Analogous to Landau quantization related to a neutral particle possessing an electric quadrupole moment, we generalize such Landau quantization to include position-dependent mass (PDM) neutral particles. Using cylindrical coordinates, the exact solvability of PDM neutral particles with an electric quadrupole moment moving in electromagnetic fields is reported. The interaction between the electric quadrupole moment of a PDM neutral particle and a magnetic field in the absence of an electric field is analyzed for two different radial cylindrical PDM settings. Next, two particular cases of radial electric fields (E=λ\r{ho}/\r{ho} and E=λ\r{ho}/2\r{ho}) are considered to investigate their influence on the Landau quantization (of this system using the same models of PDM settings). The exact eigenvalues and eigenfunctions for each case are analytically obtained.
Based on the single particle approximation [V. F. Dmitriev {\it et al}, Phys. Rev. C {\bf50}, 2358 (1994), C.-C. Chen, Phys. Rev. A {\bf51}, 2611 (1995)], the Landau quantization associated with an atom with a magnetic quadrupole moment is introduced, and then, rotating effects on this analogue of the Landau quantization is investigated. It is shown that rotating effects can modify the cyclotron frequency and breaks the degeneracy of the analogue of the Landau levels.
In this contribution we study the Landau levels arising within the relativistic quantum dynamics of a neutral particle which possesses a permanent magnetic dipole moment interacting with an external electric field. We consider the Aharonov-Casher coupling of magnetic dipole to the electric field to investigate an an analog of Landau quantization in this system and solve the Dirac equation for two different field configurations. The eigenfunctions and eigenvalues of Hamiltonian in both cases are obtained.
The ordinary Landau problem consists of describing a charged particle in time-independent magnetic field. In the present case the problem is generalized onto time-dependent uniform electric fields with time-dependent mass and harmonic frequency [1].The spectrum of a Hamiltonian describing this system is obtained. The configuration space wave functions of the model is expressed in terms of the generalised Laguerre polynomials. To diagonalize the time-dependent Hamiltonian we employ the Lewis-Riesenfeld method of invariants. To this end, we introduce an unitary transformation in the framework of…
It is well established that the Hilbert space for charged particles in a plane subject to a uniform magnetic field can be described by two mutually commuting ladder algebras. We propose a similar formalism for Landau level quantization involving two mutually commuting SU(2) algebras.
In this work we develop a model based on the double solution theory of de Broglie in order to reproduce the famous Landau levels splitting in a constant magnetic field.
The quantum description of an atom with a magnetic quadrupole moment in the presence of a uniform effective magnetic field is analysed. The atom is also subject to rotation and a scalar potential proportional to the inverse of the radial distance. It is shown that the spectrum of energy is modified, in contrast to the Landau-type levels, and there is a restriction on the possible values of the cyclotron frequency which stems from the influence of the rotation and scalar potential proportional to the inverse of the radial distance.
We consider the problem of multilayer graphene on a Haldane sphere and determine the Landau level spectrum for this family of systems. This serves as a generalization of the Landau quantization problem of ordinary non-relativistic Haldane sphere and spherical graphene, or Dirac-like particles on a sphere. The Hamiltonian is diagonalized in a concise algebraic fashion exploiting two mutually commuting SU(2) algebras of the problem. Additionally, using exact wave functions we demonstrate computation of Haldane pseudopotentials in the second Landau level. These exact solutions add to the current …
We investigate the arising of an analogue of the Landau quantization from a background of the violation of the Lorentz symmetry established by a time-like 4-vector and a field configuration of crossed electric and magnetic field. We also analyse the effects on this Landau-type system subject to a hard-wall confining potential by showing a particular case where a discrete spectrum of energy can be obtained. Further, we analyse the effects of a linear confining potential on the Landau-type system. We show that a quantum effect characterized by the dependence of the cyclotron frequency on the qua…
In this letter we study the quantum dyamics of a neutral particle in the presence of an external magnetic field. We demonstrate in a specific field-dipole configuration that we have a quantization similar to the Landau Levels. We investigate this quantization motivated by the recent analysis of Landau-Aharonov-Casher(LAC) quantization of Ericsson and Sjöqvist[Phys Rev. A {\bf 65} 013607 (2001)]. The energy eigenfuction and eigenvalues are obtained.
We investigate non-inertial and gravitational effects on quantum states in electromagnetic fields and present the analytic solution for energy eigenstates for the Schrödinger equation including non-inertial, gravitational and electromagnetic effects. We find that in addition to the Landau quantization the rotation of spacetime itself leads to the additional quantization, and that the energy levels for an electron are different from those for a proton at the level of gravitational corrections.
