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انجمن اپتیک و فوتونیک ایران

A Theoretical Scheme for Generation of a Class of SU(1,1) and SU(2) Entangled Nonlinear Coherent States

Amir Karimi, Mohammad Kazem Tavassoly

Published Feb 15, 2014• 0 citations
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Abstract

Recently, the entangled nonlinear coherent states are introduced via replacing coherent states with nonlinear coherent states in entangled coherent states. In this paper, in order to generate the SU(1,1) and SU(2) entangled nonlinear coherent states, an appropriate scheme is presented. The scheme is based on the resonant interaction of a  -type three-level atom with the two cavity modes of a quantized field in the presence of two strong classical fields.

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Recently, the entangled nonlinear coherent states are introduced via replacing coherent states with nonlinear coherent states in entangled coherent states. In this paper, in order to generate the SU(1,1) and SU(2) entangled nonlinear coherent states, an appropriate scheme is presented. The scheme is based on the resonant interaction of a  -type three-level atom with the two cavity modes of a quantized field in the presence of two strong classical fields.
In this paper, we first suggest a scheme for the generation of a particular class of Gilmore–Perelomov-type SU(1,1) coherent states, which may be established as nonlinear coherent states. The proposal employs a two-level atom that interacts with a single-mode quantized cavity field (by using an intensity-dependent Jaynes–Cummings model) and at the same time a strong external classical field. The time evolution of the system first leads to the generation of a superposition of SU(1,1) coherent states. Depending on the initial states of the atom and the field which may be appropriately prepared, and also under the conditions in which the atom is detected (in the excited or ground state) after the occurrence of the interaction, the field will be collapsed to arbitrary combinations or a single class of Gilmore–Perelomov-type SU(1,1) coherent states. Then, it is shown that, following a similar procedure, our proposed scheme can successfully generate various superpositions and, in particular, a single class of SU(2) coherent states, too.
In this paper a scheme for generation of a particular class of Gilmore–Perelomov type of (1,1) entangled states, which may be established as nonlinear entangled states is proposed. To achieve this purpose, the interaction of a system of two-level atoms in a cavity of high quality factor with a single-mode quantized field in the presence of a strong classical field is investigated. It is shown that, by the action of the time evolution operator concerning the interaction Hamiltonian of the above system on the appropriate initial atom-field state, depending on how many two-level atoms are in the cavity, multipartite nonlinear entangled states can be generated.
Following the approach of Solano et al (2003 Phys. Rev. Lett. 90 027903) we propose a scheme for a generation of a few classes of entangled (nonlinear) coherent states. To achieve this purpose, the interaction of a spatially narrow collection of two-level atoms with a quantized field in a high-Q factor cavity in the presence of a strong-driving classical field is studied. We perform appropriate Hamiltonians describing the atom-field interaction by focusing on two particular forms of intensity-dependent functions which are directly related to su (1, 1) and su (2) Lie algebras. It is shown that the dynamical evolution of the considered systems can generate bipartite, tripartite (nonlinear) and more complicated entangled states corresponding to the mentioned groups depending on the number of atoms in the cavity. In the processes of the abovementioned generation schemes, even and odd nonlinear coherent states are produced. In the end, in a particular circumstance with the two-mode quantized field we can turn easily from Jaynes–Cummings to anti-Jaynes–Cummings interactions which brings us to the maximally entangled number state . Finally, to quantify the degree of entanglement of the produced states, the measures of von Neumann and linear entropies are applied.
This paper proposes a scheme for the generation of entangled coherent states for two cavity modes. In the scheme a V-type three-level atom is sent through a two-mode cavity filled with a coherent field. After the atom–cavity interaction and detection of the atomic state the cavity modes may evolve to a superposition of two-mode coherent states. As the scheme is based on resonant atom–cavity interaction, the required interaction time is short, which is important in view of the decoherence. Moreover, additional classical pulses are unnecessary before and after the atom–cavity interaction.