Metastable states,the adiabatic theorem and parity violating geometric phases II

We discuss and calculate parity conserving (PC) and parity violating (PV) geometric phases for the metastable 2S states of hydrogen and deuterium. The atoms are supposed to be subjected to slowly varying electric and magnetic fields which act as external parameters for the atoms. Geometric flux density fields are introduced which allow for an easy overview how to choose the paths in parameter space in order to obtain only PC or only PV geometric phases. The PV phases are calculated in the Standard Model of particle physics. Even if numerically they come out small they have interest of principle as a new manifestation of parity violation in atomic physics. Electronic supplementary material Supplementary Online Material     

Parity violation in hydrogen and longitudinal atomic beam spin echo I

We discuss the propagation of hydrogen atoms in static electric and magnetic fields in a longitudinal atomic beam spin echo (lABSE) apparatus. There the atoms acquire geometric (Berry) phases that exhibit a new manifestation of parity-(P-)violation in atomic physics. We provide analytical as well as numerical calculations of the behaviour of the metastable 2S states of hydrogen. The conditions for electromagnetic field configurations that allow for adiabatic evolution of the relevant atomic states are investigated. Our results provide the theoretical basis for the discussion of possible measurements of P-violating geometric phases in lABSE experiments.     

Excitation of helium atoms in collisions with plasma electrons in an electric field

The rate constants are evaluated for excitation of helium atoms in metastable states by electron impact if ionized helium is located in an external electric field and is supported by it, such that a typical electron energy is small compared to the atomic excitation energy. Under these conditions, atomic excitation is determined both by the electron traveling in the space of electron energies toward the excitation threshold and by the subsequent atomic excitation, which is a self-consistent process because it leads to a sharp decrease in the energy distribution function of electrons, which in turn determines the excitation rate. The excitation rate constant is calculated for the regimes of low and high electron densities, and in the last case, it is small compared to the equilibrium rate constant where the Maxwell distribution function is realized including its tail. Quenching of metastable atomic states by electron impact results in excitation of higher excited states, rather than transition to the ground electron state for the electric field strengths under consideration. Therefore, at restricted electron number densities, the rate of emission of resonant photons of the wavelength 58 nm, which results from the transition from the 2¹ P state of the helium atom to the ground state, is close to the excitation rate of metastable atomic states. The efficiency of atomic excitation in ionized helium, i.e., the part of energy of an electric field injected in ionized helium that is spent on atomic excitation, is evaluated. The results exhibit the importance of electron kinetics for an ionized gas located in an electric field.     

A hydrogen atom in a superstrong magnetic field and the Zeldovich effect

We consider the problem of a hydrogen atom in a superstrong magnetic field, B? B _a =2.35×10⁹ G. The analytical formulas that describe the energy spectrum of this atom are derived for states with various quantum numbers n_ρ and m. A comparison with available calculations shows their high accuracy for B?B _a . We note that the derived formulas point to a manifestation of the Zeldovich effect, i.e., a rearrangement of the atomic spectrum under the influence of strong short-range Coulomb potential distortion. We discuss the relativistic corrections to level energies, which increase in importance with magnetic field and become significant for B?10¹⁴ G. We suggest the parameters in terms of which the Zeldovich effect has the simplest form. Analysis of our precision numerical calculations of the energy spectrum for a hydrogen atom in a constant magnetic field indicates that the Zeldovich effect is observed in the spectrum of atomic levels for superstrong fields, B?5×10¹¹ G. Magnetic fields of such strength exist in neutron stars and, possibly, in magnetic white dwarfs. We set lower limits for the fields B_min required for the manifestation of this effect. We discuss some of the properties of atomic states in a superstrong magnetic field, including their mean radii and quadrupole moments. We calculated the probabilities of electric dipole transitions between odd atomic levels and a deep ground level.     

Longitudinal atomic beam spin echo experiments: a possible way to study parity violation in hydrogen

We discuss the propagation of hydrogen atoms in static electric and magnetic fields in a longitudinal atomic beam spin echo (lABSE) apparatus. Depending on the choice of the external fields the atoms may acquire both dynamical and geometrical quantum mechanical phases. As an example of the former, we show first in-beam spin rotation measurements on atomic hydrogen, which are in excellent agreement with theory. Additional calculations of the behaviour of the metastable 2S states of hydrogen reveal that the geometrical phases may exhibit the signature of parity-(P-)violation. This invites for possible future lABSE experiments, focusing on P-violating geometrical phases in the lightest of all atoms.     

