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Physical Review A

Intracollisional interference in resonant collisions of Na Rydberg atoms

D. S. Thomson, R. C. Stoneman, Thomas F. Gallagher

Published Mar 1, 1989• 12 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.39.2914

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We have observed 10-MHz-wide energy-transfer resonances between colliding Na Rydberg atoms. The narrow linewidth allows us to apply a modest 5--40-G static magnetic field in addition to a static tuning electric field and resolve new resonances arising from magnetic-field-induced splitting of the Stark energy levels. When B is parallel to E, the nine resolved resonances observed with only an E field are further split into 144 possible resonances. However, only the 21 resonances corresponding to collisions in which the spins are unchanged are observable. When B is perpendicular to E, the spectrum of collisional resonances is similar to that of the vertical field case, except that the final spin states cannot be determined. With both parallel and perpendicular fields present, linear and quadratic terms of the B field interaction create more complicated spectra than with either case alone. The experimental spectra agree quantitatively with the spectra calculated using a simple Zeeman model of the energy levels.

Physical Review A•Nov 1, 1994•2 citations
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.
Resonant collisional energy transfer can be studied in uprecedented detail using Rydberg atoms. Using the dependence of the energy level spacing on principal quantum number it is possible to examine resonant energy transfer in collisions with molecules. Finer control of the level spacing is possible by varying the level spacings with an electric field. Using this approach it is possible to observe sharply resonant collisions between Rydberg atoms. They are resonant dipole-dipole collisions which have cross sections orders of magnitude larger than the geometric cross sections of the colliding Rydberg atoms. These collisions are interesting in themselves; for example, they exhibit intracollisional interference, and it is possible to know when individual collisions begin and end. Perhaps the most interesting aspect of these collisions is that, because of the large dipole moments of the Rydberg atoms, they are easily controlled by microwave and radio frequency fields.
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 describe the experimental observation of the resonant collisional energy transfer Na(ns)+Na(ns)+qh\ensuremath{\nu}\ensuremath{\rightarrow}Na(np)+Na[(n-1)p]+(q○)h\ensuremath{\nu} which occurs when the Na atoms in a strong microwave field are tuned in energy with a static field so that the energy resonance Ens{E}_{\mathrm{ns}}Ens​+Ens{E}_{\mathrm{ns}}Ens​=Enp{E}_{\mathrm{np}}Enp​+${E}_{n\mathrm{\ensuremath{-}}1}$,p\ifmmode\pm\else\textpm\fi{}mh\ensuremath{\nu} occurs. We describe our experimental observations and provide a detailed description of a nonperturbative theory which we have developed to explain our observations. The theory is essentially developed in terms of the resonant dipole-dipole collisions between ``microwave dressed'' atoms. Using an extension of the approach we used previously to describe resonant dipole-dipole collisions in the absence of microwaves, we are able to take into account all the coherences in the problem in a completely straightforward way.
A large enhancement in the resonant collisional energy-transfer process $\mathrm{Na}(\mathrm{ns})+\mathrm{Na}(\mathrm{ns})\ensuremath{\rightarrow}\mathrm{Na}[(n\ensuremath{-}1)p]+\mathrm{Na}(\mathrm{nl})$ or $\mathrm{Na}(\mathrm{ns})+\mathrm{Na}(\mathrm{ns})\ensuremath{\rightarrow}\mathrm{Na}(\mathrm{np})+\mathrm{Na}[(n\ensuremath{-}1)l]$ is observed when the initial ns\mathrm{ns}ns state lies midway between $(n\ensuremath{-}1)p$ and an nl\mathrm{nl}nl state or between np\mathrm{np}np and an $(n\ensuremath{-}1)l$ state. This resonance condition, achieved by the electric field tuning of the levels, leads to large cross sections \ensuremath{\sim} 109{10}^{9}109 A˚2{\mathrm{\AA{}}}^{2}A˚2 and narrow linewidths \ensuremath{\sim} 1 GHz. These cross sections and linewidths are comparable to the previously observed resonant process $\mathrm{Na}(\mathrm{ns})+\mathrm{Na}(\mathrm{ns})\ensuremath{\rightarrow}\mathrm{Na}[(n\ensuremath{-}1)p]+\mathrm{Na}(\mathrm{np})$. We have also observed a similar collisional energy transfer starting from a completely different initial state, i.e., $\mathrm{Na}(15d)+\mathrm{Na}(15d)\ensuremath{\rightarrow}\mathrm{Na}(16f)+\mathrm{Na}(15p)$. In this case the enhancement in the cross section (\ensuremath{\sim} 108{10}^{8}108 A˚2{\mathrm{\AA{}}}^{2}A˚2) is observed at a relatively low electric field \ensuremath{\sim} 17 V/cm.
We have explored the dipole-dipole mediated, resonant energy transfer reaction, $32{p}_{3/2}+32{p}_{3/2}\ensuremath{\rightarrow}32s+33s$, in an ensemble of cold 85Rb^{85}\mathrm{Rb}85Rb Rydberg atoms. Stark tuning is employed to measure the population transfer probability as a function of the total electronic energy difference between the initial and final atom-pair states over a range of Rydberg densities, $2\ifmmode\times\else\texttimes\fi{}{10}^{8}\ensuremath{\le}\ensuremath{\rho}\ensuremath{\le}3\ifmmode\times\else\texttimes\fi{}{10}^{9} {\mathrm{cm}}^{\ensuremath{-}3}$. The observed line shapes provide information on the role of beyond nearest-neighbor interactions, the range of Rydberg atom separations, and the electric field inhomogeneity in the sample. The widths of the resonance line shapes increase approximately linearly with the Rydberg density and are only a factor of 2 larger than expected for two-body, nearest-neighbor interactions alone. These results are in agreement with the prediction [B. Sun and F. Robicheaux, Phys. Rev. A 78, 040701(R) (2008)] that beyond nearest-neighbor exchange interactions should not influence the population transfer process to the degree once thought. At low densities, Gaussian rather than Lorentzian line shapes are observed due to electric field inhomogeneities, allowing us to set an upper limit for the field variation across the Rydberg sample. At higher densities, non-Lorentzian, cusplike line shapes characterized by sharp central peaks and broad wings reflect the random distribution of interatomic distances within the magneto-optical trap (MOT). These line shapes are well reproduced by an analytic expression derived from a nearest-neighbor interaction model and may serve as a useful fingerprint for characterizing the position correlation function for atoms within the MOT.
We have observed 10-MHz-wide energy-transfer resonances between colliding Na Rydberg atoms. The narrow linewidth allows us to apply a modest 5--40-G static magnetic field in addition to a static tuning electric field and resolve new resonances arising from magnetic-field-induced splitting of the Stark energy levels. When B is parallel to E, the nine resolved resonances observed with only an E field are further split into 144 possible resonances. However, only the 21 resonances corresponding to collisions in which the spins are unchanged are observable. When B is perpendicular to E, the spectrum of collisional resonances is similar to that of the vertical field case, except that the final spin states cannot be determined. With both parallel and perpendicular fields present, linear and quadratic terms of the B field interaction create more complicated spectra than with either case alone. The experimental spectra agree quantitatively with the spectra calculated using a simple Zeeman model of the energy levels.