Landau quantization of neutral particles in an external field

Abstract

The quantum dynamics of an induced electric dipole in the presence of a configuration of crossed electric and magnetic fields is analyzed. This field configuration confines the dipole in a plane and produces a coupling similar to the coupling of a charged particle in the presence of external magnetic field. In this work we investigate the analog of Landau levels in induced electric dipoles in a sistem of neutral particles. The energy levels and eigenfunctions are obtained exactly.The quantum dynamics of cold atoms in the presence of an electromagnetic field promises new possibilities to study the quantum properties of many body systems. This system can be easily controlled and manipulated by electromagnetic fields. The cold atoms make then ideal candidates for the study of several intrinsically quantum phenomena. In recent years the advance of cold atom technology made it possible to simulate several solid state effects employing neutral atoms and techniques from quantum optics [1,2,3]. Recently, the neutral atoms techniques to simulate the behavior of a charged particle in this systems [3,4,5,6] has been developted. In this way, the study of systems that simulate the strongly interacting system in a cold atom has attract much attention in recent years [7,8].Electric dipole moment of atoms in the presence of an appropriate electromagnetic field configuration has been utilized in literature to inquire above some physical effects [9,10,11,12]. The study of quantum phases in the quantum dynamics of the electromagnetic dipole has its origin in the Aharonov-Casher effect [14] for the magnetic dipole in the presence of an electric field, that is reciprocal effect of the well known Aharonov-Bohm[15] effect. The dual effect of Aharonov-Casher effect was studied independently by He and McKellar[18] and Wilkens [19], which investigated the quantum dynamics of the electric dipole in the presence of magnetic field. In fact, electric dipoles can give rise to a variety of different phenomena that generate geometric phases [12,13,18,19,20] in different field-dipole configurations. Wei, Han and Wei [21] have proposed a more realistic field configuration that generate a He-McKellar-Wilkens effect. In fact, all quantum effects in the dynamics of the dipole occur due to the coupling of electric/magnetic dipole with external magnetic/electric field make a mimic of minimal coupling of charged particle with an external magnetic field. In this work we use this configuration to study a possibility of an analog Landau quantization due to induced electric dipoles in cold atom systems.The interaction of the electromagnetic field with a * Electronic Address: furtado@fisica.ufpb.br charged particle, plays an important role in the generation of collective phenomena, such as, fractional statistics [22] and the quantum Hall effect. The quantum motion of a charged particle in the presence of a constant magnetic field is described by the theory of Landau [23]. The Landau quantization in two dimensions makes the energy levels coalesce into a disc...

Relativistic Landau quantization for a neutral particle

“…The last terms of (19) correspond to the non-relativistic analog of the Landau levels obtained in [13], where these non-relativistic energy levels are infinitely degenerated.…”

“…Within the HMW effect, the phase shift is generated by the interaction between an external magnetic field and the electric dipole moment of the neutral particle. Thus, considering the HMW effect, Ribeiro et al [18] have studied the analog of Landau quantization for a neutral particle which possesses a permanent electric dipole moment, and Furtado et al [19] have investigated the Landau quantization for induced electric dipoles, being motivated by the paper of Wei et al [20].…”

Landau quantization for an induced electric dipole in the presence of topological defects

“…Following [18], we can write the Hamiltonian which describes the non-relativistic dynamics of the induced electric dipole interacting with the external electric and magnetic fields (without spin) as…”

“…For a system involving initially non-polarized neutral particles, we proposed a field configuration of crossed electric and magnetic fields, which polarizes the particle, so, it gets an electric dipole moment [18]. In this case, we…”

Quantum Effects on an Atom with a Magnetic Quadrupole Moment in a Region with a Time-Dependent Magnetic Field

“…Atoms with an induced electric dipole moment that interacts with electric and magnetic fields have also shown quantum effects associated with geometric quantum phases [3] and the Landau-type quantization [4]. Besides, by dealing with neutral particles with a permanent electric dipole moment that interacts with a magnetic field, it has been shown in Refs.…”