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AIP conference proceedings

Theory of ultracold atomic collisions in optical traps

Paul S. Julienne

Published Jan 1, 1990• 2 citations
Publisher

Abstract

Ultracold collisions of neutral atoms can now be studied in the laboratory in the temperature range below 0.001 K. Rate coefficients for ultracold collisions of excited states are decreased by spontaneous emission during the long duration of the collision, but can be dramatically modified by intense laser effects on collision dynamics. Generalized MCQDT is used to develop criteria for the onset of quantum threshold behavior, which generally begins at temperatures above the Doppler cooling limit of light traps. Threshold Penning ionization of He metastable atoms in a light trap is predicted to occur with a rate coefficient larger than 5×10 (−11) cm3/sec.

DOI
10.1063/1.39229

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Collisions of ultracold atoms can now be investigated in the laboratory at temperatures below 0.001 K. Such collisions are qualitatively different in many ways from collisions at normal energies, where T ≫ 1 K, because of the long time and distance scales associated with such collisions. Spontaneous emission can strongly modify collision dynamics of excited-state species produced by near-resonant optical excitation if the temperature is less than the characteristic temperature TS, where the collision time is comparable with the spontaneous-emission lifetime. We also estimate the temperature TQ that is characteristic of the onset of quantum threshold behavior, where the WKB approximation fails to apply as the de Broglie wavelength becomes large. We find that TQ is generally larger than TD, the Doppler cooling limit, except for collisions controlled by long-range potentials varying as 1/R3.TQ may be larger or smaller than TS. Expressions for estimating the magnitude of rate coefficients in the T → 0 limit are given. As an example, a model for the threshold behavior of Penning ionization of two He 3S1 metastable atoms is given, and the threshold rate coefficient is estimated to be >5 × 10−10 cm3 sec−1.

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Measurements of the temperature dependence of trap loss collisions of laser-cooled rubidium atoms are presented. A significant suppression of the rate of collisions between ground- and excited-state atoms is observed for temperatures below $\\sim$70 $\\mu$K. In such inelastic collisions, the atomic excitation takes place at long range and must survive against spontaneous decay to short range. Our results are consistent with recent predictions for the low temperature suppression of these collisions due to reduced survival of atomic excitation at low collision velocities.^ We report on measurements of trap loss collisions between ultracold Rb atoms which are confined in a magneto-optical trap. Both isotopes $\\sp{85}$Rb and $\\sp{87}$Rb have been studied over wide range of trap laser intensities and detunings. The trap loss collision rates exhibit variations over 3 orders of magnitude. We observe significant differences between the isotopes. At large detunings the ability of the trap to recapture products of the hyperfine-changing collisions is significantly diminished. This finding is supported by our numerical simulations of the recapture process. The trap loss rates due to collisions with room temperature background gas have also been measured.^ Using laser light tuned to a repulsive molecular potential, we have been able to suppress inelastic ground-state hyperfine changing collisions between ultracold $\\sp{87}$Rb atoms. Adiabatic excitation to the repulsive curve alters the atomic trajectories and prevents the atoms from approaching close enough for the hyperfine change to occur. Experimental results show suppressions up to $\\sim$50% and are in reasonable agreement with a simple Landau-Zener model.^ Finally, we have observed a significant cooperative effect in ultracold trap loss collisions induced by two separate lasers. One laser, tuned close to the atomic resonance, excites the atom pair to an attractive potential at long range. The resulting acceleration and deflection give rise to an enhancement in the collisional flux of ground-state atoms reaching short range, as probed by a second laser. Enhancements up to a factor of $\\sim$3 have been observed. ^

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Atomic collisions in an optical trap

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Spontaneous force light traps1,2 have provided a way to obtain relatively deep static traps for neutral atoms. However, the usefulness of any such trap will depend strongly on the density of the trapped atoms. We have studied the collisions within such a trap which limit the atomic density. These collisions are of considerable interest in their own right because the temperatures of the trapped atoms (10−4 K) are far lower than in usual atomic collision experiments. As a result the collision times are very long, and the collision dynamics are dominated by long-range interactions and spontaneous emission.

