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arXiv:2106.10418 · Physical Review Research

Low-energy scattering of ultracold atoms by a dielectric nanosphere

Takaaki Yamaguchi, Daisuke Akamatsu, Rina Kanamoto

Published Dec 27, 2021• 3 citations

Abstract

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 $s$-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.

DOI: 10.1103/physrevresearch.3.043214

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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

s

-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.

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

\mathrm{He}(2\phantom{\rule{0.2em}{0ex}}^{3}S)

atoms scattered by a nanosphere with radius

200\phantom{\rule{0.3em}{0ex}}\mathrm{a.u.}

or

2000\phantom{\rule{0.3em}{0ex}}\mathrm{a.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.

We design and build a new experimental setup to demonstrate a mixture of a single nanoparticle and laser-cooled atoms. This system aims for investigating the low-energy scattering of ultracold atoms by a dielectric nanoparticle. The wave nature of the cold atoms manifests itself in both elastic and inelastic cross sections. In the new experimental system at Yokohama National University, we demonstrated optical trapping and cooling of a glass nanoparticle in vacuum. The ballistic Brownian motion of the nanoparticle in the harmonic potential was observed. We also demonstrated parametric cooling of the center of mass motion of the nanoparticle. We discuss the prospects for realization of a mixture of a single nanoparticle and laser-cooled atoms.

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.

Collisions between ultracold atoms and material surfaces are characterized by the reflection of the atomic matter wave from the attractive Casimir-Polder potential. This quantum reflection is particularly relevant to experiments such as GBAR, which will determine the gravitational acceleration of a cold antihydrogen atom by timing its fall onto a detection plate. In this thesis, the Casimir-Polder potential is computed from the electromagnetic scattering properties of the atom and surface and it is found to depend notably on the dielectric response, thickness and density of the medium. We show that reflection on this potential is associated with a breakdown of the semiclassical approximation and that it is enhanced for slow atoms and weak potentials. Liouville transformations relate Schrödinger equations with different potential landscapes but identical scattering properties. We gain new insights on the problem of quantum reflection on a potential well by mapping it onto an equivalent problem of tunneling through a wall. We also discuss the effect of gravity on the atomic wavepacket and its implications for free fall experiments with atoms. When combined with quantum reflection from a horizontal mirror, gravity can be used to trap particles in long lived states with promising applications for metrology. In particular, we suggest a scheme to improve the precision of the GBAR experiment by reducing the velocity dispersion of the falling atoms.

The role of shape resonances and many-body effects on universal quantum sticking of ultracold atoms onto solid surfaces is examined analytically and computationally using an exactly solvable representation of the Dyson equation. We derive the self-energy renormalization of the transition amplitude between an ultracold scattering atom and the bound states on the surface in order to elucidate the role of virtual phonon exchanges in the limiting behavior of the sticking probability. We demonstrate that, to first order in the interactions for finite ranged atom–surface potentials, virtual phonons can only rescale the strength of the atom–surface coupling and do not rescale the range of the coupling. Thus, universal sticking behavior at ultralow energies is to be expected for all finite ranged potentials. We demonstrate that the onset of the universal sticking behavior depends greatly on the position of the shape resonance of the renormalized potential and for sufficiently low energy shape resonances, deviations from the universal s(E)∝√E can occur near these energies. We believe that this accounts for many of the low energy sticking trends observed in the scattering of submillikelvin H atoms from superfluid 4He films.

Quantum reflection is a universal property of atoms and molecules when scattered from surfaces in ultracold collisions. Recent experimental work has documented the quantum reflection and diffraction of He atoms, dimers, trimers, and neon atoms when reflected from a grating. Conditions for the observation of emerging beam resonances have been discussed and measured. In this paper, we provide a theoretical simulation of the quantum reflection from a grating for those systems. We confirm the universal dependence on the incident de Broglie wavelength with the threshold angles where the emerging beam resonances are observed. However, the angular dependence of the reflection efficiencies, that is, the ratio of scattered intensity into specific diffraction channels relative to the total intensity is found to be dependent on the details of the particle surface interaction.