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Physical Review A

State-projective scheme for generating pair coherent states in traveling-wave optical fields

Christopher C. Gerry, Jihane Mimih, Richard J. Birrittella

Published Aug 9, 2011• 24 citations
Publisher

Abstract

The pair coherent states of a two-mode quantized electromagnetic field introduced by Agarwal [Phys. Rev. Lett. 57, 827 (1986)] have yet to be generated in the laboratory. The states can mathematically be obtained from a product of ordinary coherent states via projection onto a subspace wherein identical photon number states of each mode are paired. We propose a scheme by which this projection can be engineered. The scheme requires relatively weak cross-Kerr nonlinearities, the ability to perform a displacement operation on a beam mode, and photon detection ability able to distinguish between zero and any other number of photons. These requirements can be fulfilled with currently available technology or technology that is on the horizon.

DOI
10.1103/physreva.84.023810

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The pair coherent states of a two-mode quantized electromagnetic field introduced by Agarwal [Phys. Rev. Lett. 57, 827 (1986)] have yet to be generated in the laboratory. The states can mathematically be obtained from a product of ordinary coherent states via projection onto a subspace wherein identical photon number states of each mode are paired. We propose a scheme by which this projection can be engineered. The scheme requires relatively weak cross-Kerr nonlinearities, the ability to perform a displacement operation on a beam mode, and photon detection ability able to distinguish between zero and any other number of photons. These requirements can be fulfilled with currently available technology or technology that is on the horizon.
Abstract Pair coherent state (PCS) is a two-mode non-Gaussian state recently generated within spatially confined superconducting cavities. Under typical conditions, it is unsuitable for performing global quantum missions in open space. Several methods have been proposed to generate this state with the capability to propagate unrestrictedly. However, these methods employed an excessive amount of unnecessary physical resources or relied on coherent displacement within the low regime. This paper presents a novel experimental approach to generate this state, specifically designed for facilitating long-distance quantum information processing and communication tasks. The method involves the utilization of two weak cross-Kerr nonlinear media, two balanced beam splitters, and an on/off photodetector. Furthermore, the input comprises three CSs with high amplitudes. These physical resources are potentially accessible within existing technology. The analysis of success probability and fidelity demonstrates that the PCS can be successfully generated with a high coherent parameter amplitude, even in scenarios where the photodetector efficiency is low, provided that the coherent amplitudes are sufficiently high.
We propose a scheme for generating entangled states of light fields. This scheme only requires the cross-Kerr nonlinear interaction between coherent light beams, followed by a homodyne detection. Therefore, this scheme is within the reach of current technology. We study in detail the generation of the entangled states between two modes, and that among three modes. In addition to the Bell states between two modes and the W states among three modes, we find plentiful new kinds of entangled states. Finally, the scheme can be extended to generate the entangled states among more than three modes.
We propose a scheme for generating entangled states of light fields. This scheme only requires the cross-Kerr nonlinear interaction between coherent light-beams, followed by a homodyne detection. Therefore, this scheme is within the reach of current technology. We study in detail the generation of the entangled states between two modes, and that among three modes. In addition to the Bell states between two modes and the W states among three modes, we find plentiful new kinds of entangled states. Finally, the scheme can be extend to generate the entangled states among more than three modes.
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, Phys. Rev. A 65, 33 833 (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 Schr\"odinger cat state, which is a superposition of two distinct coherent states, is briefly exposed. This is based on nonlinear 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 an 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.
We propose a nearly perfect optical scheme for the quantum teleportation of entangled coherent states using optical devices such as nonlinear Kerr media, beam splitters, phase shifters, and photon detectors. Different from those previous schemes, our scheme needs only ``yes'' or `no' measurements of the photon number of the related modes, i.e. nonzero- and zero-photon measurements, while in previous schemes one has to exactly identify the even or odd parity character of the photon numbers detected by detectors.