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Physical Review A

Effects of the dipole-dipole interaction on atomic dynamics inM-photon processes

Zhi‐Ming Zhang, Lei Xu, Zhenfei Luo

Published Feb 1, 1993• 9 citations
Publisher

Abstract

The effects of the dipole-dipole interaction on atomic dynamics in M-photon processes are studied. The general expression for atomic inversion in an arbitrary initial field state is presented. We find that, generally, there are three series of collapse revivals. If the dipole-dipole interaction can be neglected, there will be two series of collapse revivals. If the field is strong enough, there will be only one series of collapse revival; this is similar to the one-atom case.

DOI
10.1103/physreva.47.1557

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The effects of the dipole-dipole interaction on atomic dynamics in M-photon processes are studied. The general expression for atomic inversion in an arbitrary initial field state is presented. We find that, generally, there are three series of collapse revivals. If the dipole-dipole interaction can be neglected, there will be two series of collapse revivals. If the field is strong enough, there will be only one series of collapse revival; this is similar to the one-atom case.
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.
A study of multiatom effects, i.e., dipole-dipole interactions and phase-interrupting collisions between atoms in the Jaynes-Cummings model, is presented here. For this purpose we consider two identical two-level atoms interacting with a single-mode field in a lossless cavity and study the effect of the dipole-dipole interaction between these two atoms on the collapse-and-revival phenomenon of Rabi oscillations by calculating the analytical expression of the excitation probability in the coherent field. We also consider another situation in which a single atom interacting with a single-mode field in a damped cavity undergoes phase-interrupting collisions. The effect of phase-interrupting collisions along with the usual cavity damping on the collapse-and-revival phenomenon has been explicitly calculated using the dressed-atom approach under the secular approximation.
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The state evolution in the two-photon atom-field interaction with large initial fields is studied. It is shown that under certain conditions, for the initial coherent field, at one-quarter and three-quarters of the revival time the atom is converged into unique pure states, and at the revival time both the atom and field return to their initial states. The possibility for the field macroscopic superposition states to be generated is discussed. The effects of the cavity damping, photon statistics, and dynamic Stark shifts are investigated. Our results give some further insight into the validity of the effective two-photon Hamiltonian which neglects the Stark shifts.
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.