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Quantização de Landau para partículas neutras emanéis quânticos

Lincoanderson Oliveira Dantas

Published Aug 19, 2011• 0 citations
OpenAlex

Abstract

In this work, we shall show that a Landau quantization analog is possible for neutral particles in two-dimensional quantum rings. For that we have used the Tan Inkson model for a quantum ring to confine neutral atoms in the ring. We have also used two different fields configurations to induce a electric dipole moment on the particle. In addition, we have made a review of some quantum effects, such that Aharonov-Bohm like effects and Landau quantization for neutral and charged particles.

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In this work, we shall show that a Landau quantization analog is possible for neutral particles in two-dimensional quantum rings. For that we have used the Tan Inkson model for a quantum ring to confine neutral atoms in the ring. We have also used two different fields configurations to induce a electric dipole moment on the particle. In addition, we have made a review of some quantum effects, such that Aharonov-Bohm like effects and Landau quantization for neutral and charged particles.
In this work, we investigate the system in which a neutral particle with magnetic dipole momentum interacts with an external electric field subject to the central potentials, such as scalar potentials proportional to the radial distance and Coulomb like potential. In addition, we analyse the same system when it is confined to a two-dimensional quantum ring and to a quantum dot. In the search for analytical solutions for the Schrödinger-Pauli equation we show that the energy states for this system of a neutral particle subject to the central potentials depend on the quantum geometric phase φAC and the quantum numbers associated with the radial modes, angular momentum, and spin of the system {n, l, s}. Furthermore, we present the quantization of Landau for a neutral particle with a permanent magnetic dipole moment in the presence of external fields and under the influence of a Coulomb like potential. We use the idea of Ericsson e Sjöqvist which consists in using the system proposed by Aharonov and Casher to generate an analogue of the quantization of Landau for neutral atom systems. Moreover, we observe that when the analogue of the Landau quantization is subject to a Coulomb like potential its cyclotron frequency is modified in contrast with the behavior found by of reference. Finally, we discuss the quantum effect characterized by the dependence of quantum numbers with the angular frequency.
In this thesis, we investigate by the first time the impact of non-inertial effects associated with the rotation of the reference system on charged and neutral particles confined by a quantum ring, which is described by the potential of Tan-Inkson. The contribution of the rotation is introduced by its coupling with angular momentum of the system. We show that the rotation is introduced via a non-minimum coupling to the kinetic part of the Hamiltonian describing the quantum dynamics of systems studied here. Thus, we show that non-inertial effects of the rotation induce on the quantum properties of the particles similar effects generated by a magnetic field. We also investigated the contribution of a screw dislocation on the physical properties of the particles. The topological defect contributes as a torsion source, presenting a contribution similar to the Aharonov-Bohm flux. Besides charged particles (electrons and holes), we also study the effects of rotation on neutral particles in three different scenarios: a neutral particle with a permanent magnetic dipole moment coupled by the Aharanov-Casher interaction; a neutral particle with a permanent electric dipole moment coupled by the interaction proposed by He-McKellar-Wilkens and a neutral particle with an electric dipole moment induced by the field configuration proposed by Wei-Han-Wei. In all three cases it is shown the similarity between the neutral and charged particles. We analyze the non-relativistic quantum dynamics of these particles by solving the Schrödinger equation. In addition to the energy spectrum and wave functions, we calculate the persistent current and the magnetization for the four systems studied here, and we also analyzed, from the expression for the persistent current for quantum rings, the limit case for quantum dots.
Neste trabalho discutimos a importância das fases quânticas usando o Efeito Aharonov-Bohm para particulas carregadas e particulas neutras com momento de dipolo magnetico (Efeito Aharonov-Casher) e momento de dipolo eletrico (Efeito He-McKellar-Wilkens), e atomos com momento de quadrupolo eletrico. Tira-se vantagem do estudo inicial de tais sistemas para mostrar a emersao de niveis de Landau na dinâmica de uma particula em duas situacoes: quando a particula esta carregada e quando ela e neutra. No caso de uma particula neutra e considerado que esta possui momento de dipolo eletrico. Alem disso e a primeira vez que e abordado um atomo neutro com momento de quadrupolo eletrico.
We show the emergence of a new type of dispersion relation for neutral atoms with an interesting similarity to the spectrum of two-dimensional electrons in an applied perpendicular constant magnetic field. These neutral atoms can be confined in toroidal optical traps and give quasi-Landau spectra. In strong contrast to the equidistant infinitely degenerate Landau levels for charged particles, the spectral gap for such two-dimensional neutral particles increases in particular electric-field configurations. The idea in the paper is motivated by the development in cold atom experiments and builds on the seminal paper of Aharonov and Casher [Phys. Rev. Lett. 53, 319 (1984)].