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Journal of Physics Conference Series

Quantum effects in collisions of ultracold atoms with walls and nanostructures

Florian Arnecke, Hanno Friedrich, Javier Madroñero

Published Nov 1, 2007• 2 citations
Publisher

Abstract

We study scattering of ultracold atoms by absorbing surfaces. Loss of flux through inelastic reactions and adsorption is described in an unambiguous and model-independent way by incoming boundary conditions in the semiclassical region near the surface. The near-threshold behaviour of the scattering amplitude is determined by a few parameters of the potential tail beyond the semiclassical region. Investigation of quantum reflection and scattering by flat and spherical surfaces shows that the curvature of the surface strongly influences the range to which the scattering amplitudes are sensitive in the atom-surface interaction.

DOI
10.1088/1742-6596/88/1/012041

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We study scattering of ultracold atoms by absorbing surfaces. Loss of flux through inelastic reactions and adsorption is described in an unambiguous and model-independent way by incoming boundary conditions in the semiclassical region near the surface. The near-threshold behaviour of the scattering amplitude is determined by a few parameters of the potential tail beyond the semiclassical region. Investigation of quantum reflection and scattering by flat and spherical surfaces shows that the curvature of the surface strongly influences the range to which the scattering amplitudes are sensitive in the atom-surface interaction.
We study elastic scattering of ultracold atoms by a conducting sphere. Loss of flux through inelastic reactions and adsorption is described in an unambiguous and model-independent way by incoming boundary conditions in the semiclassical region near the surface of the sphere. Differential cross sections are presented for Na and metastable He(23S)\mathrm{He}(2\phantom{\rule{0.2em}{0ex}}^{3}S)He(23S) atoms scattered by a nanosphere with radius 200a.u.200\phantom{\rule{0.3em}{0ex}}\mathrm{a.u.}200a.u. or 2000a.u.2000\phantom{\rule{0.3em}{0ex}}\mathrm{a.u.}2000a.u. Their near-threshold behavior is determined by a small number of parameters which are properties of the potential tail beyond the semiclassical regime, and it depends sensitively on the characterstic lengths ${\ensuremath{\beta}}_{6}$, ${\ensuremath{\beta}}_{7}$ which describe the strength of the nonretarded van der Waals part and the highly retarded Casimir part of the atom-sphere interaction, respectively. These lengths can be tuned to probe various regions of the atom-sphere interaction by appropriate choice of the radius of the sphere.
Quantum reflection refers to the reflection of particles by attractive long-range potentials in nonclassical regions of coordinate space without reaching a classical turning point. Recent advances in nanotechnology and in cooling processes of atoms and molecules give rise to the creation of hybrid systems involving ultracold atoms and nanostructures, where quantum reflection might play an important role. In this work we review some fundamental aspects of quantum reflection. These include the description of atom-surface interactions -which are originated from the vacuum fluctuations of the electromagnetic field-, the near-threshold characterization of quantum reflection, possible applications for trapping and guiding ultracold atoms, and the description of scattering processes in a basic hybrid system: ultracold atoms interacting with nanotubes.
We theoretically study the low-energy scattering of ultracold atoms by a dielectric nanosphere of silica glass levitated in a vacuum. The atom and dielectric surface interact via dispersion force of which strength sensitively depends on the polarizability, dielectric function, and geometry. For cesium and rubidium atoms, respectively, we compute the atom-surface interaction strength and characterize the stationary scattering states by taking adsorption of the atoms onto the surface into account. As the energy of the incoming atoms is lowered, we find that differences between quantum and classical scatterings emerge in two steps. First, the quantum-mechanical differential cross section of the elastic scattering starts to deviate from the classical one at an energy scale comparable to a few microkelvin in units of temperature due to the de Broglie matter-wave diffraction. Second, the differences are found in the cross sections in a regime lower than a few nanokelvin, where the classically forbidden reflection occurs associated with the sss-wave scattering and the discrete nature of angular momentum. We also study the dependencies of quantum and classical scattering properties on the radius of the nanosphere. This paper paves the way to identify the quantum regime and to understand the physical origin of quantum effects in the collisions between a nanoparticle and environmental gas over various temperatures.
In paper I (physics/0010068) entitled "The No-sticking Effect in Ultra-cold Collisions", we showed that under very general circumstances, atoms approaching a surface will not stick as its incoming energy approaches zero. This is true of either warm or cold surfaces. Here we explore the transition region from non sticking to sticking as energy is increased. The key to understanding the transition region is the WKB approximation and the nature of its breakdown. Simple rules for understanding the rollover to higher energy, post-threshold behavior, including analytical formulae for some asymptotic forms of the attractive potential are presented. We discuss a practical example of atom-surface pair in various substrate geometries. We also discuss the case of low energy scattering from clusters.
We present a simple model used for investigating the quantum reflection and quantum coherence in ultracold molecular collisions. Analytical expressions of reflection and transmission coefficients, short-range SSS matrix, and transition matrix TTT are derived for the hard-core plus inverse power potentials in the vicinity of the threshold. The effect of the quantum reflection and coherence on the loss rate depends on the scattering length and short-range loss parameter. The quantum coherence results from the phase difference $\ensuremath{\theta}$ between reflection paths. As an applied example, we calculate the loss rate of 23Na87Rb^{23}\mathrm{Na}^{87}\mathrm{Rb}23Na87Rb molecules in the ultracold $^{23}\mathrm{Na}^{87}\mathrm{Rb}\ensuremath{-}^{23}\mathrm{Na}^{87}\mathrm{Rb}$ collision. We can well interpret the experimental results of the ultracold 23Na87Rb^{23}\mathrm{Na}^{87}\mathrm{Rb}23Na87Rb molecular collision [Ye et al., Sci. Adv. 4, eaaq0083 (2018)]. It is found that the quantum coherence has a significant influence on the loss rate of 23Na87Rb^{23}\mathrm{Na}^{87}\mathrm{Rb}23Na87Rb molecules in ultracold molecule-molecule collisions.
In the absence of inelastic scattering, Feshbach resonances produce poles in scattering lengths and very large peaks in elastic cross-sections. However, inelastic scattering removes the poles. Whenever the resonant state is coupled comparably to the elastic and inelastic channels, the scattering length exhibits only a small oscillation and peaks in cross-sections are significantly suppressed. A resonant scattering length is defined to characterize the amplitude of the oscillation, and is shown to be small for many collisions of ultracold molecules. The results suggest that cross-sections for some ultracold collision processes will be much less sensitive to details of the potential than has been expected.