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Modern Physics Letters B

The influence of atomic dipole–dipole interaction on the dynamics of the population inversion and entanglement of two atoms interacting non-resonantly with two coupled modes field

Elham Faraji, Hamid Reza Baghshahi, Mohammad Kazem Tavassoly

Published Feb 15, 2017• 14 citations
Publisher

Abstract

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.

DOI
10.1142/s0217984917500385

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Jan 29, 2014•1 citation
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.
In this paper we study the interaction between two two-level atoms with a two-mode quantized field in the presence of damping. Dipole–dipole interaction between the two atoms and the correlation between the two modes of field are also taken into account. To solve the model, using appropriate transformations, we reduce the considered model to a well-known Jaynes–Cummings model. After finding the analytical solution for the atom–field system, the effects of damping, field–field correlation and atomic dipole–dipole interaction on the entanglement between atoms and population inversion are investigated, numerically. It is observed that the dynamical behavior of the degree of entanglement for damped systems, in relatively large domains of time, takes a low but constant value adequately far from the beginning of the interaction. In addition, it is found that the value of population inversion after the initial oscillations takes negative values for damped systems and eventually vanishes by increasing time. Also, it is seen that simultaneous presence of both dipole–dipole interaction and field–field correlation provides typical collapse–revival phenomenon in the time-behavior of atomic inversion.
Recalling that counter rotating terms (CRTs) in atom–field interaction are not always ignorable, particularly in the strong coupling regimes of atom–field systems, in this paper we are going to study the interaction between two qubits (two-level atoms) with a two-mode field in a high quality cavity by considering CRTs while the dipole–dipole (D–D) interaction is also taken into account. Indeed, by performing an appropriate dynamical Hamiltonian associated with the Jaynes–Cummings and anti-Jaynes–Cummings terms, as well as the D–D interaction for the system, we solve the corresponding time-dependent Schrödinger equation with specific initial conditions for atoms and field. In the continuation, concurrence, as an appropriate measure of the degree of entanglement of the two qubits, and atomic population inversion of the qubits, as the rate of energy exchange between atoms and field, are evaluated. Meanwhile, we investigate the influence of CRTs and D–D interaction (as well as other involved parameters in the model interaction) on the mentioned quantities. Our numerical results indicate that collapse-revival phenomenon can be observed in the absence of D–D interaction with or without rotating wave approximation, however, CRTs cause an increase or decrease in the number of collapse-revivals in a finite interval of time, depending on the chosen parameters. In fact, by entering the D–D interaction term, this phenomenon is destroyed and the time behaviour of the quantities experiences irregular oscillations. Noticing that the initial field is considered in the vacuum state, the occurrence of collapse-revival in the population inversion of the two qubits is an interesting feature of this work. As is shown, the degree of entanglement and atomic population inversion of the qubits can generally be tuned, and the death of entanglement can be prevented, both by adjusting the evolved parameters in the model.
Our aim is to present an analytical solution for the quantum optics model that has two two-level atoms interacting together and interacting with an intensity-dependent quantized field. The quantized field is initially in binomial state and based on the Lamb–Dicke parameter and associated Laguerre polynomials. While two atoms are symmetric and initially in superposition state. Besides, the quantum entanglement between the quantum system components under the effect of the parameters of detuning, coupling, binomial, Lamb–Dicke and the initial state of the model is discussed. Several phenomena have been clearly observed and analyzed, such as entanglement sudden death (ESD) followed by entanglement sudden birth (ESB) in the concurrence and the negativity curves, and long-lived quantum coherence in the von Neumann entropy curve. In addition, the presence of revivals and collapses in the atomic population inversion curves has been figured out. Our analysis aims to help the scientists to determine the critical values required of quantum system parameters to control entanglement dynamics.
We have investigated the dynamics of entanglement of two identical qubits non-resonantly interacting with one mode of a thermal electromagnetic field in a lossless cavity in the presence of a direct dipole-dipole interaction. On the basis of the exact solution the evolution equation the negativity for qubits has been found. Numerical simulation of the negativity for various model parameters has been carried out. It has been shown that the interaction of qubits with the cavity thermal field can lead to their entanglement. It has been established that the detuning and dipole-dipole interaction of qubits can be used to manipulate and control the degree of their entanglement.
We investigate the time evolution and asymptotic behavior of a system of two two-level atoms (qubits) interacting off-resonance with a single mode radiation field. The two atoms are coupled to each other through dipole-dipole as well as Ising interactions. An exact analytic solution for the system dynamics that spans the entire phase space is provided. We focus on initial states that cause the system to evolve to entanglement sudden death (ESD) between the two atoms. We find that combining the Ising and dipole-dipole interactions is very powerful in controlling the entanglement dynamics and ESD compared with either one of them separately. Their effects on eliminating ESD may add up constructively or destructively depending on the type of Ising interaction (Ferromagnetic or anti-Ferromagnetic), the detuning parameter value, and the initial state of the system. The asymptotic behavior of the ESD is found to depend substantially on the initial state of the system, where ESD can be entirely eliminated by tuning the system parameters except in the case of an initial correlated Bell state. Interestingly, the entanglement, atomic population and quantum correlation between the two atoms and the field synchronize and reach asymptotically quasi-steady dynamic states. Each one of them ends up as a continuous irregular oscillation, where the collapse periods vanish, with a limited amplitude and an approximately constant mean value that depend on the initial state and the system parameters choice. This indicates an asymptotic continuous exchange of energy (and strong quantum correlation) between the atoms and the field takes place, accompanied by diminished ESD for these chosen setups of the system. This system can be realized in spin states of quantum dots or Rydberg atoms in optical cavities, and superconducting or hybrid qubits in linear resonators.
The entanglement of two dipole-coupled superconducting flux qubits with degenerate and nondegenerate twophoton transitions interacting with one-mode or two-mode field in lossless cavity has been investigated. The influence of dipole-dipole interaction on the entanglement between two qubits for different initial atom-field entangled states has been considered. The results show that the entanglement between two artificial atoms can be increased by means of dipole-dipole interaction and for some initial states the entanglement sudden death effect can be weakened.