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Physical Review A

Inelastic collisions in ultracold gases confined by one-dimensional optical lattices

Zhiying Li

Published Jan 14, 2010• 2 citations
Publisher

Abstract

We present a formalism for rigorous multichannel scattering calculations of cross sections for inelastic collisions of atoms and molecules confined in one-dimensional optical lattices. We obtain analytical expressions for the mean frequency of inelastic collisions in a confined gas in the temperature regime $T~\ensuremath{\hbar}\ensuremath{\omega}$ and at temperatures $T\ensuremath{\gg}\ensuremath{\hbar}\ensuremath{\omega}$, where $\ensuremath{\omega}$ is the oscillation frequency of trapped particles in the confining potential. Our numerical calculations for the gaseous mixture of Li and Rb atoms show that inelastic collisions in the temperature regime $T~\ensuremath{\hbar}\ensuremath{\omega}$ exhibit a deviation from three-dimensional scattering. This deviation is more significant for systems with stronger confinement and larger scattering lengths. We find that the ratios of rate constants for inelastic scattering and elastic collisions are suppressed in confined gases at $T~\ensuremath{\hbar}\ensuremath{\omega}$, and this suppression is significant for Li-Rb collisions at $T<40$ $\ensuremath{\mu}$K.

DOI
10.1103/physreva.81.012701

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We present a formalism for rigorous multichannel scattering calculations of cross sections for inelastic collisions of atoms and molecules confined in one-dimensional optical lattices. We obtain analytical expressions for the mean frequency of inelastic collisions in a confined gas in the temperature regime T \ensuremathℏ\ensuremathωT~\ensuremath{\hbar}\ensuremath{\omega}T \ensuremathℏ\ensuremathω and at temperatures T\ensuremath≫\ensuremathℏ\ensuremathωT\ensuremath{\gg}\ensuremath{\hbar}\ensuremath{\omega}T\ensuremath≫\ensuremathℏ\ensuremathω, where \ensuremathω\ensuremath{\omega}\ensuremathω is the oscillation frequency of trapped particles in the confining potential. Our numerical calculations for the gaseous mixture of Li and Rb atoms show that inelastic collisions in the temperature regime T \ensuremathℏ\ensuremathωT~\ensuremath{\hbar}\ensuremath{\omega}T \ensuremathℏ\ensuremathω exhibit a deviation from three-dimensional scattering. This deviation is more significant for systems with stronger confinement and larger scattering lengths. We find that the ratios of rate constants for inelastic scattering and elastic collisions are suppressed in confined gases at T \ensuremathℏ\ensuremathωT~\ensuremath{\hbar}\ensuremath{\omega}T \ensuremathℏ\ensuremathω, and this suppression is significant for Li-Rb collisions at T<40T<40T<40 \ensuremathμ\ensuremath{\mu}\ensuremathμK.
We present a formalism for rigorous calculations of cross sections for inelastic and reactive collisions of ultracold atoms and molecules confined by laser fields in quasi-two-dimensional geometry. Our results show that the elastic-to-inelastic ratios of collision cross sections are enhanced in the presence of a laser confinement and that the threshold energy dependence of the collision cross sections can be tuned by varying the confinement strength and external magnetic fields. The enhancement of the elastic-to-inelastic ratios is inversely proportional to $\sqrt{ϵ/\ensuremath{\hbar}{\ensuremath{\omega}}_{0}}$, where ϵϵϵ is the kinetic energy and ${\ensuremath{\omega}}_{0}$ is the oscillation frequency of the trapped particles in the confinement potential.
We present a formalism for rigorous calculations of cross sections for inelastic and reactive collisions of ultracold atoms and molecules confined by laser fields in quasi-2D geometry. Our results show that the elastic-to-inelastic ratios of collision cross sections are enhanced in the presence of a laser confinement and that the threshold energy dependence of the collision cross sections can be tuned by varying the confinement strength and external magnetic fields. The enhancement of the elastic-to-inelastic ratios is inversely proportional to ε/ℏω0\sqrt{ε/\hbar ω_0}ε/ℏω0​​, where εεε is the kinetic energy and ω0ω_0ω0​ is the oscillation frequency of the trapped particles in the confinement potential.
Inelastic collisions of ultracold atoms or molecules are analyzed using very general arguments. In free space, the deactivation rate can be enhanced or suppressed together with the scattering length of the corresponding elastic collision via a Feshbach resonance, and by interference of deactivation of the closed and open channels. In reduced dimensional geometries, the deactivation rate decreases with decreasing collision energy and does not increase with resonant elastic scattering length. This has broad implications; e.g., stabilization of molecules in a strongly confining two-dimensional optical lattice, since collisional decay of excited states due to inelastic collisions is suppressed. The relation of our results to the Lieb-Liniger model for bosonic atoms is addressed.
This Thesis describes new mechanisms for controlling elastic and inelastic collisions of ultracold atoms and molecules with static electromagnetic and laser fields. The dynamical properties of ultracold atoms are usually tuned in experiments by applying an external magnetic field to induce a Feshbach resonance. The work presented in this Thesis demonstrates the possibility of inducing and manipulating Feshbach resonances with electric fields. We discuss in detail the mechanisms of electric-field-induced resonances in ultracold mixtures of alkali metal atoms and demonstrate that electric fields may shift and split the magnetic resonances. We show that electric fields may spin up the collision complex of ultracold atoms and induce anisotropic scattering which may be exploited in experiments on many-body dynamics of ultracold gaseous mixtures. The mechanisms of electric-field-induced resonances described in this Thesis allow for two-dimensional control of inter-particle interactions, leading to total control over ultracold gases. To guide future experiments, we generate accurate interaction potentials for ultracold Li--Rb mixtures by fitting positions and widths of experimentally measured Feshbach resonances. Ultracold atomic and molecular gases can be confined by laser fields in one or two dimensions which produces an optical lattice of ultracold particles. We develop a multichannel scattering theory for collisions of atoms and molecules in two dimensions and explore the effects of the confining laser potential on inelastic and reactive collisions of ultracold atoms and molecules in a 1D optical lattice. We show that ultracold collisions can be controlled in a quasi-2D geometry by varying the orientation of a magnetic field with respect to the confinement plane normal and demonstrate that the threshold energy dependence of cross sections for inelastic collisions in an optical lattice can be tuned by varying the confining potential and the magnetic field. Our results show that applying laser confinement in one dimension may stabilize ultracold systems with large scattering lengths, which may open up interesting opportunities for studies of ultracold controlled chemistry and might lead to a new research direction of ultracold chemistry in restricted geometries.
We show that cross sections for inelastic collisions of ultracold atoms or molecules confined by a harmonic potential have the same energy dependence as in pure 2D geometry. This indicates that chemical reactions and inelastic collisions may be suppressed in an ultracold gas under strong confinement in one dimension. We present a numerical proof of the threshold collision laws in 2D. Our results indicate that inelastic collisions in weak electromagnetic fields may be controlled by varying the orientation of the external field axis with respect to the plane of confinement.
We show that cross sections for inelastic collisions of ultracold atoms or molecules confined by a harmonic potential have the same energy dependence as in pure 2D geometry. This indicates that chemical reactions and inelastic collisions may be suppressed in an ultracold gas under strong confinement in one dimension. We present a numerical proof of the threshold collision laws in 2D. Our results indicate that inelastic collisions in weak electromagnetic fields may be controlled by varying the orientation of the external field axis with respect to the plane of confinement.