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Optical and Quantum Electronics

Atomic non-locality dynamics of two moving atoms in a hybrid nonlinear system: concurrence, uncertainty-induced non-locality and Bell inequality

A.‐B. A. Mohamed, Eied Mahmoud Khalil

Published Oct 13, 2021• 6 citations
Publisher

Abstract

Abstract The paper explores the non-locality dynamics of two moving atoms in a hybrid nonlinear system, which describes a nondegenerate parametric amplifier cavity containing two moving atoms with Stark shift interactions. Based on the Bell function, uncertainty-induced non-locality and concurrence, the two moving atomic non-locality is calculated numerically, when the cavity is filled initially by pair coherent fields. The results showed that the hybrid nonlinear qubit-cavity interactions have a high ability to generating quantum correlations. The amount of the generated quantum correlation can be improved and accelerated significantly with the increase of the time-dependent qubit location parameter. The increase of the Stark shift ratio and the difference between the mean-number photons of the two cavity fields leads to a clear deterioration of the generated quantum correlation.

DOI
10.1007/s11082-021-03264-5

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Abstract The paper explores the non-locality dynamics of two moving atoms in a hybrid nonlinear system, which describes a nondegenerate parametric amplifier cavity containing two moving atoms with Stark shift interactions. Based on the Bell function, uncertainty-induced non-locality and concurrence, the two moving atomic non-locality is calculated numerically, when the cavity is filled initially by pair coherent fields. The results showed that the hybrid nonlinear qubit-cavity interactions have a high ability to generating quantum correlations. The amount of the generated quantum correlation can be improved and accelerated significantly with the increase of the time-dependent qubit location parameter. The increase of the Stark shift ratio and the difference between the mean-number photons of the two cavity fields leads to a clear deterioration of the generated quantum correlation.
We have explored the non-locality of two qubits interacting time-dependently with a nondegenerate parametric amplifier cavity fields in the presence of the Stark shift interaction term. The time-dependent two-qubit reduced density matrix is calculated numerically when the cavity fields are initially in two entangled coherent states. We investigate the non-locality via local Fisher information and negativity. It is shown that, the generated non-locality depends on the time-dependent two-qubit location, the Stark shift interaction, the difference between the mean photon numbers of the two cavity fields as well as the initial intensity coherent fields. The agreement of the generated correlations presented by the local Fisher information and the negativity depends on the physical parameters. The Stark shift non-linearity and the difference between the mean photon numbers leads to reducing the generated correlations. The local Fisher information is more robust against the Stark shift interaction than the negativity.
Abstract This work delves into the nonlocal correlation dynamics of the maximum-Bell nonlocality (MBN), uncertainty-induced nonlocality (UIN), and concurrence of two two-level atoms having time-dependent atomic locations within Tavis-Cummings model. By considering a scenario where the pure two qubits resonantly interact with an even coherent cavity field through a two-photon transition, we explore the nonlocal correlation dynamics of both moving and stationary two-atom configurations under varying conditions and coupling parameters. Our findings reveal that the coherent cavity induces the successful generation of nonlocal correlations between atoms in both modes, with moving atoms exhibiting higher and symmetrical nonlocal correlations. Interestingly, dynamical maps showcase distinct behaviors for atoms at rest, exhibiting precocity at higher atom-cavity strengths. Moreover, equal coupling strength results in lower quantum correlations. The UIN measure emerges as the most robust quantum function, showing enhancements with sustained unequal coupling strengths, contrasting with the MBN and concurrence. These insights offer a nuanced understanding of nonlocal correlations in the Tavis-Cummings model, essential for advancing quantum information science and technology.
The nonlinearity effect on the various formed quantum correlations between two atoms interacting locally with a bimodal cavity is explored in this work. The local quantum Fisher information, local quantum uncertainty, and negativity are used to investigate the quantum correlation’s sensitivity to the cavity modes characteristics. It is demonstrated that when the ratio of the Stark shift of the two modes increases, the atomic quantum correlations rise. During the time intervals of sudden death negativity entanglement, the three two-atom correlation quantifiers reveal that the two-atom system can contain local Fisher information and local uncertainty correlations. The Stark shift may be utilized to amplify the produced atomic correlation, while the Kerr-like medium can be used to suppress it. The regularity, the amount of generated atomic correlations, and their immunity to the Stark shift as well as the Kerr-like medium non-linearities are improved when the mean photon number is increased. As a result, the cavity modes’ nonlinear parameters might be utilized as a controller to optimize atomic quantum correlations.
Studying the ability of atom-photon interactions, especially in two two-level atomic systems, to generate quantum information resources has recently become an important research topic in quantum information science. Therefore, this paper explores the ability of two moving atoms coupling with a coherent field through a two-photon transition to generate atomic quantum correlations by using local quantum uncertainty (LQU), local quantum Fisher information (LQFI) as well as logarithmic negativity (LN). Schrödinger equation is used to obtain the time evolution of the atom-cavity-atom interactions with an initial coherent cavity state and an initial atomic uncorrelated pure state. The generation of atomic LQU, LQFI, and LN correlations are exactly examined under the unitary interaction parameter effects, including the atom-cavity coupling strengths, the cavity field half-wave number, and the initial coherent state intensity. The atom-cavity-atom interaction parameters lead to notable changes in the amplitudes, speed, and regularity of the LQU, LQFI, and LN dynamics, which can be enhanced by increasing the initial coherent intensity. The cavity field half-wave number leads to generating atomic quantum correlations with regular oscillatory behavior. The sudden death-birth phenomenon of the logarithmic negativity depends on the atom-cavity-atom interaction and the atomic location parameter.
Abstract In this paper, we study the dynamics of two coupled qubits interacting with a two-mode parametric amplifier cavity through the nonlinear interactions of the photon processes under the intrinsic decoherence. The nonlinear unitary interactions lead to generating different types of nonlocal correlations via Bell nonlocality, trace-norm measurement-induced non-locality (MIN), and Bures-distance entanglement. Based on the intrinsic decoherence, the two-qubit states have stationary amounts of the MIN-correlation and Bures distance entanglement with more stability. It is found that the qubit–qubit interaction coupling is affected as additional decoherence. It leads to more oscillations and stability. The enhancement of the amount of the generated nonlocal correlations depends on the superposition of Barut-Girardello coherent states. The phenomenon of sudden birth/death and the Bell non-locality can be enhanced when the two-mode parametric amplifier cavity is initially prepared in the coherent states.
An analytical solution is obtained when the Kerr medium and Stark shift are considered as nonlinear interaction terms to the system containing two-qubit and two-mode electromagnetic field from the parametric amplifier. Dynamics of the population inversion, cavity–qubit and qubit–qubit entanglements are analyzed under the unitary cavity–qubit interaction, the Kerr medium and the Stark shift. The population inversion of a qubit presents periodic revivals and collapses. The results show that the entanglement and the population inversion as well as the inversion have the same stable intervals, that is, the collapse intervals. It is found that the Kerr medium and the Stark shift may lead to reduction of the periods and the amplitudes of the population inversion and the cavity–qubit/qubit–qubit entanglement. The deteriorated qubit–qubit/cavity–qubit entanglement and the population inversion, due to the Kerr medium, may be increased by increasing the Stark shift and vice versa.