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Journal of the Optical Society of America B

Dynamics of two coupled qubits interacting with two-photon transitions via a nondegenerate parametric amplifier: nonlocal correlations under intrinsic decoherence

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

Published Sep 14, 2020• 4 citations
Publisher

Abstract

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.

DOI
10.1364/josab.405098

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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.
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.
In this paper, we analytically explore two qubits interacting with a coherent harmonic oscillator field under intrinsic noise. The interaction of the uncorrelated two qubits with a harmonic oscillator initially in the superposition of coherent states leads to the generation of nonclassical correlations (NCCs). The NCCs are quantified by local quantum uncertainty (LQU), uncertainty-induced non-locality (UIN), concurrence and Bell’s inequality. It is found that the generated NCCs are enhanced via the intensity coherence and the parameters of the initial harmonic oscillator state. For the even coherent state, the generated NCCs are more robust against the influence of intrinsic noise rate than that the ones of the coherent state. The appearance of the special type of skew-information correlation (in which, LQU and UIN are equal) depends on the superposition of the coherent states. The phenomena of sudden death and birth of entanglement depend not only on the intrinsic noise rate but also on the initial harmonic oscillator field. The generated NCCs could be controlled by adjusting these parameters.
Two two-level systems generated by su(2) algebra are initially prepared in a maximum nonsymmetric Bell state and having no mutual interaction. Each su(2)-system spatially interacts with two-mode cavity field in the nondegenerate parametric amplifier type cast through operators governed by su(1, 1) Lie algebra. An analytical description for the time evolution of the final state of the total system with the effect of intrinsic decoherence is found. Therefore, the robustness of the quantum correlations between the two su(2)-system is investigated by means of geometric quantum discord, measurement-induced nonlocality and negativity. We analyze in some detail the influence of initial coherence intensities, detuning and phase decoherence parameters on the steady-state correlation. We find that the steady-state correlations can be generated and enhanced by controlling the parameters of: the initial coherence intensities, the Bargmman index and the detuning. It is shown that the phenomenon of sudden death and re-birth of entanglement, and the sudden changes of the geometric quantum correlation can be controlled by these parameters. We find that the robustness of the quantum correlation can be greatly enhanced by the Bargmman index and the resonance detuning. Negativity is the measure most susceptible to phase decoherence, while geometric quantum discord and measurement-induced nonlocality are the more robust measures.
In this paper, we use the su(1,1)-algebraic treatment to explore the effects of the intrinsic decoherence in a two-mode cavity containing a two-level atom. Each field is resonant with the qubit through a four-photon process. The role of the intrinsic decoherence and the superposition of the initial generalized Barut-Girardello coherent state on the quantum effects is investigated via different quantifiers as: atomic inversion, linear entropy and negativity. It is found that the non-linearity of the four-photon process leads to generate non-classical effects with a high oscillatory behavior. The superposition of the Barut-Girardello coherent state controls the dynamics of the purity loss and the entanglement. It is found that the nonclassical effects are very sensitive to the nonlinear interactions between the qubit and the two-mode cavity.
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.
This study analytically explored two coupled two-level atomic systems (TLAS) as two qubits interacting with two modes of an electromagnetic field (EMF) cavity via two-photon transitions in the presence of dipole–dipole interactions between the atoms and intrinsic damping. Using special unitary su(1,1) Lie algebra, the general solution of an intrinsic noise model is obtained when an EMF is initially in a generalized coherent state. We investigated the population inversion of two TLAS and the generated quantum coherence of some partitions (including the EMF, two TLAS, and TLAS–EMF). It is possible to generate quantum coherence (mixedness and entanglement) from the initial pure state. The robustness of the quantum coherence produced and the sudden appearance and disappearance of coherence depended not only on dipole–dipole coupling but also on the intrinsic noise rate. The growth of mixedness and entanglement may be enhanced by increasing dipole–dipole coupling, leading to more robustness against intrinsic noise.