Two charges on plane in a magnetic field: II. Moving neutral quantum system across a magnetic field
M. A. Escobar-Ruiz, A. V. Turbiner
备注：
24 pages, 5 figures, 13 tables (6 in main body and 7 moved in a supplementary material), several clarifying sentences and 3 extra references added, Chapter II rectified, typos fixed, Annals of Physics (to be published)
The moving neutral system of two Coulomb charges on a plane subject to a constant magnetic field $B$ perpendicular to the plane is considered. It is shown that the composite system of finite total mass is bound for any center-of-mass momentum $P$ and magnetic field strength; the energy of the ground state is calculated accurately using a variational approach. Their accuracy is cross-checked in a Lagrange-mesh method for $B=1$ a.u. and in a perturbation theory at small $B$ and $P$. The constructed trial function has the property of being a uniform approximation of the exact eigenfunction. For a Hydrogen atom and a Positronium a double perturbation theory in $B$ and $P$ is developed and the first corrections are found algebraically. A phenomenon of a sharp change of energy behavior for a certain center-of-mass momentum and a fixed magnetic field is indicated.
We discuss the properties of thermal electromagnetic radiation produced by a neutral polarizable nanoparticle moving with an arbitrary relativistic velocity in a heated vacuum background with a fixed temperature. We show that the particle in its own rest frame acquires the radiation temperature of vacuum, multiplied by a velocity-dependent factor, and then emits thermal photons predominantly in the forward direction. The intensity of radiation proves to be much higher than for the particle at rest. For metal particles with high energy, the ratio of emitted and absorbed radiation power is propo…
Based on a fully relativistic framework and the assumption of local equilibrium, we describe a simple mechanism of quantum friction for a particle moving parallel to a dielectric. The Cherenkov effect explains how the bare ground state becomes globally unstable and how fluctuations of the electromagnetic field and the particle's dipole are converted into pairs of excitations. Modelling the particle as a silver nano-sphere, we investigate the spectrum of the force and its velocity dependence. We find that the damping of the plasmon resonance in the silver particle has a relatively strong impact…
We predict and study the quantum-electrodynamical effect of parametric self-induced excitation of a molecule moving above the dielectric or conducting medium with periodic grating. In this case the radiation reaction force modulates the molecular transition frequency which results in a parametric instability of dipole oscillations even from the level of quantum or thermal fluctuations. The present mechanism of instability of electrically neutral molecules is different from that of the well-known Smith-Purcell and transition radiation in which a moving charge and its oscillating image create an…
For the first time, based on the fluctuation-electromagnetic theory, we have calculated the drug force, the radiation heat flux and the frictional torque on a small rotating particle moving at a relativistic velocity through the equilibrium background radiation (photon gas). The particle and background radiation are characterized by different temperatures corresponding to the local thermodynamic equilibrium in their own reference frames.
We calculate tangential forces applied to a ground state atom (nanoparticle) moving with nonrelativistic velocity parallel to the surface of Drude -modelled or Lorentz -modelled half -space using the formalism of fluctuation electrodynamics.The obtained formulae assume the nonretarded regime and arbitrary temperatures of the particle and medium. The quantum frictional force is realized at zero temperature of the particle and medium and can reach about 1/3 of the static value of the Casimir -Polder force in the case of ground state atom. In the case of nanoparticles and nonzero temperature, the…
In this paper, we construct the coherent states for a system of an electron moving on plane in uniform external magnetic and electric fields. These coherent states are built in the context of both discrete and continuous spectra and satisfy the Gazeau-Klauder coherent states properties [1].
It has recently been suggested that an Aharonov-Bohm phase should be capable of detection using beams of neutral polarizable particles. A more careful analysis of the proposed experiment suffices to show, however, that it cannot be performed regardless of the strength of the external electric and magnetic fields.
