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Physical Review A

s -wave scattering of a polarizable atom by an absorbing nanowire

Martin Fink, A. Naranjo-Uribe, Florian Arnecke, Johannes Eiglsperger, Harald Friedrich, Javier Madroñero, Patrick Raab, A. Wirzba

Published Jun 28, 2010• 6 citations
Publisher

Abstract

We study the scattering of a polarizable atom by a conducting cylindrical wire with incoming boundary conditions, that is, total absorption, near the surface of the wire. Based on the explicit expression given recently [C. Eberlein and R. Zietal, Phys. Rev. A 75, 032516 (2007)] for the nonretarded atom-wire potential, we formulate a hierarchy of approximations that enables the numerical determination of this potential to any desired accuracy as economically as possible. We calculate the complex $s$-wave scattering length for the effectively two-dimensional atom-wire scattering problem. The scattering length $\mathfrak{a}$ depends on the radius $R$ of the wire and a characteristic length $\ensuremath{\beta}$ related to the polarizability of the atom via a simple scaling relation, $\mathfrak{a}=R \stackrel{~}{\mathfrak{a}}(\ensuremath{\beta}/R)$. The ``scaled scattering length'' $\stackrel{~}{\mathfrak{a}}$ tends to unity in the thick-wire limit $\ensuremath{\beta}/R\ensuremath{\rightarrow}0$, and it grows almost proportional to $1/R$ in the opposite thin-wire limit.

DOI
10.1103/physreva.81.062714

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We study the scattering of a polarizable atom by a conducting cylindrical wire with incoming boundary conditions, that is, total absorption, near the surface of the wire. Based on the explicit expression given recently [C. Eberlein and R. Zietal, Phys. Rev. A 75, 032516 (2007)] for the nonretarded atom-wire potential, we formulate a hierarchy of approximations that enables the numerical determination of this potential to any desired accuracy as economically as possible. We calculate the complex sss-wave scattering length for the effectively two-dimensional atom-wire scattering problem. The scattering length a\mathfrak{a}a depends on the radius RRR of the wire and a characteristic length \ensuremathβ\ensuremath{\beta}\ensuremathβ related to the polarizability of the atom via a simple scaling relation, a=Ra (\ensuremathβ/R)\mathfrak{a}=R \stackrel{~}{\mathfrak{a}}(\ensuremath{\beta}/R)a=Ra (\ensuremathβ/R). The ``scaled scattering length'' a \stackrel{~}{\mathfrak{a}}a  tends to unity in the thick-wire limit \ensuremathβ/R\ensuremath→0\ensuremath{\beta}/R\ensuremath{\rightarrow}0\ensuremathβ/R\ensuremath→0, and it grows almost proportional to 1/R1/R1/R in the opposite thin-wire limit.
We study low-energy scattering of a neutral atom by a perfectly conducting cylindrical nanowire. Based on the exact atom-wire potential given recently by Eberlein and Zietal [Phys. Rev. A 80, 012504 (2009)] we derive tractable expressions for both the nonretarded van der Waals limit and the highly retarded limit as well as a realistic description of the transition between these two limits. For real atoms and wire radii greater than a few atomic units, the nonretarded van der Waals limit is insufficient, whereas the highly retarded limit of the atom-wire potential gives an accurate description of low-energy elastic scattering and absorption cross sections.
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.
We provide accurate expressions for the sss-wave scattering length for a Gaussian potential well in one, two, and three spatial dimensions. The Gaussian potential is widely used as a pseudopotential in the theoretical description of ultracold-atomic gases, where the sss-wave scattering length is a physically relevant parameter. We first describe a numerical procedure to compute the value of the sss-wave scattering length from the parameters of the Gaussian, but find that its accuracy is limited in the vicinity of singularities that result from the formation of new bound states. We then derive simple analytical expressions that capture the correct asymptotic behavior of the sss-wave scattering length near the bound states. Expressions that are increasingly accurate in wide parameter regimes are found by a hierarchy of approximations that capture an increasing number of bound states. The small number of numerical coefficients that enter these expressions is determined from accurate numerical calculations. The approximate formulas combine the advantages of the numerical and approximate expressions, yielding an accurate and simple description from the weakly to the strongly interacting limit.
A pair of atoms interacts with nonresonant light via its anisotropic polarizability. This effect can be used to tune the scattering properties of the atoms. Although the light-atom interaction varies with interatomic separation as 1/R31/{R}^{3}1/R3, the effective sss-wave potential decreases more rapidly as 1/R41/{R}^{4}1/R4 such that the field-dressed scattering length can be determined without any formal difficulty. The scattering dynamics are essentially governed by the long-range part of the interatomic interaction and can thus be accurately described by an asymptotic model [A. Crubellier et al., New J. Phys. 17, 045020 (2015)]. Here we use the asymptotic model to determine the field-dressed scattering length from the sss-wave radial component of a particular threshold wave function. Applying our theory to the scattering of two strontium isotopes, we calculate the variation of the scattering length with the intensity of the nonresonant light. Moreover, we predict the intensities at which the scattering length becomes infinite for any pair of atoms.
The Aharonov-Bohm (AB) scattering of charged particles by the magnetic field of an infinitely long and infinitely thin solenoid (magnetic string) in an absorbing medium is studied. We discuss the partial-wave approach to this problem and show that the standard partial-wave method can be adjusted to this case. The effect of absorption leads to oscillations of the AB cross section. Based on this we investigate the scattering of neutral atoms with induced electric dipole moments by a charge wire of finite radius, which is placed in a uniform magnetic field. The physical realistic and practically important case that all atoms that collide with the wire are totally absorbed at its surface is studied in detail. The dominating terms of the scattering amplitude are evaluated analytically for different physical constellations. The remaining terms are written in a form suitable for a numerical computation. We show that if the magnetic field is absent, the absorbing charged wire causes oscillations of the cross section. In the presence of the magnetic field the cross section increases and the dominating Aharonov-Bohm peak appears in the forward direction, suppressing the oscillations.