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Technical Physics Letters

On the problem of spatial focusing of ultracold neutrons in an inhomogeneous magnetic field: An eikonal approximation

T. Tchen

Published Mar 1, 2002• 0 citations
Publisher

Abstract

The motion of ultracold neutrons in a magnetic field featuring a quadratic inhomogeneity with respect to two coordinates is considered. The Schrödinger equation is solved within the framework of a quasiclassical (eikonal) approach. The theory demonstrates that it is basically possible to provide for a spatial focusing of neutrons with the formation of a point focus on neutron bunches.

DOI
10.1134/1.1467269

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The motion of ultracold neutrons in a magnetic field featuring a quadratic inhomogeneity with respect to two coordinates is considered. The Schrödinger equation is solved within the framework of a quasiclassical (eikonal) approach. The theory demonstrates that it is basically possible to provide for a spatial focusing of neutrons with the formation of a point focus on neutron bunches.
The motion of ultracold neutrons in a magnetic field featuring a quadratic inhomogeneity is considered. A partial solution to the stationary Schrödinger equation is found, which leads to a harmonic oscillator equation for the X coordinate. It is demonstrated that, under certain conditions, it is basically possible to provide for a spatial focusing of neutrons with the formation of either a single point focus or two side foci. Dependence of the focusing on the degree of monochromaticity of the neutron beam is considered.
The paper presents solution of quantum problem of neutron propagation in the magnetic field with multipole field expansion. Rigorous solution of the Pauli equation for neutron reveals existence of two solutions, finite and infinite, for any multipole configuration. As an example, we present detailed study of neutron motion in quadrupole and sextupole magnets. Our predictions agree with the results of Stern-Gerlach experiment for neutrons. To verify existence of finite and infinite motion, we discuss an experiment which could be performed in the Budker Institute of Nuclear Physics using existing equipment. We conclude with considerations of neutron storage ring with straight section and discrete magnets focusing the beam.
Abstract The problem of the interaction of ultracold neutrons with a neutron interference filter oscillating in space is investigated. In the problem, the evolution of the wave packet is considered by means of numerically solving the non-stationary Schrödinger equation by splitting the evolution operator. The filter oscillating in space acts as a quantum modulator of the ultracold neutron flux. The resulting spectra of the transmitted and reflected states are obtained depending on the motion parameters of the interferometer.
Polaritons are the collective excitations of many atoms dressed by resonant photons, which can be used to explain the slow light propagation with the mechanism of electromagnetically induced transparency. As quasiparticles, these collective excitations possess the typical feature of the matter particles, which can be reflected and deflected by the inhomogeneous medium in its spatial motion with some velocity. In this paper we develop a quantum theory to systematically describe the spatial motion of polaritons in inhomogeneous magnetic and optical fields. This theoretical approach treats these quasiparticles through an effective Schr\"odinger equation with anisotropic dispersion that the longitudinal motion is similar to an ultrarelativistic motion of a ``slow light velocity'' while the transverse motion is of nonrelativity with certain effective mass. We find that, after passing through the EIT medium, the light ray bends due to the spatial-dependent profile of external field. This phenomenon explicitly demonstrates the exotic corpuscular and anisotropic property of polaritons.
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.