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انجمن اپتیک و فوتونیک ایران

Generation of Nonlinear Entangled States in a Quantized Field by Strong-Field Approach

Roohollah Daneshmand, Mohammad Kazem Tavassoly

Published Feb 15, 2014• 0 citations
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Abstract

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.

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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.
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.
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.
We propose the methods of generating multipartite entanglement by considering the interaction of a system of N two-level atoms in M cavities of high quality factor with a strong classical driving field. It is shown that, with the cavity detuning, the applied driving field detuning and vacuum Rabi coupling, we can produce an entangled coherent state in two single-mode cavities and generate the entangled coherent cluster states in two bimodal vacuum cavities. Tuning these parameters also allows us to acquire the anti-Jaynes–Cummings (AJC) interaction, with which we can generate the maximally two-photon entangled states, and the two-atom and the two-photon entangled cluster states.
The proposed schemes in this paper involve the interaction of a two-level atom with single- or two-mode quantized cavity fields (for different purposes) in the presence of a classical field. Indeed, following the path of Solano et al. in [Phys. Rev. Lett.90, 027903 (2003)], the behavior of the entire atom-field system may be described by the Jaynes–Cummings (JC)- and anti-Jaynes–Cummings (anti-JC)-like models. It is illustrated that, under specific conditions, the effective Hamiltonian of the system can be switched from a JC- to an anti-JC-like model. During the process, the two-level atom in the cavity is alternately affected by the above two effective interactions. Ultimately, after the occurrence of the desired interactions in appropriate setups, the cavity field will arrive at a specific superposition of number states, a fixed number state, and in particular, two-mode binomial field states. Moreover, the entanglement property of the two-mode binomial state is investigated by evaluating the entropy criterion. While there exist various proposals for preparation of number states and their superpositions in the literature, our scheme has the advantage that it is independent of the detection of the atomic state after the interaction occurs.