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This thesis presents investigations into the collision dynamics of cold metastable neon atoms in a magneto-optical trap (MOT). At very cold temperatures (approx. 1 mK) the atomic interaction occurs at long range and cannot be treated classically as the interaction between two nuclear point particles. In addition, the collision dynamics can be considerably altered in the presence of an optical eld. In this thesis results are presented for collisions that are altered by the presence of an optical eld and also collisions where the optical eld can be neglected. Controlled optical collisions of cold, metastable Ne atoms are performed by using a control laser tuned close to the (3s)3P2 to (3p)3D3 cooling transition. The control laser modies the rate of ionizing collisions by promoting a pair of colliding atoms onto an excited state potential. In order to induce collisions between pairs of trapped metastables, a control laser is tuned to the red of the transition where we measure a factor of 4 increase in the rate for ionizing collisions. We also investigate the eect of optical shielding by tuning the laser to the blue of the transition and observe a factor of 5 suppression in the ionization rate. However, the measured ionization spectrum does not contain resonances due to the formation of photoassociated molecules as predicted by Doery et al [1]. Instead, we observe a broad unresolvable ionization spectrum that is well described by established theory [2]. Collision cross sections are measured for neon in the (3s)3P2 metastable state with ground state, thermal atoms and molecules. The technique is based on the measurement of the loss rate due to collisions with a background gas. Generally, these type of collisions are considered undesirable, however, it is possible to infer information about the collision cross section if the rate of collisions is accurately known. This novel technique is described and collision cross section measurements are presented for metastable neon in the (3s)3P2 state with He, Ne, Ar, H2, O2, and N2. The average thermal energy of the collision ranges from 11 meV to 27 meV and the measurements have relatively small errors, of the order of 10%.

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Laser modification of ultracold atomic collisions: Theory

Paul S. Julienne, Robert Heather

Specific molecular mechanisms are proposed for associative ionization collisions of ultracold sodium atoms in a hybrid optical trap. When an intense, strongly detuned optical trap laser is on, the ionization rate is modulated by molecular bound-state resonances which are strongly affected by field dressing. When the weak, slightly detuned optical molasses lasers are on to provide cooling, an excitation mechanism which produces the two excited atoms at large internuclear separation in different hyperfine states accounts for the lower observed ionization rate.

