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Annalen der Physik

Entanglement and Entropic Uncertainty of Two Two‐Level Atoms

Nour Zidan, Haytham Bakry, Atta Ur Rahman

Published Feb 2, 2022• 21 citations
Publisher

Abstract

Abstract In a system of two two‐level atoms with a cavity field, the dynamics of entropic uncertainty relations, nonlocality, entanglement, and the degree of mixedness are investigated. In addition to the dynamical map, the interaction between two two‐level systems and the Fock state cavity field, the effects of various parameters, such as temperature dependence, Ising interaction, and dipole–dipole interaction are discussed. It is shown that Ising and dipole–dipole interactions promote entanglement and nonlocal correlations while lowering mixedness and entropy. In order to maintain optimal entanglement and nonlocal correlations, numerical values for improving the current cavity fields are also proposed. The cavity field exhibits both Markovian and non‐Markovian behavior, depending on the type of interaction.

DOI
10.1002/andp.202100555

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The entanglement dynamics of two partially entangled two-level atoms interacting with a single mode vacuum field is investigated.The entanglement dynamics between two partially entangled two-level atoms and the vacuum field is explored by using the quantum re- duced entropy,and that between two two-level atoms is studied by using the quantum relative entropy.The influences of the atomic dipole-dipole interaction intensity on the entanglement dynamics of the system are also discussed.The results show that the system exhibits periodic entanglement dynamics,and the magnitude and the period of entanglement depend on the atomic dipole-dipole interaction.The atom-field maximal entanglement state and atom-atom maximal entanglement state can be preparated by selecting appropriate system parameters and the interaction time.
In this paper, the non-resonant interaction of two two-level atoms with two quantized cavity fields is studied by considering the dipole–dipole interaction between the two atoms. The correlation between the fields has been taken into account and the parametric down conversion is considered. Under certain initial conditions which is determined for the atoms and the fields, the analytical solution for the time-dependent Schrödinger equation is obtained. Employing this solution, we are able to discuss about some physical properties such as atomic population inversion and entanglement between various subsystems, i.e. “atoms–fields” and “atom–atom” by using respectively von Neumann entropy and negativity. It is deduced from the numerical results that, the mentioned quantities can be controlled by the atomic dipole–dipole interaction and detuning parameter, appropriately. The results show that the degree of entanglement between the two atoms is increased due to the presence of dipole–dipole coupling of the atoms at the beginning of atom–field interaction. Furthermore, it is found that, in the non-resonance condition, the so-called entanglement sudden death occurs in the presence of dipole–dipole interaction.
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Quantum systems are inherently open and fragile, leading to the loss of information and quantum properties to the environment. This study investigates the behavior of quantum entanglement (QE), quantum nonlocality (QN), and measurement uncertainty in a two-atom system interacting with a common dissipative thermal reservoir under the Markovian approximation. QE is measured using concurrence, QN through the CHSH-Bell inequality, and uncertainty through the quantum memory-assisted entropic uncertainty relation (QMA-EUR). The findings show that both QE and QN decay as the scaled time and excitation numbers increase, with QE being more resilient. In contrast, QMA-EUR shows an anticorrelation with concurrence and CHSH-Bell violation, increasing as these properties diminish. Adjusting the system initial-state parameters improves QE and CHSH degree of violation, while reducing uncertainty. Over long durations, concurrence and CHSH-Bell violations disappear, while QMA-EUR stabilizes at its maximum value. These results highlight the importance of precise parameter control to enhance quantum features and predict outcomes, especially for bipartite systems initialized in a Werner-like state.