We present a method that uses dynamic decoupling of a multi-level quantum probe to distinguish small frequency shifts that depend on $m^2_{j}$, where $m^2_{j}$ is the angular momentum of level $\left|j\right\rangle$ along the quantization axis, from large noisy shifts that are linear in $m_{j}$, such as those due to magnetic field noise. Using this method we measured the electric quadrupole moment of the $4D_{\frac{5}{2}}$ level in $^{88}Sr^{+}$ to be $2.973^{+0.026}_{-0.033}\, ea_{0}^{2}$. Our measurement improves the uncertainty of this value by an order of magnitude and thus helps mitigate …
We investigate the two-dimensional motion of relativistic cold electrons in the presence of `strictly' spatially varying magnetic fields satisfying, however, no magnetic monopole condition. We find that the degeneracy of Landau levels, which arises in the case of the constant magnetic field, lifts out when the field is variable and the energy levels of spin-up and spin-down electrons align in an interesting way depending on the nature of change of field. Also the varying magnetic field splits Landau levels of electrons with zero angular momentum from positive angular momentum, unlike the const…
Quantum effects on a Landau-type system associated with a moving atom with a magnetic quadrupole moment subject to confining potentials are analysed. It is shown that the spectrum of energy of the Landau-type system can be modified, where the degeneracy of the energy levels can be broken. In three particular cases, it is shown that the analogue of the cyclotron frequency is modified, and the possible values of this angular frequency of the system are determined by the quantum numbers associated with the radial modes and the angular momentum and by the parameters associated with confining poten…
Alternating current RLC electric circuits form an accessible and highly tunable platform simulating Hermitian as well as non-Hermitian (nH) quantum systems. We propose here a circuit realization of nH Dirac and Weyl Hamiltonians subject to time-reversal invariant pseudo-magnetic field, enabling the exploration of novel nH physics. We identify the low-energy physics with a generic real energy spectrum from the nH Landau quantization of exceptional points and rings, which can avoid the nH skin effect and provides a physical example of a quasiparticle moving in the complex plane. Realistic detect…
We study the directional dependence of the coupling between a nanofiber-guided light field and a two-level atom with an electric quadrupole transition. We examine the situation where the atom lies on the fiber transverse axis $x$, the quantization axis for the atomic internal states is the other orthogonal transverse axis $y$, the atomic upper and lower levels are the magnetic sublevels $M'$ and $M$ of hyperfine-structure levels of an alkali-metal atom, and the field is in a quasilinearly polarized fundamental guided mode HE$_{11}$ with the polarization $ξ=x$ or $y$. We find that the absolute …
We study ultracold atom-ion collisions in the presence of an external magnetic field. At low collision energy the field can drastically modify the translational motion of the ion, which follows quantized cyclotron orbits. We present a rigorous theoretical approach for the calculation of quantum scattering amplitudes in these conditions. Collisions in different magnetic field regimes, identified by the size of the cyclotron radius with respect to the range of the interaction potential, are investigated. Our results are important in cases where use of a magnetic field to control the atom-ion col…
The quantum description of an atom with a magnetic quadrupole moment in the presence of a time-dependent magnetic field is analysed. It is shown that the time-dependent magnetic field induces an electric field that interacts with the magnetic quadrupole moment of the atom and gives rise to a Landau-type quantization. It is also shown that a time-independent Schrödinger equation can be obtained, i.e., without existing the interaction between the magnetic quadrupole moment of the atom and the time-dependent magnetic field, therefore, the Schrödinger equation can be solved exactly. It is also ana…
In this paper, we analyze Dirac fermions in Gödel-type background space-times with torsion. We also consider the Gödel-type spacetimes embedded in a topological defect background. We show that relativistic bound states solutions to the Dirac equation can be obtained by dealing with three cases of the Gödel-type solutions with torsion, where a cosmic string passes through these three cases of the space-time. We obtain the relativistic energy levels for all cases of the Gödel-type solutions with torsion with a cosmic string, where we show that there exists an analogy with the Landau levels for D…
In this paper, we investigate the influence of a screw dislocation on the energy levels and the wavefunctions of an electron confined in a two-dimensional pseudoharmonic quantum dot under the influence of an external magnetic field inside a dot and Aharonov-Bohm field inside a pseudodot. The exact solutions for energy eigenvalues and wavefunctions are computed as functions of applied uniform magnetic field strength, Aharonov-Bohm flux, magnetic quantum number and the parameter characterizing the screw dislocation, the Burgers vector. We investigate the modifications due to the screw dislocatio…
We investigate the gravitational effect on Landau levels. We show that the familiar infinite Landau degeneracy of the energy levels of a quantum particle moving inside a uniform and constant magnetic field is removed by the interaction of the particle with a gravitational field. Two independent approaches are used to solve the relevant Schrödinger equation within the Newtonian approximation. It is found that both approaches yield qualitatively similar results within their respective approximations. With the goal of clarifying some results found in the literature concerning the use of a third i…
We study two anyons with Coulomb interaction in a uniform magnetic field $B$. By using the torus quantization we obtain the modified Landau and Zeeman formulas for the two anyons. Then we derive a simple algebraic equation for the full spectral problem up to the second order in $B$.
