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arXiv:1709.06778 · Journal of the Optical Society of America B

Entanglement of two two-level atoms mediated by a cylindrical optical black hole

Mahnaz Tavakoli, Ehsan Amooghorban

Published Dec 18, 2017• 5 citations
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Abstract

We consider the dynamics of a system consisting of two two-level atoms interacting with the electromagnetic field near a cylindrical optical black hole. We obtain the reduced density operator of the two-atom system in the weak coupling regime for the case where one atom is in the excited state and the other in the ground state. The time evolution of the negativity between the atoms is discussed for two nonresonance and resonance cases. In both cases, we show that the two atoms can become entangled due to the indirect interaction mediated through the optical black hole.

DOI
10.1364/josab.35.000156

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We consider the dynamics of a system consisting of two two-level atoms interacting with the electromagnetic field near a cylindrical optical black hole. We obtain the reduced density operator of the two-atom system in the weak coupling regime for the case where one atom is in the excited state and the other in the ground state. The time evolution of the negativity between the atoms is discussed for two nonresonance and resonance cases. In both cases, we show that the two atoms can become entangled due to the indirect interaction mediated through the optical black hole.
We consider radiative processes of a quantum system composed by two identical two-level atoms in a black-hole background. We assume that these identical two-level atoms are placed at fixed radial distances outside a Schwarzschild black hole and interacting with a quantum electromagnetic field prepared in one of the usual vacuum states, namely, the Boulware, Unruh, or Hartle-Hawking vacuum states. We study the structure of the rate of variation of the atomic energy. The intention is to identify in a quantitative way the contributions of vacuum fluctuations and the radiation reaction to the entanglement generation between the atoms as well as the degradation of entangled states in the presence of an event horizon. We find that for a finite observation time the atoms can become entangled for the case of the field in the Boulware vacuum state, even if they are initially prepared in a separable state. In addition, the rate of variation of atomic energy is not well behaved at the event horizon due to the behavior of the proper accelerations of the atoms. We show that the thermal nature of the Hartle-Hawking and Unruh vacuum state allows the atoms to get entangled even if they were initially prepared in the separable ground state.
We study the entanglement between two identical two-level atoms located near an ideal model of invisibility cloaks by monitoring the time evolution of the concurrence measure. We obtain the reduced density operator of the atomic subsystem based on a canonical quantization scheme presented for the electromagnetic field interacting with atomic systems in the presence of an anisotropic, inhomogeneous, and absorbing magnetodielectric medium. It is shown that two atoms, which are prepared initially in an unentangled state, are correlated in the weak coupling regime via the spontaneous emission and the dipole-dipole interaction of two atoms mediated by the invisibility cloak. We therefore find that the invisibility cloak, independent of the hidden object, works fairly well at frequencies far from the resonance frequency of the object and the cloak, whereas near the resonance frequency the hidden object becomes detectable due to a sharp reduction of the concurrence.
Abstract Entanglement between two identical two-level atoms (qubits) that interact nonresonantly with the thermal field of a single-mode ideal resonator via effective degenerate two-photon transitions is studied. Based on an exact solution for the time-dependent density matrix, negativity is calculated as a measure of atom entanglement. The effect detuning between the atomic frequencies and the doubled frequency of the resonator field has on the dynamics of qubit entanglement in cases of separable and entangled initial atomic states is investigated.
This work presents the entanglement between an electromagnetic field and two-level atom situated inside a quantum optical system. Our optical model is based on cylindrical tube with a hole diameter of the order of nanoscale which leads to only the lowest order mode can exist. Numbers of the statistical features of effective Hamiltonian such as the temporal evolution of the atomic inversion and the von Neumann entropy are evaluated. We have evaluated the atomic inversion and we demonstrate that the atom still in maximal entangled state when the radius of tube a is large. We have used the von Neumann entropy to measure the degree of that entanglement. The results illustrate that the effect of the radius of tube a changes the quasi-period of the field entropy and therefore the entanglement process.
The exact dynamics of a model consisting of two two-level atoms interacting with the electromagnetic field mode of an ideal resonator through degenerate Raman transitions are found for coherent and thermal field states. The exact solution is used to calculate atom-atom negativity. It is shown that for separable initial states of atoms, their interaction with the resonator field does not lead to the occurrence of atom-atom entanglement. It was found that for the Bell initial states of atoms in the case of a coherent resonator field, the effect of sudden death of entanglement takes place for large average values of the number of photons in the resonator, while in case of thermal noise, this effect is absent for any intensities of the resonator field.
The center-of-mass motion of two two-level atoms coupled to a single damped mode of an electromagnetic resonator is investigated. For the case of one atom being initially excited and the cavity mode in the vacuum state, it is shown that the atomic time evolution is dominated by the appearance of dark states. These states, in which the initial excitation is stored in the internal atomic degrees of freedom and the atoms become quantum mechanically entangled, are almost immune against photon loss from the cavity. Various properties of the dark states within and beyond the Raman-Nath approximation of atom optics are worked out.