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Physical Review A

Theory of coherences produced by radiatively assisted inelastic collisions: Weak-field impact-core limit

P. R. Berman

Published Nov 1, 1980• 24 citations
Publisher

Abstract

A theoretical calculation of the final-state coherences produced by a radiatively assisted inelastic collision (RAIC) is presented. Two atoms, $A$ and ${A}^{\ensuremath{'}}$, collide in the presence of an external radiation field to produce the RAIC reaction ${A}_{i}+{A}_{{i}^{\ensuremath{'}}}^{\ensuremath{'}}+\ensuremath{\hbar}\ensuremath{\Omega}\ensuremath{\rightarrow}{A}_{f}+{A}_{f}^{\ensuremath{'}}$, where $|{\mathrm{ii}}^{\ensuremath{'}}〉$ is the initial state, $|{\mathrm{ff}}^{\ensuremath{'}}〉$ is the final state, and $\ensuremath{\Omega}$ is the frequency of the external field. It is assumed that the final states consist of a number of nearly degenerate levels and the coherences produced in these levels by the RAIC reaction is calculated. These final-state coherences can be monitored by standard techniques (polarization of fluorescence, quantum beats) enabling one to use the final-state coherences as a probe of the RAIC reaction. The calculation is limited to the weak-field (perturbation-theory) limit and is valid only in the impact core of the RAIC profile.

