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Physical Review A

Resonance collisions between three-level systems in an intense laser field

Stephen Michael Radley Young, D. M. Segal, H. Shah, Keith R. Burnett

Published Apr 1, 1994• 1 citation
Publisher

Abstract

Theory relevant to the treatment of resonance collisions between two-level dressed atoms has been extended to the three-level case in a self-contained calculation of field-dependent collision rates. With the laser field tuned close to the \ensuremath{\Vert}${\mathit{e}}_{1}$〉\ensuremath{\leftrightarrows}\ensuremath{\Vert}${\mathit{e}}_{2}$〉 transition, dressing of the upper two-level system is achieved. We solve coupled equations of motion for two-atom states that describe one atom in the ground state and the other in one of two dressed states. Dressed-state collision rates are calculated within the impact approximation using S-matrix theory. The coupled equations of motion are simplified in the limit of intense field. We have applied the theory to describe approximately collisions between Ne atoms in fields intense enough to dress the collision complex.

DOI
10.1103/physreva.49.2748

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Theory relevant to the treatment of resonance collisions between two-level dressed atoms has been extended to the three-level case in a self-contained calculation of field-dependent collision rates. With the laser field tuned close to the \ensuremath{\Vert}e1{\mathit{e}}_{1}e1​〉\ensuremath{\leftrightarrows}\ensuremath{\Vert}e2{\mathit{e}}_{2}e2​〉 transition, dressing of the upper two-level system is achieved. We solve coupled equations of motion for two-atom states that describe one atom in the ground state and the other in one of two dressed states. Dressed-state collision rates are calculated within the impact approximation using S-matrix theory. The coupled equations of motion are simplified in the limit of intense field. We have applied the theory to describe approximately collisions between Ne atoms in fields intense enough to dress the collision complex.
We propose a method for studying the modification of atomic collision rates in the presence of an intense laser field. This method employs a three-level lambda-system driven by two laser pulses: one strong and the other weak. The weak laser is used to populate a particular dressed state produced by the intense laser at some time during the pulse history. We show that this point can be selected by tuning the frequency of the weak laser. The spectrum of the emission produced by the dressed state is then recorded. Measuring this spectrum, both in the presence and in the absence of collisions, enables one to deduce the dependence of the collision rates on laser intensity. The method has other advantages discussed in the text.
The authors have studied resonance collisions amongst atoms dressed by a strong laser field. The equations of motion have been solved numerically to yield collisional transition rates for various values of the Rabi frequency (V) due to the laser and its detuning ( Delta ) from the atomic transition frequency ( omega 0 ). The atoms are assumed to follow classical rectilinear paths and only undergo binary collisions. The resonance interaction is taken to be the first-order dipole-dipole interaction acting within the ground and resonance levels of a pair of atoms. A qualitative explanation is offered for the results obtained by splitting the Hamiltonian into parts that represent the collision-free evolution of the system at the Rabi frequency, the 'normal' resonance interaction, and the 'dressed interaction' responsible for opening new scattering channels. The latter interaction depends upon the relative strengths of the resonance interaction (R), the generalized Rabi frequency ( Omega ) and the ratio V/ Delta .
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.
We extend the theory of light scattering from an atom undergoing collisions to the case of strong laser fields, where the expansion in powers of $\ensuremath{\Omega}{\ensuremath{\tau}}_{c}$ that was used formerly in a series of papers by Burnett et al. breaks down. In particular we consider in detail the conditions necessary to relate the observable quantities to intense-field collisional rate constants in a dressed-state basis (such as those calculated by Light and Sz\"oke). We also show (following Rabin and Ben-Reuven) that by studying the spectrum emitted by the atoms in the presence of a strong field one may measure the collisional rates for transfer between the dressed states of atom plus radiation field.
Dressed states of an atom in a classical laser field of frequency close to an atomic transition frequency are obtained, which are a considerable improvement over the usual two-level rotating-wave approximation. These wave functions are used in a calculation of the cross section for elastic electron-atom scattering in a laser field. Numerical calculations for electron-hydrogen scattering demonstrate that scattering involving absorption or emission of photons can be strongly influenced by coupling to the nonresonant states, regardless of the field strength. Inclusion of the counter-rotating terms in the calculation is shown to be essential for extending the applicability of the theory to scattering in nonresonant fields, where a first-order perturbation-theoretic treatment of the atom-field interaction would be expected to be quite justified.
Abstract We theoretically analyze the interactions and decay rates for atoms dressed by multiple laser fields to strongly interacting Rydberg states using a quantum master equation approach. In this framework a comparison of two-level and three-level Rydberg-dressing schemes is presented. We identify a resonant enhancement of the three-level dressed interaction strength which originates from cooperative multiphoton couplings as well as small distance dependent decay rates. In this regime the soft-core shape of the potential is independent of the sign of the bare Rydberg–Rydberg interaction, while its sign can be repulsive or attractive depending on the intermediate state detuning. As a consequence, near-resonant Rydberg dressing in three-level atomic systems may enable the realization of laser driven quantum fluids with long-range and anisotropic interactions and with controllable dissipation.