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Chinese Physics Letters

Analytic Solutions of Three-Level Dressed-Atom Model

Zhengling Wang, Yin Jian-Ping

Published Oct 1, 2004• 2 citations
Publisher

Abstract

On the basis of the dressed-atom model, the general analytic expressions for the eigenenergies, eigenstates and their optical potentials of the Λ-configuration three-level atom system are derived and analysed. From the calculation of dipole matrix element of different dressed states, we obtain the spontaneous-emission rates in the dressed-atom picture. We find that our general expressions of optical potentials for the three-level dressed atom can be reduced to the same as ones in previous references under the approximation of a small saturation parameter. We also analyse the dependences of the optical potentials of a three-level 85 Rb atom on the laser detuning and the dependences of spontaneous-emission rates on the radial position in the dark hollow beam, and discuss the probability (population) evolutions of dressed-atomic eigenstates in three levels in the hollow beam.

DOI
10.1088/0256-307x/21/10/017

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On the basis of the dressed-atom model, the general analytic expressions for the eigenenergies, eigenstates and their optical potentials of the Λ-configuration three-level atom system are derived and analysed. From the calculation of dipole matrix element of different dressed states, we obtain the spontaneous-emission rates in the dressed-atom picture. We find that our general expressions of optical potentials for the three-level dressed atom can be reduced to the same as ones in previous references under the approximation of a small saturation parameter. We also analyse the dependences of the optical potentials of a three-level 85 Rb atom on the laser detuning and the dependences of spontaneous-emission rates on the radial position in the dark hollow beam, and discuss the probability (population) evolutions of dressed-atomic eigenstates in three levels in the hollow beam.
On the basis of the dressed-atom model, the general analytic expressions for the eigenenergies, eigenstates and their optical potentials of the A-configuration three-level atom system are derived and analysed. From the calculation of dipole matrix element of different dressed states, we obtain the spontaneous-emission rates in the dressed-atom picture. We find that our general expressions of optical potentials for the three-level dressed atom can be reduced to the same as ones in previous references under the approximation of a small saturation parameter. We also analyse the dependences of the optical potentials of a three-level ^85Rb atom on the laser detuning and the dependences of spontaneous-emission rates on the radial position in the dark hollow beam, and discuss the probability (population) evolutions of dressed-atomic eigenstates in three levels in the hollow beam.
We present a general theory of atom guiding in a blue-detuned hollow laser beam. Using the dressed-atom approach, we obtain the mean dipole gradient force, the radiation pressure force, and the momentum diffusion coefficients for three-level Λ-type cold atoms. Using Monte Carlo simulation, we calculate the guiding efficiencies and the final velocity distributions of atoms for various conditions. We find that the guiding efficiency depends not only on the intensity and detuning of the guiding hollow beam but also on the atom-guiding direction with respect to the propagation direction of the hollow laser beam. Comparing our analyses with recent experimental results, we find that they are mutually consistent. The results that we present can also be applied to atom guiding by hollow optical fibers.
Recent experiments with single atomic ions isolated in electromagnetic traps have demonstrated abrupt changes in observed fluorescence intensities, which have been interpreted as evidence for quantum jumps as the atom changes energy levels. This presents the seeming paradox of discontinuously changing observables from a system whose dynamical evolution is governed by the continuous optical Bloch equations. In this paper I present an analysis of the dynamics of a model three-level atom interacting with two laser fields in terms of the dressed states of the atom-laser system. These dressed states are eigenstates of a Hamiltonian which includes laser-atom interactions, and thus they simplify the discussion of the time evolution of the combined laser-atom system. This dressed-state description is particularly useful in the regime in which both laser intensities are strong enough to saturate their respective transitions. I calculate the radiative lifetimes of the different species of dressed states and the branching ratios for decay to other dressed states, and demonstrate the consequences of these quantities for the observed fluorescence pattern. The calculated duration of bright and dark periods shows a pronounced dependence on the detunings of the lasers.
Firstly the interaction of a three-level /spl Lambda/-type atom with a blue-detuning dark hollow beam is described in the dressed-atom picture. The dipole potential and radiation pressure forces are derived, and the spontaneous emission processes between both adjacent manifolds are analyzed in detail. Then through Monte Carlo simulation, the relations between the guiding efficiency and the detuning in varieties of conditions are acquired. We found that the guiding efficiency also depends on guiding direction relative to the propagation direction of the hollow beam except for the intensity and configuration of the hollow beam and pressure of the chamber, when both directions are opposite, the optimal detuning is in high detuning region, the value is similar to the experimental value. Furthermore, we calculated the final velocity distribution of atoms guided by the hollow beam, we found that in same direction case, even though in low detuning region the guiding efficiency is high, but the radial and longitudinal coherence are seriously destroyed, the most atoms are much heated. It is not useful in application to atom optics experiments. The main factors are the radiation pressure forces and photon scattering effects. Finally we found that the atoms can only be guided in the high detuning region, and their coherence will be held whether same or opposite direction.
An analytical expression of the emission and absorption spectra, for a Λ-type three-level cavity-bound atom interacting with a two-mode cavity field, is given using the dressed states of the system. We take explicitly into account the existence of forms of nonlinearities of both the field and the intensity-dependent atom–field coupling. The characteristics of the emission and absorption spectra for binomial and squeezed coherent states of the modes are exhibited. The effects of the mean number of photons, detuning and the nonlinearity forms on the spectra are analysed.
A dressed-state study of lasing without population inversion from a three level atom interacting with a bi-chromatic laser field, in the ladder configuration, is formulated. We allow the atomic system to be dressed by both laser filed photons (double dressing). The evolution of the system under consideration is being explored both analytically and numerically, within the transient regime. Time dependent approximate analytic solutions for dressed-state populations and coherences are derived, within the so called “secular approximation,” under resonant conditions. We also present time dependent numerical solutions for population and coherences in the off-resonance regime. A spectral analysis is also performed revealing the structure of various dressed states transitions. These are shown to be composed of quintets centered about the frequencies of the coupling and probe laser fields and having sidebands located symmetrically at positions shifted from line center at the Rabi and double Rabi frequencies.