We report a measurement of the rate constant for associative ionization (AI) between excited Na(3p) atoms colliding within a single beam at a velocity of 11.9 ${\mathrm{msec}}^{\mathrm{\ensuremath{-}}1}$, corresponding to a temperature of 65 mK. The collisions take place in a narrow velocity class of excited atoms produced by crossing the collimated Na beam with a monomode dye laser at an angle of 45\ifmmode^\circ\else\textdegree\fi{}. Light polarized linearly in the collision plane yields an AI rate constant greater than that for circular polarization by a factor of 2. We find
K65mKlin =(12.2\ifmmode\pm\else\textpm\fi{}4.3)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}13}$
cm3 ${\mathrm{sec}}^{\mathrm{\ensuremath{-}}1}$ and
K65mKcir =(6.1\ifmmode\pm\else\textpm\fi{}1.8)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}13}$
cm3 ${\mathrm{sec}}^{\mathrm{\ensuremath{-}}1}$. The experimental arrangement also permits absolute calibration of earlier crossed-beam measurements of the excitation function (cross section versus velocity) at conventional thermal beam kinetic energies. Present results together with earlier work show that the cross-sectional temperature dependence is in qualitative accord with theory.
We have measured the rate of production of
Na2+ ions in collisions of ultracold Na atoms held in a magneto-optical trap (MOT) as a function of probe laser detuning using a single-color probe beam. The ion rate is measured with the atoms mainly in the
3S(f=2) level (``bright MOT'') or the
3S(f=1) level (``dark MOT''). Using recent experimental information about the doubly excited autoionizing states of
Na2, we find that the large structures in the first 5 GHz red of the atomic transition frequency are due to a doubly resonant excitation process with levels in the ${0}_{g}^{\ensuremath{-}}$ potential (asymptotically connected to
3S1/2+3P3/2) as the intermediate states, and levels in the ${0}_{u}^{\ensuremath{-}}$ and
1u potentials (asymptotically connected to
3P3/2+3P3/2) as the final autoionizing states. We can account for nearly all of the observed structure in this region of the spectra for both the bright and dark MOT.
We report cross-section measurements of the associative-ionization process, Na(3
p2P3/2)+Na(3
p2P3/2)\ensuremath{\rightarrow}
Na2++e as a function of velocity, alignment, and orientation in the collision energy range from 300 to 5 K. Two independently tunable laser beams select narrow velocity classes of excited sodium in a well-collimated atomic beam. Circular and linear polarization of the excitation lasers permits alignment and orientation of the excited atoms in the two velocity classes. The excitation functions show pronounced differences reflecting different molecular pathways to the final product, and they bridge the energy range between conventional and ``cold'' collision dynamics.
The rate coefficient for the laser-induced associative-ionization reaction of ultracold Na in an optical trap is calculated as a function of the trap laser detuning from the Na
(2S1/2,F=2)\ensuremath{\rightarrow}Na
(2P3/2,F=3) resonance. Aided by a knowledge of the excited-state potential-energy curves and of the nature of the free-atom optical-pumping process, we propose the following mechanism, which we call photoassociative ionization (PAI): 2Na
(3${\mathrm{\ensuremath{\Sigma}}}_{\mathit{u}}^{+}$)${\ensuremath{\rightarrow}}^{\mathrm{\ensuremath{\Elzxh}}\mathrm{\ensuremath{\omega}}}$
Na2∗(${0}_{\mathit{g}}^{\mathrm{\ensuremath{-}}}$ and
1g)${\ensuremath{\rightarrow}}^{\mathrm{\ensuremath{\Elzxh}}\mathrm{\ensuremath{\omega}}}$
Na2∗∗(
1u)\ensuremath{\rightarrow}
Na2++${\mathit{e}}^{\mathrm{\ensuremath{-}}}$. Maxima in the calculated PAI rate coefficient occur at detunings that are simultaneously one-photon resonant with bound levels of the long-range ${0}_{\mathit{g}}^{\mathrm{\ensuremath{-}}}$ state and two-photon resonant with the lower rotational levels of a vibrational level lying 9 GHz below the dissociation threshold of the autoionizing
1u state. The calculated PAI spectrum (PAI rate coefficient versus trap-laser detuning) displays a series of broad peaks between -0.5 and -4 GHz detuning and a cutoff at -5 GHz detuning, as does the experimentally measured spectrum of Lett et al. [Phys. Rev. Lett. 67, 2139 (1991)].The broad widths of the peaks in the PAI spectrum is due in part to the orientation averaging of the collision vector with respect to the electric-field vector and to the optical pumping of the
Na2\ensuremath{\rightarrow}
Na2∗ rovibronic transition. The calculated PAI rate coefficient at -0.6 GHz detuning is a factor of 4 higher than the experimental value. Fine-structure-changing transitions play a role in the doubly excited states, because of the
1u avoided crossing, but not in the intermediate states, because they have gerade symmetry and the only states that have been shown to undergo fine-structure-changing transitions with large probability have ungerade symmetry. Several predictions based on the proposed model and suggestions for future experiments are discussed.
We report new calculations of two-body associative ionization collisions between sodium atoms confined in a magneto-optic trap at ultracold temperatures. These collisions represent a new kind of {open_quotes}open{close_quotes} or dissipative collision for which the energy of the atom + applied light field need not be conserved due to spontaneous emission coupling to the vacuum modes of the radiation field and require density matrix methods rather than wavefunction methods to describe the collision. In these collisions the Na atoms must absorb a photon when they are in close enough proximity that a significant fraction of the excited population survives relaxation back to the ground state. The Na atoms accelerate towards each other on the excited molecular state and absorbs a second photon to a doubly excited state which then proceeds to associatively ionize at close range. Our calculations incorporate a molecular picture of the atomic collision, laser optical-field dressing of the molecular states participating in the dynamics, and population and coherence decay due to spontaneous emission. The effect of excited state hyperfine structure, which plays a critical role in the dynamics, is simulated by simplified models with a reduced number of states based on the full set of molecular-hyperfine adiabatic potentialmore » curves. Comparison is made with recent measurements of photo-associative ionization. rates as a function of optical field intensity from about 20 to 130 mW cm{sup -2}.« less
An experimental investigation of the atomic-Na 3s
2${\mathit{S}}_{1/2--}$5s
2S1/2 two-color two-photon polarization spectrum has been made. Measurements of the linear polarization degree of the two-photon transition were made for one laser tuned within a \ifmmode\pm\else\textpm\fi{}100 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ range of the atomic-Na 3p
2Pj levels, with the second adjusted to satisfy the two-photon resonance condition. The relatively short-pulse (\ensuremath{\sim}0.5 ns) lasers used eliminate effects on the spectrum due to atomic-Na hyperfine interactions and radiation trapping, while greatly reducing depolarization due to collisions with Ar gas. In the absence of collisions, the measured polarization spectrum is in excellent agreement with calculations. Measurements of the Ar pressure dependence of the spectrum revealed strong depolarization in the vicinity of resonant excitation through the 3p
2P3/2 level. A collisional depolarization cross section of 200(30) \AA{} for this process was deduced from the data.