Low-energy scattering of ultracold atoms by a dielectric nanosphere

T Yamaguchi,R Kanamoto,D Akamatsu

doi:10.1103/physrevresearch.3.043214

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.

Highlights

IntroductionThere has been growing interest in optically levitated nanoparticles [1] because of their potential applicabilities to unexplored fields such as nonequilibrium dynamics and thermodynamics at the nanoscale [2], suspension-free ultrahigh-Q optomechanics [3,4,5], studies of quantum-classical boundaries [6,7,8], nonlinear dynamics [9,10], weak-force sensing [11,12,13], and control of translational, librational [14], rotational [15,16,17], and precessional [18] motions
As the energy of the incident atomic beam is lowered, we found that the first quantum effect reveals in the differential cross section of the elastic scattering at an energy scale of a few microkelvin in units of temperature, where the thermal de Broglie wavelength of the atom is comparable to the size of the nanosphere
We numerically determined the classical capture range, which was found to be more than one order of magnitude larger than the geometric radius of the nanosphere around the experimentally achievable lowest energy, while it approaches the geometric radius of the nanosphere in the high-energy limit

Summary

Introduction

There has been growing interest in optically levitated nanoparticles [1] because of their potential applicabilities to unexplored fields such as nonequilibrium dynamics and thermodynamics at the nanoscale [2], suspension-free ultrahigh-Q optomechanics [3,4,5], studies of quantum-classical boundaries [6,7,8], nonlinear dynamics [9,10], weak-force sensing [11,12,13], and control of translational, librational [14], rotational [15,16,17], and precessional [18] motions.

Objectives

Results

Conclusion