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Physical Review A

Quantum dynamical calculations of ultracold collisions induced by nonlinearly chirped light

J. L. Carini, J. A. Pechkis, C. E. Rogers, P. L. Gould, Shimshon Kallush, Ronnie Kosloff

Published Jan 31, 2012• 9 citations
Publisher

Abstract

We describe quantum dynamical calculations of ultracold ${}^{85}$Rb trap-loss collisions induced by pulses of light whose frequency is chirped on the nanosecond time scale. The chirped light excites the ground-state collisional wave function to the long-range attractive potential and escape from the trap is modeled by an absorbing boundary at short range. Both positive and negative chirps are considered and various chirp shapes and detunings are examined. For positive chirps, the loss rates are rather independent of the chirp shape. Negative chirps, on the other hand, show a dependence on chirp shape for detunings where collisional flux can be coherently returned to the ground state. These trends are consistent with the results of a recent experiment.

DOI
10.1103/physreva.85.013424

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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. ^

•Jan 1, 1996•0 citations
We describe quantum dynamical calculations of ultracold 85{}^{85}85Rb trap-loss collisions induced by pulses of light whose frequency is chirped on the nanosecond time scale. The chirped light excites the ground-state collisional wave function to the long-range attractive potential and escape from the trap is modeled by an absorbing boundary at short range. Both positive and negative chirps are considered and various chirp shapes and detunings are examined. For positive chirps, the loss rates are rather independent of the chirp shape. Negative chirps, on the other hand, show a dependence on chirp shape for detunings where collisional flux can be coherently returned to the ground state. These trends are consistent with the results of a recent experiment.
We present results on coherent control of ultracold trap-loss collisions using 40-ns pulses of nonlinearly frequency-chirped light. The chirps, either positive or negative, sweep $~$1 GHz in 100 ns and are centered at various detunings below the D2{D}_{2}D2​ line of 85Rb^{85}\mathrm{Rb}85Rb. At each center detuning, we compare the collisional rate constant $\ensuremath{\beta}$ for chirps that are linear in time, concave-down, and concave-up. For positive chirps, we find that $\ensuremath{\beta}$ generally depends very little on the shape of the chirp. For negative chirps, however, we find that $\ensuremath{\beta}$ can be enhanced by up to 50(20)% for the case of the concave-down shape. This occurs at detunings where the evolution of the wave packet is expected to be coherent. An enhancement at these detunings is also seen in quantum-mechanical simulations of the collisional process.
We demonstrate the ability to coherently control ultracold atomic Rb collisions using frequency-chirped light on the nanosecond time scale. For certain center frequencies of the chirp, the rate of inelastic trap-loss collisions induced by negatively chirped light is dramatically suppressed compared to the case of a positive chirp. We attribute this to a fundamental asymmetry in the system: an excited wave packet moves inward on the attractive molecular potential. For a positive chirp, the resonance condition moves outward in time, while for a negative chirp, it moves inward, in the same direction as the excited wave packet; this allows multiple interactions between the wave packet and the light, enabling the wave packet to be returned coherently to the ground state. Classical and quantum calculations support this interpretation.
We report on the dynamics of ultracold collisions induced by near-resonant frequency-chirped light. A series of identical chirped pulses, separated by a variable delay, is applied to an ultracold sample of 85Rb^{85}\mathrm{Rb}85Rb, and the rate of inelastic trap-loss collisions is measured. For small detunings of the chirped light below the atomic resonance, we observe that the rate of collisions induced by a given pulse can be increased by the presence of an earlier pulse. We attribute this to the enhancement of short-range collisional flux by the long-range excitation of atom pairs to an attractive molecular potential. For larger detunings and short delays, we find that a leading pulse can suppress the rate of collisions caused by a following pulse. This is due to a depletion of short-range atom pairs by the earlier pulse. Comparison of our data to classical Monte Carlo simulations of the collisions yields reasonable agreement.
We present results on coherent control of ultracold trap-loss collisions and molecule formation using frequency-chirped light. The chirps, either positive or negative, sweep 1 GHz in 100 ns and are red-detuned below the D2 line in either 85Rb or 87Rb. The pulses are Gaussian and have a full-width at half-maximum (FWHM) of 40 ns. In our collision experiments, we demonstrate coherent control of ultracold 85Rb collisions using nonlinear (either concave-down or concave-up) frequency chirps in the region of pulse detunings where coherent collision blocking occurs. We attribute this to the excitation radius of the negative chirp following the excited-wavepacket trajectory. We find that this process is dependent on the nonlinearity of the negative chirp. Specifically, the concave-down negative chirp yields a higher value of the collisional loss rate constant β than those of the concave-up and linear negative chirps. For nonlinear positive chirps, we find no significant dependence of β on the nonlinearity of the chirp. Our measurements are supported by quantum mechanical simulations of the collisional process. ^ In our molecule formation experiments, we use resonantly-enhanced multi- photon ionization to directly detect ground-state 87Rb 2 formed though photoassociation (PA) by linearly frequency-chirped pulses and subsequent spontaneous decay. In particular, we measure the rates of formation (R) and photodestruction (Γ PD) for positive and negative frequency-chirped pulses, as well as for unchirped pulses. We find that the unchirped pulse yields higher values of both R and ΓPD than those of the positively-chirped pulse, whose values in turn are greater than those of the negatively-chirped pulse. Our results are important steps towards coherent control of ultracold ground-state molecule formation. ^
We present results on the effects of nanosecond-timescale frequency-chirped laser light on the formation of 87Rb2 ultracold ground-state molecules. We investigate these effects through photoassociation (PA) experiments and quantum mechanical simulations. The PA experiments show that at higher intensities, the positive chirps have a higher formation rate than the unchirped or negative linear chirps. The quantum mechanical simulations reveal the mechanism responsible for this enhancement. Contributions from stimulated emission cause the positive chirp to be the most efficient for molecule formation.
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. ^