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Symmetry

Fisher and Skew Information Correlations of Two Coupled Trapped Ions: Intrinsic Decoherence and Lamb-Dicke Nonlinearity

Abdel‐Baset A. Mohamed, Ahmed Farouk, Mansour F. Yassen, Hichem Eleuch

Published Nov 24, 2021• 6 citations
Publisher

Abstract

It is well known that many quantum information processing methods in artificial atoms depend largely on their engineering properties and their ability to generate quantum correlations. In this paper, we investigate the non-classical correlation dynamics of two trapped ions by using local quantum Fisher information, local quantum uncertainty, as well as logarithmic negativity. The system engineering is designed such that the two-trapped-ions work as two diploe-coupled qubits in a Lamb-Dicke regime. The center-of-mass vibrational modes are initially in coherent/even coherent states. It is found that the two-trapped-ions correlations can be controlled by the Lamb-Dicke nonlinearity, the nonclassicality effect of the initial center-of-mass vibrational mode, as well as the trapped-ion coupling and the intrinsic decoherence. The sudden changes in the non-classical correlations and their stability are shown against Lamb-Dicke nonlinearity, the nonclassicality, the trapped-ion coupling, and the intrinsic decoherence.

DOI
10.3390/sym13122243

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It is well known that many quantum information processing methods in artificial atoms depend largely on their engineering properties and their ability to generate quantum correlations. In this paper, we investigate the non-classical correlation dynamics of two trapped ions by using local quantum Fisher information, local quantum uncertainty, as well as logarithmic negativity. The system engineering is designed such that the two-trapped-ions work as two diploe-coupled qubits in a Lamb-Dicke regime. The center-of-mass vibrational modes are initially in coherent/even coherent states. It is found that the two-trapped-ions correlations can be controlled by the Lamb-Dicke nonlinearity, the nonclassicality effect of the initial center-of-mass vibrational mode, as well as the trapped-ion coupling and the intrinsic decoherence. The sudden changes in the non-classical correlations and their stability are shown against Lamb-Dicke nonlinearity, the nonclassicality, the trapped-ion coupling, and the intrinsic decoherence.
In this paper, we explore the nonlinear dynamics of two dipole-coupled-trapped ions in the Lamb–Dicke regime. The dynamics of the generated two-trapped-ions correlations under intrinsic decoherence is quantified by Bell function, the uncertainty-induced nonlocality, and the concurrence. We investigate the effects of the Lamb–Dicke nonlinearity, the intrinsic decoherence, and the two-trapped-ions coupling. It is found that the two-trapped-ions state has different nonlocal correlations. These correlations can be controlled. In the absence of decoherence, the nonlocal correlations can be enhanced by the Lamb–Dicke nonlinearity and the two-trapped-ions coupling. The stable value and the sudden death-birth phenomenon of the entanglement can be apperceived due to the increase of the Lamb–Dicke nonlinearity. The intrinsic decoherence reduces and stabilizes the nonlocal correlations. They are more pronounced with large Lamb–Dicke values. The decoherence effects are reduced by the strong Lamb–Dicke nonlinearity.
The engineering properties of trapped ions and their capacity to engender numerous quantum information resources determine many aspects of quantum information processing. We devise a setup of coherent and even coherent fields acting on two trapped ions to generate quantum memory, non-locality, and entanglement. Various effects, such as intrinsic decoherence, Lamb–Dicke regime, and dipole–dipole interaction are investigated. The inter-coupling of trapped ions, as well as the generation and dynamics of correlations between them, are analyzed. Using quantum memory assisted entropic uncertainty, trace-norm measurement induced non-locality, and concurrence, we find that the coherent and even coherent fields successfully generate non-local correlations in trapped-ions, with the latter being more resourceful for the dynamics and preservation of the non-local correlations. Furthermore, we observe that the entropic uncertainty and the trace norm induced non-locality present symmetrical dynamics. The dipole–dipole interaction improves correlation’s generation, robustness, and entropic uncertainty suppression.
In this paper, we study a Hamiltonian system constituted by two coupled two-level atoms (qubits) interacting with a nonlinear generalized cavity field. The nonclassical two-qubit correlation dynamics are investigated using Bures distance entanglement and local quantum Fisher information under the influences of intrinsic decoherence and qubit-qubit interaction. The effects of the superposition of two identical generalized coherent states and the initial coherent field intensity on the generated two-qubit correlations are investigated. Entanglement of sudden death and sudden birth of the Bures distance entanglement as well as the sudden changes in local Fisher information are observed. We show that the robustness, against decoherence, of the generated two-qubit correlations can be controlled by qubit-qubit coupling and the initial coherent cavity states.
The dynamics of two charged qubits containing Josephson Junctions inside a cavity are investigated under the intrinsic decoherence effect. New types of quantum correlations via local quantum Fisher information and Bures distance norm are explored. We show that we can control the quantum correlations robustness by the intrinsic decoherence rate, the qubit-qubit coupling as well as by the initial coherent states superposition. The phenomenon of sudden changes and the freezing behavior for the local quantum Fisher information are sensitive to the initial coherent state superposition and the intrinsic decoherence.
This study investigates two-qubit local quantum Fisher information correlation (LQFI), entanglement of formation (EoF), and two-qubit Jensen–Shannon coherence as a result of cavity–qubit coupling via intensity dependent and qubit–qubit interactions. Initially, the cavity is filled with coherent and even coherent fields, and the two-qubit state is pure. The cavity–qubit intensity dependent interaction, in the presence of intrinsic decoherence, can produce two-qubit local quantum Fisher information, entanglement of formation, and Jensen–Shannon coherence. This ability depends on dipole–qubit interactions, intrinsic decoherence, and initial cavity sates. The phenomena of sudden changes emerge in the dynamics behavior of the local quantum Fisher information, whereas the phenomenon of sudden birth–death occurs during the entanglement of formation dynamics. These phenomena can be enhanced by modifying the initial coherent field parameters, the mean photon number, and the non-classicality. The dipole qubit–qubit interaction improves the generated two-qubit correlation and coherence, while intrinsic decoherence decreases and stabilizes the generated two-qubit correlation and coherence. For a small initial coherent field intensity and dipole qubit–qubit interaction, the LQFI and EoF non-local correlations grow while the two-qubit Jensen–Shannon coherence diminishes. The qubit–qubit interaction coupling and the initial coherent field intensity can improve the produced stationary LQFI and EoF correlations and Jensen–Shannon coherence in the presence of the intrinsic decoherence.
In this study, an analytical solution for a novel intrinsic noise model represented by two coupled qubits inside a cavity, the S u ( 1 , 1 ) and S u ( 2 ) Lie group, is investigated. Each qubit interacts with a two-mode parametric amplifier through a nondegenerate two-photon process when the two-mode system is initially in a superposition of a generalized Barut–Girardello coherent state. The nonlinearity of the interaction and the initial two-mode fields lead to the generation of different quantum correlations (QCs), which are measured by log-negativity, uncertainty-induced nonlocality, and local quantum uncertainty (LQU). The generated QC of the interaction depends not only on the two-qubit coupling but also on the intrinsic noise and the initial coherent intensity. Our results show that the ability of the two-qubit coupling to protect and enhance the robustness and generation of the QCs depends on the superposition and the coherent intensity of the initial S u ( 1 , 1 ) state. Furthermore, the sudden birth and death of the log-negativity and the sudden variations of the LQU depend on the intrinsic noise and the two-qubit coupling.