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Physical Review A

Theory of electronic-state coherences produced in radiatively-aided inelastic collisions

P. R. Berman

Published Jun 1, 1984• 3 citations
Publisher

Abstract

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 $i$ and $j$ 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 $i$ and $j$ 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.

DOI
10.1103/physreva.29.3234

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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 \ensuremathρij{\ensuremath{\rho}}_{\mathrm{ij}}\ensuremathρij​ 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 \ensuremathρij{\ensuremath{\rho}}_{\mathrm{ij}}\ensuremathρij​ 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 theoretical calculation of the final-state coherences produced by a radiatively assisted inelastic collision (RAIC) is presented. Two atoms, AAA 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.
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.
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.
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)].
We consider collisions between (quasi-) one- or two-electron atoms, each of which has been prepared in a fixed distribution of hyperfine magnetic substates. The resulting ``polarization-dependent'' reaction rates are functions of (1) the (experimentally adjustable) orientation of the quantization axis associated with the hyperfine substates, (2) the hyperfine terms of the colliding atoms, and (3) the detailed reaction dynamics as characterized by preparation- and fine-structure-independent cross sections. These effects are deconvoluted and analyzed, and their use in elucidating reaction mechanisms is discussed. Particular emphasis is placed on the associative ionization of two Na(3p) atoms, each prepared by adsorption of resonant laser photons. The quasimolecular states of Na...Na that might react in this case are limited by selection rules. More information on the reaction mechanism is then obtained by using experimental data, in combination with the formal analysis, to draw further conclusions about the active quasimolecular states.
The interaction of near-resonant laser radiation with atoms immersed in a magnetic B\mathbf{B}B field is calculated using a quantum electrodynamic model. In this model, the magnetic field is assumed to produce a small perturbation such that the degeneracy of the magnetic substates is lifted while maintaining the usual quantum numbers that define the states (the Zeeman effect). The laser radiation is considered to have a narrow bandwidth and to be temporally and spatially coherent. The model produces three general coupled differential equations that describe the state populations and their relative coherences and the optical coherences between levels coupled by the laser radiation. The model can therefore be directly applied to different experiments ranging from atom trapping and cooling experiments through to collision experiments carried out in magnetic and laser fields.