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Radiative collisions

Thomas F. Gallagher

Published Sep 15, 1994• 0 citations

Abstract

A radiative collision is a resonant energy transfer collision in which two atoms absorb or emit photons during the collision. Alternatively, a radiative collision is the emission or absorption of a photon from a transient molecule, and, as shown by Gallagher and Holstein, radiative collisions can also be described in terms of line broadening. In a line broadening experiment there are typically many atoms and weak radiation fields, and in a radiative collision experiment there are few atoms and intense radiation fields. The only real difference is whether there are many atoms or many photons. Due to the short collision times, ∼10 −12 s, simply observing radiative collisions between low lying states requires high optical powers, and entering the regime where the optical field is no longer a minor perturbation seems unlikely. Due to their long collision times and large dipole moments, Rydberg atoms provide the ideal system in which to study radiative collisions in a quantitative fashion. As we shall see, it is straightforward to enter the strong field regime in which the radiation field, a microwave or rf field to be precise, is no longer a minor perturbation. Ironically, while the experiments are radiative collision experiments, with few atoms and many photons, the description of the strong field regime is given in terms of dressed molecular states, which is more similar to a line broadening description.

DOI: 10.1017/cbo9780511524530.016

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A radiative collision is a resonant energy transfer collision in which two atoms absorb or emit photons during the collision. Alternatively, a radiative collision is the emission or absorption of a photon from a transient molecule, and, as shown by Gallagher and Holstein, radiative collisions can also be described in terms of line broadening. In a line broadening experiment there are typically many atoms and weak radiation fields, and in a radiative collision experiment there are few atoms and intense radiation fields. The only real difference is whether there are many atoms or many photons. Due to the short collision times, ∼10 −12 s, simply observing radiative collisions between low lying states requires high optical powers, and entering the regime where the optical field is no longer a minor perturbation seems unlikely. Due to their long collision times and large dipole moments, Rydberg atoms provide the ideal system in which to study radiative collisions in a quantitative fashion. As we shall see, it is straightforward to enter the strong field regime in which the radiation field, a microwave or rf field to be precise, is no longer a minor perturbation. Ironically, while the experiments are radiative collision experiments, with few atoms and many photons, the description of the strong field regime is given in terms of dressed molecular states, which is more similar to a line broadening description.

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

{E}_{\mathrm{ns}}

+

{E}_{\mathrm{ns}}

=

{E}_{\mathrm{np}}

+${E}_{n\mathrm{\ensuremath{-}}1}$,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.

We have observed radiatively assisted collisions between velocity-selected K Rydberg atoms in radio-frequency (rf) fields. The low relative velocity of the atoms leads to long collision times, or equivalently, narrow, 1-MHz, collisional resonances. We have carried out systematic measurements with rf fields in the strong-field regime, and have shown that the cross sections agree quantitatively with the predictions of the strong-field theory. We have also shown experimentally and theoretically that the sum over m of the cross sections for m photon-assisted cross sections is larger than the resonant-collision cross section in the absence of a rf field.

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

m

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.

Rydberg atoms excited in microwave resonators are ideal systems to test quantum electrodynamics on an unusual scale.1 Owing to their very large electric dipole sizes, these atoms are indeed coupled so strongly to infrared and millimeter-wave radiation that the field of a few photons—ultimately the one of a single photon—stored in a cavity is large enough to induce important transition rates during the atomic time of flight across the cavity. As a result quantum radiative effects are observed in a range of frequencies where usual atomic systems behave as purely classical radiators. The enhancement of the spontaneous emission rate of a single atom prepared in a tuned cavity has already been observed.2 For a resonant cavity with very small losses, a point should be reached where the atom can no longer decay but instead reversibly oscillates between the two states involved in the transition resonant with the cavity mode. Experiments aimed at the observation of this new regime of quantum electrodynamics evolution are under way

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.