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Physical Review Letters

Microwave-Assisted Resonant Collisional Energy Transfer in Na Rydberg States

Ravinder Kachru, Nam Huu Tran, Thomas F. Gallagher

Published Jul 19, 1982• 15 citations
Publisher

Abstract

Microwave-assisted resonant collisional energy transfer process $\mathrm{Na}(\mathrm{ns})+\mathrm{Na}(\mathrm{ns})+h\ensuremath{\nu}\ensuremath{\rightarrow}\mathrm{Na}(\mathrm{np})+\mathrm{Na}((n\ensuremath{-}1)p)$ is observed between two colliding $\mathrm{Na}(\mathrm{ns})$ atoms. The collisional resonance occurs when the microwave frequency $\ensuremath{\nu}$ equals the collisional energy defect $\frac{\ensuremath{\Delta}W}{h}$. The observed cross sections are very large (\ensuremath{\sim}${10}^{8}$ ${\mathrm{\AA{}}}^{2}$) and require very low microwave power, \ensuremath{\sim}10 W/${\mathrm{cm}}^{2}$. These observations are in good agreement with an intuitive two-photon absorption model for these collisions.

DOI
10.1103/physrevlett.49.191

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Physical Review Letters•May 30, 1983•22 citations
Microwave-assisted resonant collisional energy transfer process Na(ns)+Na(ns)+h\ensuremathν\ensuremath→Na(np)+Na((n\ensuremath−1)p)\mathrm{Na}(\mathrm{ns})+\mathrm{Na}(\mathrm{ns})+h\ensuremath{\nu}\ensuremath{\rightarrow}\mathrm{Na}(\mathrm{np})+\mathrm{Na}((n\ensuremath{-}1)p)Na(ns)+Na(ns)+h\ensuremathν\ensuremath→Na(np)+Na((n\ensuremath−1)p) is observed between two colliding Na(ns)\mathrm{Na}(\mathrm{ns})Na(ns) atoms. The collisional resonance occurs when the microwave frequency \ensuremathν\ensuremath{\nu}\ensuremathν equals the collisional energy defect \ensuremathΔWh\frac{\ensuremath{\Delta}W}{h}h\ensuremathΔW​. The observed cross sections are very large (\ensuremath{\sim}108{10}^{8}108 A˚2{\mathrm{\AA{}}}^{2}A˚2) and require very low microwave power, \ensuremath{\sim}10 W/cm2{\mathrm{cm}}^{2}cm2. These observations are in good agreement with an intuitive two-photon absorption model for these collisions.
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 measured the n dependence of the microwave field required to make the single-photon radiatively assisted collision process Na(ns)+Na(ns)+kh\ensuremath{\nu}\ensuremath{\rightarrow}Na(np)+Na ((n-1)p)+(k+m)h\ensuremath{\nu}, m=1, 10% as likely as the resonant collision process in which no photons are absorbed, m=0. Experimentally we find an n∗{n}^{\mathrm{*}}n∗ dependence of [2.06(15)\ifmmode\times\else\texttimes\fi{}103{10}^{3}103]${n}^{\mathrm{*}\mathrm{\ensuremath{-}}2.0}$ (V/cm), where n∗{n}^{\mathrm{*}}n∗ is the effective quantum number of the Na ns state. Over the range of n studied, 16\ensuremath{\le}n\ensuremath{\le}24, this field is within 20% of the field calculated using a theory based on resonant dipole-dipole collisional energy transfer of microwave dressed atoms.
We have observed the sharply resonant enhancement of the cross section of the collision process $ns+ns\ensuremath{\rightarrow}np+(n\ensuremath{-}1)p$ between two Nans\mathrm{Na}nsNans (16< n< 2716<~n<~2716< n< 27) atoms which occurs when the levels are shifted by an electric field so that the nsnsns level lies midway between the two ppp states. The widths of the collisional resonances scale as ${n}^{\ensuremath{-}2}$ and the magnitudes of the cross sections as n4{n}^{4}n4, with values of 0.5 GHz and 8\ifmmode\times\else\texttimes\fi{}108{10}^{8}108 A˚2{\mathrm{\AA{}}}^{2}A˚2 for the 20s20s20s state. These results are in good agreement with calculations based on the long-range dipole-dipole interaction between the two atoms.
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 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.
The observation of radiative collisions in the strong-field regime is reported, specifically the multiphoton-microwave-assisted resonant collisional energy-transfer process $\mathrm{Na}(\mathrm{ns})+\mathrm{Na}(\mathrm{ns})\ensuremath{\rightarrow}\mathrm{Na}(\mathrm{np})+\mathrm{Na}((n\ensuremath{-}1)p)+mh\ensuremath{\nu}$, where mmm is as high as 4. By use of a "dressed-atom" approach in a low-frequency (or adiabatic) approximation, a theoretical interpretation valid for the strong-field regime is given which is in good agreement with the present experimental results.