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Chinese Optics Letters

Generation of three-mode W-type entangled coherent states in free-travelling optical fields

郭裕 郭裕, 匡乐满, Guo Yu

Published Jan 1, 2008• 5 citations
Publisher

Abstract

We propose a scheme for generation of three-mode W-type entangled coherent states (ECSs) in free-travelling optical fields by using a single-photon source, coherent state sources, beam splitters, photodetectors, and three-mode cross-Kerr media. The scheme consists of a Mach-Zehnder interferometer (MZI) in which each arm contains a cross-Kerr medium. We calculate the success probability of the generated W-type ECSs, and the total success probability is unity under the ideal conditions.

DOI
10.3788/col20080604.0303

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We propose a scheme for generation of three-mode W-type entangled coherent states (ECSs) in free-travelling optical fields by using a single-photon source, coherent state sources, beam splitters, photodetectors, and three-mode cross-Kerr media. The scheme consists of a Mach-Zehnder interferometer (MZI) in which each arm contains a cross-Kerr medium. We calculate the success probability of the generated W-type ECSs, and the total success probability is unity under the ideal conditions.
In this paper, we propose an optical scheme to generate four-mode W -type entangled coherent states (ECSs) in free travelling optical fields by using a single-photon source, coherent state sources, beam splitters, photodetectors and cross-Kerr media. Our scheme consists of a symmetric optical setup in which there are two Mach–Zehnder interferometers in which each arm contains a cross-Kerr medium. We calculate the average fidelity of generated W -type ECSs, the success probability of producing four-mode W -type ECSs and the average fidelity of the generated four-mode W -type ECSs. It is indicated that our protocol is nearly deterministic.
In this paper, we propose an optical scheme to generate three-mode W -type entangled coherent states (ECSs) in free-travelling optical fields by using a single-photon source, coherent state sources, beam splitters, photodetectors and cross-Kerr media. The success probability of our protocol approaches unity in the ideal case. We also analyse that our scheme can be generalized to produce other N -mode W -type ECSs ( N ≠ 2 n ) nearly deterministically through choosing the beam splitters with appropriate reflectance.
Trio coherent states (TCSs) are non-Gaussian three-mode entangled states which can serve as a useful resource for continuous-variable quantum tasks, so their generation is of primary importance. Schemes exist to generate stable TCSs in terms of vibrational motion of a trapped ion inside a crystal. However, to perform quantum communication and distributed quantum computation the states should be shared beforehand among distant parties. That is, their modes should be able to be directed to different desired locations in space. In this work, we propose an experimental setup to generate such free-traveling TCSs in terms of optical fields. Our scheme uses standard physical resources, such as coherent states, balanced beam splitters, phase shifters, nonideal on-off photodetectors, and realistic weak cross-Kerr nonlinearities, without the need of single photons or homodyne or heterodyne measurements. We study the dependences of the fidelity of the state generated by our scheme with respect to the target TCS and the corresponding generation probability for the parameters involved. In theory, the fidelity could be nearly perfect for whatever weak nonlinearities $\ensuremath{\tau}$ and low photodetector efficiency $\ensuremath{\eta}$, provided that the amplitude $|\ensuremath{\alpha}|$ of an input coherent state is large enough, namely, $|\ensuremath{\alpha}|\ensuremath{\ge}5/(\sqrt{\ensuremath{\eta}}\ensuremath{\tau})$.
We study Greenberger-Horne-Zeilinger--type (GHZ-type) and WWW-type three-mode entangled coherent states. Both types of entangled coherent states violate Mermin's version of the Bell inequality with threshold photon detection (i.e., without photon counting). Such an experiment can be performed using linear optics elements and threshold detectors with significant Bell violations for GHZ-type entangled coherent states. However, to demonstrate Bell-type inequality violations for WWW-type entangled coherent states, additional nonlinear interactions are needed. We also propose an optical scheme to generate WWW-type entangled coherent states in free-traveling optical fields. The required resources for the generation are a single-photon source, a coherent state source, beam splitters, phase shifters, photodetectors, and Kerr nonlinearities. Our scheme does not necessarily require strong Kerr nonlinear interactions; i.e., weak nonlinearities can be used for the generation of the WWW-type entangled coherent states. Furthermore, it is also robust against inefficiencies of the single-photon source and the photon detectors.