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Physical Review A

Scaling of radiative collisions between Rydberg atoms

Panming Fu, J. D. Newman, D. S. Thomson, Thomas F. Gallagher

Published Sep 1, 1989• 1 citation
Publisher

Abstract

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 ${n}^{\mathrm{*}}$ dependence of [2.06(15)\ifmmode\times\else\texttimes\fi{}${10}^{3}$]${n}^{\mathrm{*}\mathrm{\ensuremath{-}}2.0}$ (V/cm), where ${n}^{\mathrm{*}}$ 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.

DOI
10.1103/physreva.40.2745

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Bulletin of the American Physical Society•May 1, 1993•0 citations
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∗\ensuremath−2.0{n}^{\mathrm{*}\mathrm{\ensuremath{-}}2.0}n∗\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 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.
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 Na(ns)\mathrm{Na}(\mathrm{ns})Na(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}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.
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.
We have observed the process $\mathrm{Rb}ns+\mathrm{Rb}\phantom{\rule{4pt}{0ex}}ns+2h\ensuremath{\nu}\ensuremath{\rightarrow}\mathrm{Rb}\phantom{\rule{4pt}{0ex}}n{p}_{1/2}+\mathrm{Rb}\phantom{\rule{4pt}{0ex}}n{p}_{3/2}$ from n=34n=34n=34 to n=40n=40n=40 in a frozen gas of Rb Rydberg atoms. It is resonant when the microwave frequency is halfway between the $ns\phantom{\rule{0.16em}{0ex}}\ensuremath{\rightarrow}\phantom{\rule{0.16em}{0ex}}n{p}_{1/2}$ and $ns\ensuremath{\rightarrow}n{p}_{3/2}$ frequencies, which range from 57 to 106 GHz. The process cannot occur in isolated atoms, nor can it occur if the magnetic quantum numbers are unchanged, an implicit assumption of one-dimensional models. A Floquet-Forster model shows that the coupling between the initial and final states involves the absorption of two microwave photons and the dipole-dipole interaction, which leads to a coupling proportional to the product of the density, the microwave field squared, and n∗14{n}^{*14}n∗14, where n∗{n}^{*}n∗ is the effective quantum number of the np3/2n{p}_{3/2}np3/2​ state. We have experimentally verified these dependences. The observed resonances are asymmetric, with a low-frequency tail, which we attribute to the van der Waals shift of the final np1/2np3/2n{p}_{1/2}n{p}_{3/2}np1/2​np3/2​ state due to its dipole-dipole interaction with the nearby ns(n+1)sns(n+1)sns(n+1)s state. While the van der Waals shift is negligible for most of the atoms in the Rydberg gas, it is not for the pairs of close atoms which undergo this transition.
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.