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Journal of Optics B Quantum and Semiclassical Optics

Resonant interaction modified by the atomic environment

Isabel Sainz, A. B. Klimov, S. M. Chumakov

Published Apr 1, 2003• 8 citations
Publisher

Abstract

The dynamics of a resonant atom interacting with a quantum cavity field in the presence of many off-resonant atoms is studied. In the framework of the effective Hamiltonian approach we show that the results of elimination of non-resonant transitions are (a) a dynamical Stark shift of the field frequency, dependent on the populations of non-resonant atoms, (b) dependence of the coupling constant between the resonant atom and the field on the populations of non-resonant atoms, and (c) an effective dipole–dipole interaction between non-resonant atoms. Two effects (the coherent influence and dephasing) of the off-resonant environment on the dynamics of the resonant atom are discussed.

DOI
10.1088/1464-4266/5/2/312

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The dynamics of a resonant atom interacting with a quantum cavity field in the presence of many off-resonant atoms is studied. In the framework of the effective Hamiltonian approach we show that the results of elimination of non-resonant transitions are (a) a dynamical Stark shift of the field frequency, dependent on the populations of non-resonant atoms, (b) dependence of the coupling constant between the resonant atom and the field on the populations of non-resonant atoms, and (c) an effective dipole–dipole interaction between non-resonant atoms. Two effects (the coherent influence and dephasing) of the off-resonant environment on the dynamics of the resonant atom are discussed.
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.
At the most fundamental level of quantum electrodynamics, there is no such thing as two-body interactions between atoms. The potentials that describe these interactions are effective potentials resulting from a series of approximations whose validity depends on the precise situation at hand. Considering a one-dimensional geometry for simplicity, we discuss under which conditions the familiar form of the near-resonant dipole-dipole interaction is valid, paying particular attention to the effects of interatomic propagation of light, and to what extent it can be modified in the tailored electromagnetic environments provided by optical resonators. We find that once the atoms have established that they are inside a resonator, the dipole-dipole potential may or may not remain a useful concept, depending upon the strength of the atom-field interaction. In the weak-coupling regime, one finds a two-body dipole-dipole interaction that can be enhanced or inhibited by varying the atom-field detuning. In the strong-coupling regime, by contrast, the two-body dipole-dipole potential ceases to be meaningful.
We study the quantum dynamics of an effective two-level atom interacting with two modes via Raman process inside an ideal cavity in the presence of Kerr non-linearity. The cavity modes interact both with the atom as well as the Kerr-like medium. The unitary transformation method presented here, not only solves the time-dependent problem, but also provides the eigensolutions of the interacting Hamiltonian at the same time. We study the atomic-population dynamics and the dynamics of the photon statistics in the two cavity modes. The influence of the Kerr-like medium on the statistics of the field is explored and it is observed that Kerr medium introduces antibunching in mode 1 and this effect is enhanced by a stronger interaction with the non-linear medium. In the high non-linear coupling regime anticorrelated beam become correlated. Kerr medium also introduces non-classical correlation between the two modes.
The influence of the dipole-dipole interaction on the final atomic state of a two-atom system driven by a coherent laser field and damped by a broad-band squeezed vacuum is discussed. It is shown that in the absence of a coherent laser field the final atomic state is independent of the dipole-dipole interaction and can be the pure two-atom squeezed state only if detuning of the squeezed vacuum field from atomic resonance is equal to zero. In the presence of a coherent laser field, the final atomic state depends on the dipole-dipole interaction. As the latter increases, the final atomic state shifts from a mixed state to the pure two-atom squeezed state. However, this happens only if the driving field and the squeezed field frequencies are tuned to the atomic transition frequency. For the driving field and the squeezed vacuum field frequencies detuned from atomic resonance the system decays into a mixed state irrespective of the dipole-dipole interaction between the atoms.
A coherent dynamics of two-and three-level atoms in the ideal cavity were investigated. In particular, the investigation of the dynamics of three-level atoms (qutrits) interacting with photons in the cavity having two resonant frequencies close to the frequencies of the two allowed atomic transitions were performed. This model generalizes the well-known Tavis-Cummings model. Time dependencies of mean number of the cavity photons and level populations of atoms are computed and entanglement of atoms and photon fields states are discussed.
We study the entanglement properties of two three-level Rydberg atoms passing through a single-mode cavity. The interaction of an atom with the cavity field allows the atom to make a transition from the upper most (lower most) to the lower most (upper most) level by emission (absoprtion) of two photons via the middle level. We employ an effective Hamiltonian that describes the system with a Stark shifted two-photon atomic transition. We compute the entanglement of formation of the joint two-atom state as a function of Rabi angle gtgtgt. It is shown that the Stark shift can be used to enhance the magnitude of atomic entanglement over that obtained in the resonant condition for certain parameter values. We find that though the two-atom entanglement generally diminishes with the increase of the two-photon detuning and the Stark shift, it is possible to sustain the entanglement over a range of interaction times by making the detuning and the Stark shift compensate each other. Similar characteristics are obtained for a thermal state cavity field too.