[D。Petrosyan和G. Kurizki，{ \sl Phys.Rev.A} { \bf 65}，33833（2002）]：采用完全哈密顿方法执行量化步骤。这使我们能够为两个相互作用的量子光场写出有效的运动方程，表明一个场的动力学如何取决于另一个场的光子数算符。薛定谔猫态是两个不同相干态的叠加态，其制备过程被简单地揭示出来。这是基于经由两个光场（最初以相干态制备）的双EIT的非线性相互作用以及基于使用$50:50$分束器和两个光电检测器执行的检测步骤。为了显示所产生的纠缠相干态的纠缠，我们建议测量光场的联合正交方差。我们证明了纠缠相干态满足基于正交方差测量的纠缠的充分条件。我们还展示了我们的方案是如何强大的零差检测器的低检测效率。

英文摘要：

The generation of an entangled coherent state is one of the most important ingredients of quantum information processing using coherent states. Recently, numerous schemes to achieve this task have been proposed. In order to generate travelling-wave entangled coherent states, cross phase modulation, optimized by optical Kerr effect enhancement in a dense medium in an electromagnetically induced transparency (EIT) regime, seems to be very promising. In this scenario, we propose a fully quantized model of a double-EIT scheme recently proposed [D. Petrosyan and G. Kurizki, {\sl Phys. Rev. A} {\bf 65}, 33833 (2002)]: the quantization step is performed adopting a fully Hamiltonian approach. This allows us to write effective equations of motion for two interacting quantum fields of light that show how the dynamics of one field depends on the photon-number operator of the other. The preparation of a Schrödinger cat state, which is a superposition of two distinct coherent states, is briefly exposed. This is based on non-linear interaction via double-EIT of two light fields (initially prepared in coherent states) and on a detection step performed using a $50:50$ beam splitter and two photodetectors. In order to show the entanglement of a generated entangled coherent state, we suggest to measure the joint quadrature variance of the field. We show that the entangled coherent states satisfy the sufficient condition for entanglement based on quadrature variance measurement. We also show how robust our scheme is against a low detection efficiency of homodyne detectors.

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