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Physical Review A

Line-shape analysis of resonant energy transfer collisions

James Veale, W. Anderson, M. Gatzke, Michael J. Renn, Thomas F. Gallagher

Published Aug 1, 1996• 6 citations
Publisher

Abstract

We have investigated the resonant collision process 26s+24d\ensuremath{\rightarrow}26p+25p in K, which occurs when the 26s and 24d states are tuned by a static electric field so that the intervals 26s-26p and 24d-25p are equal. Resonant collision line shapes are observed and analyzed for three collision velocity distributions: a thermal beam, a small band of velocities in a laser-cooled beam, and two well-separated velocity groups in a laser-cooled beam. Collisions between atoms with a broad distribution of relative velocities produce cusp line shapes. In contrast, collisions occurring between atoms in two well-defined velocity groups produce approximately Lorentzian line shapes. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.54.1430

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Line-shape expressions for two-step resonant excitation in the presence of low-pressure perturbers are derived. These expressions allow for velocity-dependent broadening rates and are well suited for studying the line-shape contributions due to coherent excitation, incoherent excitation (due to dephasing collisions), interference between coherent and incoherent excitation, and velocity-changing collisions. Using the sodium 3S-3P-4D system perturbed by noble-gas atoms as an example and assuming C6{C}_{6}C6​ interaction potentials, line shapes at a variety of laser detunings (Doppler selected atomic velocities) are numerically calculated to study variation in the line shape due to competing excitation paths and speed-dependent collision rates. In order to deal with both the line core and the line wing a composite collision kernel consisting of a Lorentzian kernel for small \ensuremath{\Delta}vz{v}_{z}vz​ collisions and a Keilson-Storer kernel for large \ensuremath{\Delta}vz{v}_{z}vz​ collisions is used. It is also demonstrated how the inelastic (3P3/2{P}_{3/2}P3/2​-3P1/2{P}_{1/2}P1/2​) velocity-changing collision kernel may be obtained from experimental data at low pressures. Theoretical line shapes and broadening rates are compared with experiment.
The theory of resonant dipole-dipole energy transfer in an electric field E indicates substantial differences between the collision velocities v\ensuremath{\parallel}E and v\ensuremath{\perp}E. For v\ensuremath{\parallel}E the cross section vanishes at exact resonance due to a destructive interference in the transition amplitude, producing a double-peaked line shape. The presence of the permanent dipole moments in the field produces slight shifts and asymmetries of the collisional resonance line shapes. A high-resolution experimental study of the cases v\ensuremath{\parallel}E and v\ensuremath{\perp}E indicates that the theoretical predictions are correct and further allows the resolution of the spin-orbit structure in the resonant collisions.
By reducing the collision velocity of Rydberg atoms in resonant energy-transfer collisions, we have observed collisional resonances as narrow as 1 MHz, or collision times as long as 1.0 \ensuremath{\mu}s. Restricting the collision to a time less than the natural collision time results in transform broadening of the resonances, allowing us to know when an individual collision begins and ends. The latter point is verified by observing the dependence of the collision line shape on the phase of an oscillating field of frequency equal to the width of the collisional resonance.
We have observed resonant-energy-transfer collisions between K Rydberg atoms. We have tuned the ns1/2{\mathrm{ns}}_{1/2}ns1/2​+(n-2)dj{\mathrm{d}}_{\mathrm{j}}dj​\ensuremath{\rightarrow}${\mathrm{np}}_{\mathrm{j}\ensuremath{'}}$+(n-1)${\mathrm{p}}_{\mathrm{j}\mathrm{\ensuremath{''}}}$ collisional process into resonance with a static electric field. The measured resonance field positions from n=24 to 29 agree well with the calculated positions. We show that the dipole-dipole selection rule, \ensuremath{\Delta}mj{\mathrm{m}}_{\mathrm{j}}mj​=0,\ifmmode\pm\else\textpm\fi{}1, is valid for these resonances but that \ensuremath{\Delta}J=0,\ifmmode\pm\else\textpm\fi{}1 is not, due to the presence of the electric field. In addition, the polarization of the lasers used to excite the Rydberg states can suppress many of the resonances.
We have studied the collisional energy transfer process K (ns) +K (n-2) d {yields} K (np) +K (n-1) p which is tuned into resonance with an applied static electric field. The initial Rydberg states are excited stepwise with two dye laser pulses. The resonant energy transfer is detected by selectively field ionizing the final K(np) state as the static field is swept over many laser shots. Due to fine structure splitting of the d and p levels 45 resonances are energetically allowed at n{sub s}=25. The actual number of resonances that are observed depends on the polarization of the laser light, the dipole-dipole selection rules, and the n state excited. Above n{sub s}=29 all resonances are energically forbidden. We have measured the position of the resonances in electric field from n{sub s}=25 to n{sub s}=29 and found them to be in good agreement with calculated positions.