DOI
10.1103/physreva.22.1848

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Physical Review A•Jul 1, 1994•1 citation
A theoretical calculation of the final-state coherences produced by a radiatively assisted inelastic collision (RAIC) is presented. Two atoms, AAA and A\ensuremath′{A}^{\ensuremath{'}}A\ensuremath′, collide in the presence of an external radiation field to produce the RAIC reaction Ai+Ai\ensuremath′\ensuremath′+\ensuremathℏ\ensuremathΩ\ensuremath→Af+Af\ensuremath′{A}_{i}+{A}_{{i}^{\ensuremath{'}}}^{\ensuremath{'}}+\ensuremath{\hbar}\ensuremath{\Omega}\ensuremath{\rightarrow}{A}_{f}+{A}_{f}^{\ensuremath{'}}Ai​+Ai\ensuremath′\ensuremath′​+\ensuremathℏ\ensuremathΩ\ensuremath→Af​+Af\ensuremath′​, where ∣ii\ensuremath′〉|{\mathrm{ii}}^{\ensuremath{'}}〉∣ii\ensuremath′〉 is the initial state, ∣ff\ensuremath′〉|{\mathrm{ff}}^{\ensuremath{'}}〉∣ff\ensuremath′〉 is the final state, and \ensuremathΩ\ensuremath{\Omega}\ensuremathΩ is the frequency of the external field. It is assumed that the final states consist of a number of nearly degenerate levels and the coherences produced in these levels by the RAIC reaction is calculated. These final-state coherences can be monitored by standard techniques (polarization of fluorescence, quantum beats) enabling one to use the final-state coherences as a probe of the RAIC reaction. The calculation is limited to the weak-field (perturbation-theory) limit and is valid only in the impact core of the RAIC profile.
A radiatively assisted inelastic collision (RAIC) is one in which two atoms collide in the presence of a radiation field to produce a reaction of the form ${A}^{*}+B+\ensuremath{\hbar}\ensuremath{\Omega}\ensuremath{\rightarrow}A+{B}^{*}$. In this paper, a general theory of RAIC is developed with special attention given to the final-state coherences produced by RAIC. These final-state coherences can be monitored by standard experimental techniques (polarization of fluorescence, quantum beats), enabling one to use such studies to gain information on the interatomic potentials that are relevant to the RAIC under consideration.
In a previous paper [P. R. Berman and E. Giacobino, Phys. Rev. A 28, 2900 (1983)], a method was proposed for producing electronic-state coherences using radiatively-aided inelastic collisions (RAIC). Two atoms collide in the presence of two simultaneously applied laser pulses and the combined action of the fields and the collision leads to a final-state coherence ${\ensuremath{\rho}}_{\mathrm{ij}}$ between levels iii and jjj in one of the atoms. In this paper a detailed calculation of the RAIC cross section is given, including effects of magnetic degeneracy and an average over all collision orientations. With an isotropic distribution of collision orientations and with one photon absorbed from each laser field in a single RAIC reaction, a final-state coherence ${\ensuremath{\rho}}_{\mathrm{ij}}$ is created only if states iii and jjj have the same parity. In order to produce a final-state coherence between states of opposite parity, an anisotropic distribution of collision orientations is needed. Estimates of RAIC cross sections are obtained for both isotropic and axially symmetric distributions of collision orientations. For final states having opposite parity, the RAIC reaction can lead to the production of coherent radiation at the sum or difference frequency of the applied laser fields.
A reaction of the form Ai+Ai\ensuremath{'}\ensuremath{'}+\ensuremath{\Elzxh}\ensuremath{\Omega}\ensuremath{\rightarrow}Af+Af\ensuremath{'}\ensuremath{'} has been referred to as light-induced collisional energy transfer (LICET). In such a reaction, atoms A and A\ensuremath{'} collide in the presence of a radiation field and absorb a photon during the collision, taking them from initial states (Ai,Ai\ensuremath{'}\ensuremath{'}) to different final states (Af,Af\ensuremath{'}\ensuremath{'}). We calculate the final-state magnetic polarization produced in LICET for detunings \ensuremath{\Delta}=[(Ef+Ef\ensuremath{'})-(Ei+Ei\ensuremath{'}+\ensuremath{\Elzxh}\ensuremath{\Omega})]/\ensuremath{\Elzxh} in the quasistatic wing: that is, for |\ensuremath{\Delta}|\ensuremath{\tau}c\ensuremath{\gg}1, where \ensuremath{\tau}c is the collision duration. Our results are compared with analogous depolarization rates for so-called ``optical'' collisions (reactions of the form Ai+Ai\ensuremath{'}\ensuremath{'}+\ensuremath{\Elzxh}\ensuremath{\Omega}\ensuremath{\rightarrow}Ai+Af\ensuremath{'}\ensuremath{'}). Similarities and differences between the LICET and ``optical'' collision theories are noted. Final-state LICET magnetic-state polarization is evaluated for a number of different A-A\ensuremath{'} level schemes, assuming a dipole-dipole collisional interaction. Our results are shown to be in good agreement with experiment [A. D\'ebarre, J. Phys. B 15, 1693 (1982)].
A method for producing electronic-state coherences using either collisionally-aided radiative excitation (or "optical collision") or laser-induced collisional energy transfer (or "radiative collision") is proposed. Two atoms, AAA and ${A}^{\ensuremath{'}}$, collide in the presence of two pulsed-laser fields having frequencies $\ensuremath{\Omega}$ and ${\ensuremath{\Omega}}_{1}$. It is shown that by choosing ${\ensuremath{\Omega}}_{1}\ifmmode\pm\else\textpm\fi{}\ensuremath{\Omega}$ such that an energy-conserving transition can occur in the composite $A{A}^{\ensuremath{'}}$ system, one can create an electronic-state coherence in the AAA or ${A}^{\ensuremath{'}}$ atoms. The coherence can be produced between states of the same or of opposite parity; if it is between states of opposite parity, coherent emission at frequency ${\ensuremath{\Omega}}_{1}\ifmmode\pm\else\textpm\fi{}\ensuremath{\Omega}$ may be generated. The relationship of this work to theories of "pressure-induced extra resonances" in four-wave mixing is discussed.
Recently, a theoretical calculation has been presented assuming that coherences can be produced in a radiatively assisted inelastic collision. The author reports the observation of final-state coherences in the simple case of dipole-dipole interaction in a strontium-europium mixture illuminated by a pi -polarised laser field. The author has measured the polarisation ratio P of the fluorescence emitted from the final degenerate Zeeman states of strontium. The result P=0.43+or-0.05 is in good agreement with theoretical predictions P=0.45.
It is shown theoretically that Ramsey fringes can be produced when a laser-assisted reaction of the form A2{\mathrm{A}}_{2}A2​+${\mathrm{A}}_{1}^{\ensuremath{'}}$+\ensuremath{\Elzxh}\ensuremath{\Omega}\ensuremath{\rightarrow}A1{\mathrm{A}}_{1}A1​+${\mathrm{A}}_{2}^{\ensuremath{'}}$ is driven by a pair of ultrafast radiation pulses, each of whose temporal widths is less than the duration ${\mathrm{\ensuremath{\tau}}}_{\mathrm{c}}$ of a collision between the A and A\ensuremath{'} atoms. The excitation profile of the laser-assisted collision is calculated as a function of detuning of the laser field frequency from the initial- to final-state transition frequency. For radiation pulses separated by time T, Ramsey fringes appear separated in frequency by ${\mathrm{T}}^{\mathrm{\ensuremath{-}}1}$. The modulation depth and shift of the central Ramsey fringe as a function of (T/${\mathrm{\ensuremath{\tau}}}_{\mathrm{c}}$) provide information about the collisional interaction. Both the weak- and strong-field regions are considered and comparison with laser-assisted collisions using excitation pulses having temporal widths greater than ${\mathrm{\ensuremath{\tau}}}_{\mathrm{c}}$ is made.