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Physical Review A

Multichannel spectrum of neutral particles trapped by a wire

James P. Burke, Chris H. Greene, Brett D. Esry

Published Oct 1, 1996• 26 citations
Publisher

Abstract

The energy spectrum of a neutral atom bound in the magnetic field created by a straight line direct current is given by the Rydberg formula for particles with spin less than 3/2. An adiabatic representation leads to a natural understanding of this spectrum and provides a good approximation to the bound state energy levels. A more accurate finite element method is applied to directly solve the time-independent Schr\"odinger equation for neutral particles with arbitrary spin. A combination of the finite element method with multichannel quantum defect theory provides a more efficient method to calculate the bound state energies. In addition, new spectral features arise for particles with spin greater than 1. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.54.3225

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The energy spectrum of a neutral atom bound in the magnetic field created by a straight line direct current is given by the Rydberg formula for particles with spin less than 3/2. An adiabatic representation leads to a natural understanding of this spectrum and provides a good approximation to the bound state energy levels. A more accurate finite element method is applied to directly solve the time-independent Schr"odinger equation for neutral particles with arbitrary spin. A combination of the finite element method with multichannel quantum defect theory provides a more efficient method to calculate the bound state energies. In addition, new spectral features arise for particles with spin greater than 1. \textcopyright{} 1996 The American Physical Society.
We consider a waveguide for cold neutral atoms with a magnetic moment proportional to their spin angular momentum. The waveguide consists of a thin wire carrying a constant current. For the spin-1 case, we find bound states for the two-dimensional part of the motion around the wire, and present numerical and approximate analytic results for these bound states. In an experiment, the bound states can decay due to various effects, and we calculate the time scales involved. \textcopyright{} 1996 The American Physical Society.
The spectrum and the wave function of neutral atoms in the magnetic field of a Kepler-guide are presented by reducing a two-dimensional stationary Schrdinger equation to a one-dimensional hydrogen atom in Rydberg states. In addition, we set the scale for the atomic orbits and binding energy i n the quantum regime, and compare it with the outcome of the experiment. At the same time, we find that reducing the current and radius of the wire properly wil l increase the loading efficiency of the Kepler-guide.
Subject of this thesis is the investigation of the quantum dynamics of ultracold atoms in the presence of external inhomogeneous magnetic fields. We discuss the behavior of ground state atoms inside typical magnetic field configurations. Such atoms can be approximately treated as neutral point-like particles which carry a certain spin. In particular we analyze the resonance spectrum and the density of states of both fermionic and bosonic atoms. We point out the existence of so-called quasi-bound states whose wave functions can be approximately calculated analytically. Moreover, we focus on studying quantum mechanical states of ultracold but electronically highly excited atoms - so-called Rydberg atoms - inside magnetic traps. In a first step we explore their internal dynamics by employing a fixed-nucleus approximation. The latter assumes the atomic nucleus to be fixed in the magnetic field minimum. Within this framework we analyze spectral properties as well as properties of the electronic spin and calculate electromagnetic transitions. Finally we present an adiabatic approach which allows for a thorough description of the coupled center of mass and electronic dynamics. We highlight ways to magnetically trap highly excited atoms and present novel quantum states in which the center of mass and the electronic wave function are equal in size. This finding shows that Rydberg atoms even in inhomogeneous fields with moderate gradients cannot be considered point-like.
The motion of a neutral atom endowed with a magnetic moment interacting with the magnetic field is determined from the Ehrenfest-like equations of motion. These equations for the average values of the translational and spin degrees of freedom are derived from the Schr\"odinger-Pauli wave equation, and they form a set of nine coupled nonlinear evolution equations. The numerical and analytic solutions of these equations are obtained for the combination of the rotating magnetic field of a wave carrying orbital angular momentum and a static magnetic field. The running wave traps the atom only in the transverse direction, while the standing wave traps the atom also in the direction of the beam.