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OSA Workshop on Entanglement and Quantum Decoherence

Entanglement of two qubits near plasmonic band gap

M. AI-Amri

Published Jan 1, 2008• 0 citations
Publisher

Abstract

We study the quantum entanglement of a two-qubit system interacting with single-frequency plasmonic excitations. Under the exact resonance condition and in the presence of both the Stark shift and phase shift, an exact solution of the time evolution of the unitary operator is obtained. Employing this solution an analytical expression for time evolution of the negative eigenvalues for the partial transposition of the density operator is obtained. Numerical investigations are carried out for the entanglement with different values of Stark shift and plasmonic excitations. It is shown that, the entanglement is affected by the plasmonic excitation and the Stark shift.

DOI
10.1364/weqd.2008.p1

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We study the quantum entanglement of a two-qubit system interacting with single-frequency plasmonic excitations. Under the exact resonance condition and in the presence of both the Stark shift and phase shift, an exact solution of the time evolution of the unitary operator is obtained. Employing this solution an analytical expression for time evolution of the negative eigenvalues for the partial transposition of the density operator is obtained. Numerical investigations are carried out for the entanglement with different values of Stark shift and plasmonic excitations. It is shown that, the entanglement is affected by the plasmonic excitation and the Stark shift.
An exact solution of the time-dependent master equation that describes the evolution of two two-level qubits (ions or atoms) within a perfect cavity for the case of multiphoton transition and in the presence of both the Stark shift and phase shift is obtained. Employing this solution, the significant features of the entanglement when a second qubit is allowed to interact with cavity mode and becomes entangled with the first qubit are investigated in the context of the measure defined by negative eigenvalues for the partial transposition of the density operator. The effects of Stark shift, distance between the two qubits, and an instantaneous phase shift experienced by the second qubit on the entanglement and probability amplitudes are indicated. It has been shown that the entanglement as well as the intensity are markedly affected by different parameters when the nonlinear two-photon process is involved. Moreover, the quasiprobability distribution function is investigated before and after the sudden phase shift experienced by the second qubit. We believe that this may throw some light on the question of the entanglement of multi-qubit systems.
Considering a quantum model consisting of two effective two-level atoms and a single-mode cavity, this paper investigates the entanglement dynamics between the two atoms, and studies the effect of the Stark shift on the entanglement. The results show that, on the one hand the atom–atom entanglement evolves periodically with time and the periods are affected by the Stark shift; on the other hand, the two atoms are not disentangled at any time when the Stark shift is considered, and for large values of the Stark shift parameter, the two atoms can remain in a stationary entangled state. In addition, for the initially partially entangled atomic state, the atom–atom entanglement can be greatly enhanced due to the presence of Stark shift. These properties show that the Stark shift can be used to control entanglement between two atoms.
In this paper, we investigated the dynamics of atomic entanglement in a quantum system consisting of two identical two-level atoms (qubits) resonantly interacting with a mode of a thermal cavity field through degenerate two-photon transitions, in the presence of a Stark energy level shift. An analytical expression is obtained for the atom entanglement (negativity) parameter for separable and entangled initial states of atoms. The influence of the Stark shift on the degree of atom-atom entanglement is considered. It is established that the Stark shift leads to a significant increase in the degree of atom entanglement in the case of separable initial states of atoms and to stabilization of atomic entanglement in the case of entangled initial states of atoms.
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In the article we consider the influence of dynamical Stark shift on entanglement degree of two atoms with degenerate two-photon transitions successively passing an ideal one-mode cavity. We suppose that the field be prepared in vacuum state and the atoms be prepared in coherent superposition of excited and ground states. Thus it was also supposed that atoms fly by the cavity for identical time. On the basis of exact expression of evolution operator we carried out atom-atom entanglement for different values of two-atom coherence parameters and different values of cavity flight time. It is shown that Stark shift of energy levels can be used for effective control on a degree of atomic entanglement.
Multi-qubit entanglement is of paramount importance to perform truly secure quantum optical communication operations. In this work, we present efficient long-range entanglement mediated by plasmonic waveguides operating at their cut-off frequency, where they exhibit an effective epsilon-near-zero (ENZ) response. Only the excited ENZ mode at plasmonic waveguides has a strong and homogeneous electric field distribution compared to different modes excited at groove and rod waveguides, resulting in an efficient two- and multi-qubit entanglement that can persist over extended time periods and long distances. Efficient multipartite entanglement from three equidistantly arranged two-level quantum emitters (qubits) inside the ENZ waveguide is also demonstrated by using three different multi-qubit entanglement criterions, i.e., pairwise concurrence, negativity, and genuine multipartite entanglement. The findings of this work stress the importance of ENZ plasmonic waveguides as an ideal nanophotonic platform to support efficient quantum optical effects.