We consider the electromagnetic vacuum field inside a perfect plane cavity with moving mirrors, in the nonrelativistic approximation. We show that low frequency photons are generated in pairs that satisfy simple properties associated to the plane geometry. We calculate the photon generation rates for each polarization as functions of the mechanical frequency by two independent methods: on one hand from the analysis of the boundary conditions for moving mirrors and with the aid of Green functions; and on the other hand by an effective Hamiltonian approach. The angular and frequency spectra are …
In this work, we construct different classes of coherent states related to a quantum system, recently studied in [1], of an electron moving in a plane in uniform external magnetic and electric fields which possesses both discrete and continuous spectra. The eigenfunctions are realized as an orthonormal basis of a suitable Hilbert space appropriate for building the related coherent states. These latter are achieved in the context where we consider both spectra purely discrete obeying the criteria that a family of coherent states must satisfies.
Velocity-Enabled Quantum Computing with Neutral Atoms
Max-Planck-Institut für Quantenoptik（马克斯·普朗克量子光学研究所）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；Harvard University（哈佛大学）；Fakultät für Physik, Ludwig-Maximilians-Universität（慕尼黑大学物理学院）
One of the most extraordinary manifestations of the coupling of the optical field and matter is the emission of light by charged particles passing through a dielectric medium: the Vavilov-Cherenkov effect. In this article, it is theoretically predicted that a related phenomenon may be observed when neutral fast polarizable particles travel near a metal surface supporting surface plasmon polaritons. Rather dramatically, it is found that at some critical velocity, even if the initial optical field is vanishingly small, the system may become unstable and may start spontaneously emitting light suc…
It is well known that any cyclic solution of a spin 1/2 neutral particle moving in an arbitrary magnetic field has a nonadiabatic geometric phase proportional to the solid angle subtended by the trace of the spin. For neutral particles with higher spin, this is true for cyclic solutions with special initial conditions. For more general cyclic solutions, however, this does not hold. As an example, we consider the most general solutions of such particles moving in a rotating magnetic field. If the parameters of the system are appropriately chosen, all solutions are cyclic. The nonadiabatic geome…
We study a string of neutral atoms with nearest neighbor interaction in a 1D beam splitter configuration, where the longitudinal motion is controlled by a moving optical lattice potential. The dynamics of the atoms crossing the beam splitter maps to a 1D spin model with controllable time dependent parameters, which allows the creation of maximally entangled states of atoms by crossing a quantum phase transition. Furthermore, we show that this system realizes protected quantum memory, and we discuss the implementation of one- and two-qubit gates in this setup.
Low-lying bound states for the problem of two Coulomb charges of finite masses on a plane subject to a constant magnetic field $B$ perpendicular to the plane are considered. Major emphasis is given to two systems: two charges with the equal charge-to-mass ratio (quasi-equal charges) and neutral systems with concrete results for the Hydrogen atom and two electrons (quantum dot). It is shown that for these two cases, but when a neutral system is at rest (the center-of-mass momentum is zero), some outstanding properties occur: in double polar coordinates in CMS $(R, ϕ)$ and relative $(ρ, φ)$ coor…
In this contribution, we investigate the interaction between electric and magnetic fields with an electric quadrupole moment of a spinless particle moving in an elastic medium which has a topological defect (screw dislocation). By considering this interaction, the Schrödinger equation is exactly solved by using the analytical method. Thus, the eigenfunction and energy eigenvalues for two configurations are found. Meanwhile, by observing a shift in the angular momentum quantum number, the energy eigenvalues and the wave function of the system are modified, due to the screw dislocation in the me…
We investigate the dynamics of neutral atoms in a 2D optical lattice which traps two distinct internal states of the atoms in different columns. Two Raman lasers are used to coherently transfer atoms from one internal state to the other, thereby causing hopping between the different columns. By adjusting the laser parameters appropriately we can induce a non vanishing phase of particles moving along a closed path on the lattice. This phase is proportional to the enclosed area and we thus simulate a magnetic flux through the lattice. This setup is described by a Hamiltonian identical to the one…
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…
