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Evolution of the two-mode entangled states with an atomic coupler

Gharib Subhi Mahmoud Ahmed, Azeddine Messikh, Taher S. Hassan

Published Feb 1, 2016• 0 citations
OpenAlex

Abstract

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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arXiv:1212.4339•Dec 18, 2012•0 citations
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
We investigate the entanglement transfer from the two-mode squeezed state (TMS) to the atomic system by studying the dependence of the negativity on the coupling between the modes of the waveguides. This study is very important since the entanglement is an important feature which has no classical counterpart and it is the main resource of quantum information processing. We use a linear coupler which is composed of two waveguides placed close enough to allow exchanging energy between them via evanescent waves. Each waveguide includes a localized atom.
We present a two-mode squeezed Jaynes–Cummings model, built upon the formalism of pair coherent states (PCSs), to investigate the dynamics of a two-level atom interacting with a two-mode quantized field. By solving the time-dependent Schrödinger equation under the rotating-wave approximation, we elucidate the system’s quantum evolution, with particular emphasis on how the squeezing degree and photon number difference modulate atomic population inversion and entanglement. We further quantify the nonclassical traits of the two-mode squeezed PCSs via Mandel’s parameter and the violation of the Cauchy–Schwarz inequality, highlighting their sensitivity to model parameters. These findings illuminate the subtle interplay of squeezing, photon statistics, and entanglement in advanced quantum optical systems.
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.
We investigate quantum nonlocality dynamics of a three-level atom and a class of two-mode non-classical states (including the entangled coherent state, the pair coherent state and the two-mode squeezed state) in the non-degenerate two-photon Jaynes-Cummings model. It is shown that the time evolution of the Bell nonlocality for the case of the entangled coherent state is closely related to the average number of photons in the two-mode field. For the cases of the pair coherent state and the two-mode squeezed state, the effect of Bell nonlocality sudden death is demonstrated, and the absolute value of the 〈BCHSH〉 exhibits exact periodic collapses and revivals.
The dynamics of the Jaynes-Cummings interaction of a two-level atom interacting with a single mode of the radiation field is investigated, as the state of the field is gradually changed from a coherent state to a squeezed coherent state. The effect of mild squeezing on the coherent light is shown to be striking: the photon number distribution gets localized and it peaks maximally for a particular value of squeezing. The atomic inversion retains its structure for a longer time. The mean linear entropy shows that the atom has a tendency to get disentangled from field within the collapse region and also in the revival region, for mild squeezing. These properties are absent for the case of a coherent state or for an excessively squeezed coherent state. We also elucidate a connection between these properties and the photon statistics of the mildly squeezed coherent state; these states have the minimum variance and are also maximally sub-Poissonian.
The Jaynes-Cummings model (JCM) describes the interaction of a two-level atom with a single quantised field mode in an optical cavity. In this BSc project we derive the basic Rabi model Hamiltonian and show how it leads to the JCM Hamiltonian. The results are then used to analyse the general time evolution of a bipartite atom-field system and its properties, such as entanglement. We extend a scheme developed by Browne and Plenio [D. Browne and M. B. Plenio, Physical Review A, vol. 67, no. 1, Jan. 2003.] to entangle two cavities that interact with an atom. Our scheme allows to produce states that are arbitrarily close to a Bell state with a success probability greater than 0.75, whereas the success rate of the original method tends to 0 for perfect fidelity. Further, we extend both schemes by allowing the atom or the cavity to be in a thermal state and find that the fidelity of the produced states is reduced with increasing temperature. Finally, we apply our scheme to quantum teleportation, where we find that the fidelity of the teleported state compared to the original state also decreases as the temperature is increased.