Physical Review Letters•Oct 1, 1991•35 citations
Ultracold collisions of neutral atoms can now be studied in the laboratory in the temperature range below 0.001 K. Rate coefficients for ultracold collisions of excited states are decreased by spontaneous emission during the long duration of the collision, but can be dramatically modified by intense laser effects on collision dynamics. Generalized MCQDT is used to develop criteria for the onset of quantum threshold behavior, which generally begins at temperatures above the Doppler cooling limit of light traps. Threshold Penning ionization of He metastable atoms in a light trap is predicted to occur with a rate coefficient larger than 5×10 (−11) cm3/sec.
Collisions of ultracold atoms can now be investigated in the laboratory at temperatures below 0.001 K. Such collisions are qualitatively different in many ways from collisions at normal energies, where T ≫ 1 K, because of the long time and distance scales associated with such collisions. Spontaneous emission can strongly modify collision dynamics of excited-state species produced by near-resonant optical excitation if the temperature is less than the characteristic temperature TS, where the collision time is comparable with the spontaneous-emission lifetime. We also estimate the temperature TQ that is characteristic of the onset of quantum threshold behavior, where the WKB approximation fails to apply as the de Broglie wavelength becomes large. We find that TQ is generally larger than TD, the Doppler cooling limit, except for collisions controlled by long-range potentials varying as 1/R3.TQ may be larger or smaller than TS. Expressions for estimating the magnitude of rate coefficients in the T → 0 limit are given. As an example, a model for the threshold behavior of Penning ionization of two He 3S1 metastable atoms is given, and the threshold rate coefficient is estimated to be >5 × 10−10 cm3 sec−1.
Intense laser fields in optical neutral-atom traps can have a profound effect on collision cross sections at ultracold temperatures, $T<{10}^{\ensuremath{-}3}$ K. A simple model is developed for the long-range interatomic potentials of two field-dressed atoms. Field dressing ensures that the cross section for associative ionization of two ultracold Na atoms is large in an optical trap, but the cross section is predicted to be about 4 orders of magnitude smaller in optical molasses.
Measurements of the temperature dependence of trap loss collisions of laser-cooled rubidium atoms are presented. A significant suppression of the rate of collisions between ground- and excited-state atoms is observed for temperatures below $\\sim$70 mu\\mumuK. In such inelastic collisions, the atomic excitation takes place at long range and must survive against spontaneous decay to short range. Our results are consistent with recent predictions for the low temperature suppression of these collisions due to reduced survival of atomic excitation at low collision velocities.^ We report on measurements of trap loss collisions between ultracold Rb atoms which are confined in a magneto-optical trap. Both isotopes sp85\\sp{85}sp85Rb and sp87\\sp{87}sp87Rb have been studied over wide range of trap laser intensities and detunings. The trap loss collision rates exhibit variations over 3 orders of magnitude. We observe significant differences between the isotopes. At large detunings the ability of the trap to recapture products of the hyperfine-changing collisions is significantly diminished. This finding is supported by our numerical simulations of the recapture process. The trap loss rates due to collisions with room temperature background gas have also been measured.^ Using laser light tuned to a repulsive molecular potential, we have been able to suppress inelastic ground-state hyperfine changing collisions between ultracold sp87\\sp{87}sp87Rb atoms. Adiabatic excitation to the repulsive curve alters the atomic trajectories and prevents the atoms from approaching close enough for the hyperfine change to occur. Experimental results show suppressions up to $\\sim$50% and are in reasonable agreement with a simple Landau-Zener model.^ Finally, we have observed a significant cooperative effect in ultracold trap loss collisions induced by two separate lasers. One laser, tuned close to the atomic resonance, excites the atom pair to an attractive potential at long range. The resulting acceleration and deflection give rise to an enhancement in the collisional flux of ground-state atoms reaching short range, as probed by a second laser. Enhancements up to a factor of $\\sim$3 have been observed. ^
Spontaneous force light traps1,2 have provided a way to obtain relatively deep static traps for neutral atoms. However, the usefulness of any such trap will depend strongly on the density of the trapped atoms. We have studied the collisions within such a trap which limit the atomic density. These collisions are of considerable interest in their own right because the temperatures of the trapped atoms (10−4 K) are far lower than in usual atomic collision experiments. As a result the collision times are very long, and the collision dynamics are dominated by long-range interactions and spontaneous emission.
This thesis presents investigations into the collision dynamics of cold metastable neon atoms in a magneto-optical trap (MOT). At very cold temperatures (approx. 1 mK) the atomic interaction occurs at long range and cannot be treated classically as the interaction between two nuclear point particles. In addition, the collision dynamics can be considerably altered in the presence of an optical eld. In this thesis results are presented for collisions that are altered by the presence of an optical eld and also collisions where the optical eld can be neglected. Controlled optical collisions of cold, metastable Ne atoms are performed by using a control laser tuned close to the (3s)3P2 to (3p)3D3 cooling transition. The control laser modies the rate of ionizing collisions by promoting a pair of colliding atoms onto an excited state potential. In order to induce collisions between pairs of trapped metastables, a control laser is tuned to the red of the transition where we measure a factor of 4 increase in the rate for ionizing collisions. We also investigate the eect of optical shielding by tuning the laser to the blue of the transition and observe a factor of 5 suppression in the ionization rate. However, the measured ionization spectrum does not contain resonances due to the formation of photoassociated molecules as predicted by Doery et al [1]. Instead, we observe a broad unresolvable ionization spectrum that is well described by established theory [2]. Collision cross sections are measured for neon in the (3s)3P2 metastable state with ground state, thermal atoms and molecules. The technique is based on the measurement of the loss rate due to collisions with a background gas. Generally, these type of collisions are considered undesirable, however, it is possible to infer information about the collision cross section if the rate of collisions is accurately known. This novel technique is described and collision cross section measurements are presented for metastable neon in the (3s)3P2 state with He, Ne, Ar, H2, O2, and N2. The average thermal energy of the collision ranges from 11 meV to 27 meV and the measurements have relatively small errors, of the order of 10%.
Specific molecular mechanisms are proposed for associative ionization collisions of ultracold sodium atoms in a hybrid optical trap. When an intense, strongly detuned optical trap laser is on, the ionization rate is modulated by molecular bound-state resonances which are strongly affected by field dressing. When the weak, slightly detuned optical molasses lasers are on to provide cooling, an excitation mechanism which produces the two excited atoms at large internuclear separation in different hyperfine states accounts for the lower observed ionization rate.