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Physical Review Letters

Line Shapes of High Resolution Photoassociation Spectra of Optically Cooled Atoms

Reginaldo de Jesus Napolitano, J. Weiner, Carl J. Williams, Paul S. Julienne

Published Sep 5, 1994• 144 citations
Publisher

Abstract

High resolution photoassociation spectra of colliding ultracold trapped atoms contain detailed information about ground and excited state interactions. We calculate the asymmetric line shapes for ultracold ${\mathrm{Na}}_{2}$ absorption using a resonance scattering expression, proportional to a free-bound Franck-Condon factor, that is justified by full quantum scattering calculations of a collision in a radiation field. The line shapes illustrate Wigner threshold law behavior, which is characteristic of the quantum limit as $T\ensuremath{\rightarrow}0$. Using an adiabatic hyperfine analysis, we calculate and compare a model spectra for $J=1,2,3, \mathrm{and} 4$ features of the ${\mathrm{Na}}_{2}$ $^{1}\ensuremath{\Pi}_{g}(\ensuremath{\nu}=48)$ state to recent high resolution experimental data.

DOI
10.1103/physrevlett.73.1352

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High resolution photoassociation spectra of colliding ultracold trapped atoms contain detailed information about ground and excited state interactions. We calculate the asymmetric line shapes for ultracold Na2{\mathrm{Na}}_{2}Na2​ absorption using a resonance scattering expression, proportional to a free-bound Franck-Condon factor, that is justified by full quantum scattering calculations of a collision in a radiation field. The line shapes illustrate Wigner threshold law behavior, which is characteristic of the quantum limit as T\ensuremath→0T\ensuremath{\rightarrow}0T\ensuremath→0. Using an adiabatic hyperfine analysis, we calculate and compare a model spectra for J=1,2,3,and4J=1,2,3, \mathrm{and} 4J=1,2,3,and4 features of the Na2{\mathrm{Na}}_{2}Na2​ 1\ensuremathΠg(\ensuremathν=48)^{1}\ensuremath{\Pi}_{g}(\ensuremath{\nu}=48)1\ensuremathΠg​(\ensuremathν=48) state to recent high resolution experimental data.
Line shapes observed in photoassociation spectroscopy of ultracold (T<1mK)(T<1\mathrm{mK})(T<1mK) atoms are asymmetric and the peak of the line is shifted by a temperature-dependent amount from the zero-temperature threshold. In principle, calculating the line shape requires a full knowledge of both the ground- and excited-state potentials. We demonstrate here that an approximation based on the Wigner threshold law for scattering yields a relatively simple expression which allows one to extract line positions and linewidths directly from the data. The formula contains a few parameters (threshold frequency, linewidth, temperature, height) and does not require a detailed knowledge of the molecular potentials involved. We illustrate the utility of this approach with examples for Na photoassociation at 500 \ensuremath{\mu}K and also discuss the limitations of the approach.
Advances in laser cooling of neutral atoms have made possible a new form of high-resolution laser spectroscopy: photoassociation of ultracold atoms. Colliding neutral atoms, confined in a laser trap, are photoassociated to bound excited states of the dimer molecule by absorbing a photon from a tunable laser. The technique can probe long range and “purely long range” molecular states that are difficult or impossible to detect by traditional means and, because of the extremely low energy of the colliding atoms (<1 mK), is capable of high resolution (<0.001 cm-1). The spectra are useful for atomic lifetime measurements, determination of atomic ground-state scattering information, and measurement of curve-crossing probabilities. Theoretical and experimental work in the field, including multiple resonance techniques and photo association line shapes, are reviewed.
The field of laser cooling and trapping of atoms has had a profound impact on many areas of atomic, molecular and optical science. In particular, ultracold atoms colliding in magneto-optical traps typically have relative kinetic energies of 300muK(sim7MHz)300\\mu K (\\sim 7 MHz)300muK(sim7MHz), so free-bound absorption lines are as sharp as bound-bound lines. Moreover, because of very long range centrifugal barriers, only a few collisional partial waves are important (Jprimeprime=0,1J^{\\prime\\prime} = 0, 1Jprimeprime=0,1 and 2 in our work on 39K^{39}K39K). Such photoassociative free-bound absorption allows observation of ``pure long-range molecule'' states (Re=28R_{e} = 28Re​=28 and 39 {\\AA} in 39K2^{39}K_{2}39K2​) as well as long-range levels of known short range states with outer classical turning points of sim20−250AA\\sim 20 - 250 {\\AA}sim20−250AA. Such spectra have been observed by ``trap loss'' (decrease in atomic fluorescence), molecular ionization, and fragment ionization. Optical-optical double resonance (OODR), e.g. through the ``Franck-Condon windows'' of the ``pure long-range'' states, produces readily assignable spectra at higher asymptotes as well. Further extensions of ultracold photoassociative spectroscopy and applications to determination of long range potentials, atomic properties, and Bose-Einstein condensate stability will be presented.
We report on the observation of photoassociation resonances in ultracold collisions between ^{23}Na^{40}K molecules and ^{40}K atoms. We perform photoassociation in a long-wavelength optical dipole trap to form deeply bound triatomic molecules in electronically excited states. The atom-molecule Feshbach resonance is used to enhance the free-bound Franck-Condon overlap. The photoassociation into well-defined quantum states of excited triatomic molecules is identified by observing resonantly enhanced loss features. These loss features depend on the polarization of the photoassociation lasers, allowing us to assign rotational quantum numbers. The observation of ultracold atom-molecule photoassociation resonances paves the way toward preparing ground-state triatomic molecules, provides a new high-resolution spectroscopy technique for polyatomic molecules, and is also important to atom-molecule Feshbach resonances.
With the ultracold temperatures (T 1012 cm-3) of atoms that can be produced with laser-cooling and trapping techniques, it is now possible to carry out a new kind of high-resolution spectroscopy.1 This photoassociation is based on optical absorption resonances between the initially free states of colliding atoms and specific, bound excited molecular states. High resolution can be obtained because of the narrow energy distribution of the ultracold gas.1 Because the initial states are formed by collisions, it becomes possible to probe unique, excited molecular states with very large interatomic separations that are impossible to probe with conventional molecular spectroscopy. The feasibility of this new spectroscopy has been demonstrated in two recent experiments.2,3
Recent experiments at NIST and the University of Maryland on cooled and trapped Na atoms have revealed several 1- and 2-color spectral features associated with the hyperfine structure of the Na atom. We have calculated the adiabatic molecular potential curves in a total angular momentum basis, including hyperfine structure, of the molecular states of the alkali dimer molecules that correlate to the {sup 2}P{sub 3/2}+{sup 2}S separated atoms. We have also calculated the hyperfine line strengths for optical coupling to the {sup 2}S +{sup 2}S ground molecular states. These are used to interpret the new experimental features for trapped Na as due to free-bound-bound or free-bound-free spectra of the Na{sub 2} molecule. New dynamical features illustrating optical control of ultracold reactions will be discussed. Supported in part by ONR.