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Journal of Modern Optics

Evolution of the pair-coherent state with the two-qubit: entanglement and cat-state generation

Faisal A. A. El-Orany, A.‐S. F. Obada, M.A. Abdelslam, Mohamed Ridza Wahiddin

Published Jun 10, 2008• 4 citations
Publisher

Abstract

In this paper, we study the interaction between two two-level atoms and two nondegenerate cavity modes when the atoms and the field are initially in the atomic superposition states and the pair-coherent state (PCS), respectively. We investigate the atomic inversions, tangles and joint probability distribution. We show that the system can generate long-living entanglement by controlling the values of the interaction parameters. Also we show generally that for obtaining a large amount of entanglement from two qubits interacting with a maximally entangled two-mode state one has to prepare the qubits initially in the decoupled states. Moreover, the system – at certain values of interaction parameters – can generate different types of nonclassical states, such as the mth-photon PCS, statistical mixtures of PCSs and superposition of PCS.

DOI
10.1080/09500340701762730

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We study the interaction between a single-mode quantized field and a quantum system composed of two qubits. We suppose that two qubits initially be prepared in the mixed and separable state, and study how entanglement between two qubits arises in the course of evolution according to the Jaynes–Cummings type interaction with nonclassical radiation field. We also investigate the relation between entanglement and purity of qubit subsystem. We show that different photon statistics have different effects on the dynamical behavior of the qubit subsystem. When the qubits are initially prepared in the maximally mixed and separable state, for coherent state field we cannot find entanglement between two qubits; for squeezed state field entanglement between two qubits exists in several short period of time; for even and odd coherent state fields of large photon number, the dynamical behavior of the entanglement between two qubits shows collapse and revival phenomenon. For odd coherent state field of small photon number, the entanglement with both qubits initially prepared in maximally mixed state can be stronger than that with both qubits initially prepared in pure states. For fields of small photon number, the entanglement strongly depends on the states they are initially prepared in. For coherent state field, and odd and even coherent state fields of large photon number, the entanglement only depends on the purity of the initial state of qubit subsystem. We also show that during the evolution the unentangled state may be purer than the entangled state, and the maximum degree of entanglement may not occur at the time when the qubit subsystem is in the purist state.
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We develop a model to investigate the behavior of atomic coupler consists of two waveguides, each of which includes a localized or a trapped atom with a two-mode pair coherent state source. The waveguides are placed close enough to each other to allow energy exchange between them. The two atoms, in the different waveguides, are located adjacent to each other. In each waveguide, one mode propagates along and interacts with the atom inside in a standard way as the Jaynes- Cummings model (JCM). The atom-mode system, in each waveguide, interacts with the other one via the evanescent wave. Pair coherent states (PCS) are one of the most important states in quantum information theory since it includes sufficient entanglement causing the violation of the Bell inequality. Moreover, the PCS possesses prominent nonclassical properties such as sub-Poissonian statistics, correlation in the number fluctuations, squeezing and violations of the Cauchy Schwartz inequalities
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