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The Journal of Chemical Physics

Molecular hyperfine structure in the photoassociation spectroscopy of laser cooled atoms

Carl J. Williams, Paul S. Julienne

Published Aug 1, 1994• 54 citations
Publisher

Abstract

The photoassociation of colliding ultracold trapped atoms permits the observation of high resolution molecular spectra of high lying vibrational levels with low total angular momentum and outer turning points greater than 50 Å. This paper describes how the hyperfine structure of alkali dimer molecules at large internuclear separation can be used to assign the electronic character of the observed photoassociation spectra and how hyperfine structure helps to explain the observed photoassociation spectrum of the attractive electronic states of the Na2 molecule that correlate with Na(3 2S)+Na(3 2P3/2) atoms.

DOI
10.1063/1.467637

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The photoassociation of colliding ultracold trapped atoms permits the observation of high resolution molecular spectra of high lying vibrational levels with low total angular momentum and outer turning points greater than 50 Å. This paper describes how the hyperfine structure of alkali dimer molecules at large internuclear separation can be used to assign the electronic character of the observed photoassociation spectra and how hyperfine structure helps to explain the observed photoassociation spectrum of the attractive electronic states of the Na2 molecule that correlate with Na(3 2S)+Na(3 2P3/2) atoms.
We have observed the spectrum of long range molecular states of singly excited Na2{\mathrm{Na}}_{2}Na2​ formed by photoassociation during ultracold associative ionization collisions of laser-cooled Na atoms. The low kinetic energy of the collision allows us to obtain very high resolution spectra and to observe states close to the dissociation limit. The spectrum shows regular vibrational series characteristic of the 1/R3{\mathit{R}}^{3}R3 long range portion of the 1g{1}_{\mathit{g}}1g​ potential (asymptotically S1/2{\mathit{S}}_{1/2}S1/2​+P3/2{\mathit{P}}_{3/2}P3/2​) as well as molecular hyperfine structure within these peaks. We extract potential parameters and compare with recent theory.
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.
Recent advances in laser cooling techniques have made possible a new type of spectroscopy. In the first experiments of this kind alkali atoms are laser cooled to temperatures around 1 mK and trapped, using laser fields, at densities around 1011 cm−3. Atoms colliding under such ultracold conditions can be resonantly photoassociated to bound states of the dimer molecules. These molecules can in turn be photoionized, providing a sensitive detection of the photoassociation spectrum and revealing in extremely high resolution the structure of the dimer molecules. The particular advantages of this technique include high resolution and signal‐to‐noise and the ability to reach extremely long range states of the molecule, accessible only through such slow collisions.
We report a full theoretical calculation of the rovibrational structure of the ${\mathrm{Na}}_{2} {0}_{g}^{\ensuremath{-}}$ state, including hyperfine structure. The purely long-range ${0}_{g}^{\ensuremath{-}}$ state has been observed in the photoassociation spectroscopy of ultracold trapped alkali-metal atoms. For the lighter alkali-metal atoms (Li, Na, and K), the purely long-range states are completely characterized by atomic data since the inner turning point of the potentials are at internuclear separations where exchange interactions are still negligible.
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.
Understanding high-precision photoassociative spectroscopy of laser-cooled alkali-metal atoms involves modeling an extremely dense level structure of weakly bound molecules in the region where coriolis and hyperfine interactions become comparable to electronic interactions. We describe an iterative eigenvalue solver suitable for resolving these bound states that is based on finding eigenvalues of the shifted inverse or Green-function operator. Nonlinear coordinate transformations applied to the nuclear motion are introduced to minimize the dimensionality of the discretized Hamiltonian. The formalism is applied to resolve the hyperfine structure of rovibrational levels of the Na(2P)+Na(2S)\mathrm{Na}{(}^{2}P)+\mathrm{Na}{(}^{2}S)Na(2P)+Na(2S) dimer.