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Physical Review A

Collisional redistribution of radiation in strong fields: Modification of the collision dynamics

Keith R. Burnett, J. Cooper, Paul D. Kleiber, A. Ben‐Reuven

Published Mar 1, 1982• 51 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.25.1345

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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 \ensuremathΩ\ensuremathτc\ensuremath{\Omega}{\ensuremath{\tau}}_{c}\ensuremathΩ\ensuremathτc​ 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.
The evaluation of the binary-collision operator Phi ( omega ), pertaining to collisional redistribution of strong laser radiation, involves the computation of a time-ordered exponential, which only reduces to a scalar exponential in the medium-coupling limit. In this approximation one neglects the alteration of the collisional dynamics due to the presence of the laser field. A two-state atom is considered, for which the authors expand Phi ( omega ) in the ratio of the Rabi frequency Omega to the detuning from resonance. This parameter vanishes in the medium-coupling case, and is small for common gas-phase experiments. It is shown that the correction to medium coupling can again be expressed in a scalar function, which represents the temporal correlation between the interaction potential and the full time evolution during a single collision. The decay constants for collisional transitions between dressed states, which are germane to the width of the spectral lines, appear to be sensitive to the deviation from medium coupling. Quite remarkably, a non-vanishing collisional contribution survives in the limit Omega to 0 of Phi ( omega ).
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.
We study laser-intensity effects in two-photon collisional redistribution of radiation. Thereby we concentrate on a special case of recent experimental interest, where the transition from the excited to the final state is saturated by a strong laser field. Both exciting lasers are, however, assumed weak in the sense that the dynamics of a collision between the radiator and a perturber is not significantly influenced by the laser fields. In particular, our treatment explains the intensity independence of the polarization dependence of total fluorescence from the final state which has been measured previously even if the transition from the excited to the final state is saturated.
The close-coupled theory of atomic collisions in the presence of a radiation field may be used to calculate the distribution of final atomic states which results from absorption of polarized light during a collision. The theory applies equally well to optical collisions (line broadening) and to radiative collisions (laser-induced collisional energy transfer). For an optical collision the detuning $\ensuremath{\omega}\ensuremath{-}{\ensuremath{\omega}}_{\ensuremath{\infty}}$ is restricted to be larger than either the Rabi frequency or the widths due to natural, Doppler, or pressure broadening. The radiation field is assumed to be weak enough that the transition probabilities are linear in field intensity. The molecular picture is emphasized in which the wave function is expanded in a basis of field-free molecular states and the Hamiltonian is blocked in accordance with molecular quantum numbers. The quantities needed to predict experimental observables are reduced radiative scattering SSS-matrix elements ${s}_{\ensuremath{\omega}}$ in the asymptotic Hund's case-(e) representation. The theory of product orientation and alignment is equivalent to that which has been developed for molecular photodissociation. It requires coherent sums of ${s}_{\ensuremath{\omega}}$ matrix elements from different transition branches, that is, for PPP-, QQQ-, and RRR-type transitions corresponding to changes of -1, 0, and +1 in total molecular angular momentum. On the other hand, the total absorption coefficient and the branching ratio to different final fine-structure states irrespective of orientation or alignment depend on incoherent sums of the same matrix elements.