Large parity violating effects in atomic dysprosium with nearly degenerate Floquet eigenvalues

In this article we study effects of parity nonconservation in atomic dysprosium, where one has a pair of nearly degenerate levels of opposite parity. We consider the time evolution of this two-level system within oscillatory electric and magnetic fields. These are chosen to have a periodical structure with the same period, such that a Floquet matrix describes the time evolution of the quantum states. We show that, if the states are unstable, the eigenvalues of the Floquet matrix may have contributions proportional to the square root of the parity violating interaction matrix element while they are almost degenerate in their parity even part. This leads to beat frequencies proportional to which are expected to be larger by several orders of magnitude compared to ordinary P-violating contributions which are of order . However, for the simple field configurations we considered, it still seems to be difficult to observe these P-violating beat effects, since the states decay too fast. On the other hand, we found that, within only a few Floquet cycles, very large parity violating asymmetries with respect to experimental setups of opposite chirality may be obtained. The electric and magnetic fields as well as the time intervals necessary for this are in an experimentally accessible range. For statistically significant effects beyond one standard deviation a number of about 10⁷ atoms is required. Our ideas may be applied directly to other 2-level atomic systems and different field configurations. We hope that these ideas will stimulate experimental work in this direction. Received 16 September 1999 and Received in final form 10 March 2000     

Non-Abelian Berry's phase effects and optical pumping of atoms

We predict experimentally verifiable manifestations of non-Abelian Berry's phase effects for atoms in external collinear electric and magnetic fields. The field strengths are arranged so as to cause accidental degeneracy between atomic states. The relevant theoretical results, which have been presented in detail elsewhere, are summarized and explained. We propose an experiment using optically pumped metastable multiplets of Pb²⁰⁸ in an atomic beam apparatus to test these predictions. We estimate required experimental parameters, and conclude that the proposed experiment can realistically be performed.     

Time-dependent harmonic oscillator in a magnetic field and an electric field on the non-commutative plane

In the non-commutative space, wave functions and geometric phases are derived for the time-dependent harmonic oscillator in external time-dependent magnetic and electric field. Explicit forms of the coherent states are also given, which are not the minimum uncertainty states for the coordinates and momenta.     

Exact Solutions Describing Collapse of Landau Levels in Graphene

The eigenequation for single-layer graphene in transverse electric and perpendicular magnetic fields is investigated at a critical value |E| = υ _F B. The critical solutions are not bound states and contain two unknown constants. Different from the case of the “classical” Hall effect, the electric current in the direction perpendicular to the electric and magnetic fields could be positive or negative depending on the values of the unknown constants.     

Ferromagnetism modulation by phase change in Mn-doped GeTe chalcogenide magnetic materials

In this work, an effective method to modulate the ferromagnetic properties of Mn-doped GeTe chalcogenide-based phase change materials is presented. The microstructure of the phase change magnetic material Ge_1?x Mn _x Te thin films was studied. The X-ray diffraction results demonstrate that the as-deposited films are amorphous, and the crystalline films are formed after annealing at 350 °C for 10 min. Crystallographic structure investigation shows the existence of some secondary magnetic phases. The lattice parameters of Ge_1?x Mn _x Te (x = 0.04, 0.12 and 0.15) thin films are found to be slightly different with changes of Mn compositions. The structural analysis clearly indicates that all the films have a stable rhombohedral face-centered cubic polycrystalline structure. The magnetic properties of the amorphous and crystalline Ge_0.96Mn_0.04Te were investigated. The measurements of magnetization (M) as a function of the magnetic field (H) show that both amorphous and crystalline phases of Ge_0.96Mn_0.04Te thin film are ferromagnetic and there is drastic variation between amorphous and crystalline states. The temperature (T) dependence of magnetizations at zero field cooling (ZFC) and field cooling (FC) conditions of the crystalline Ge_0.96Mn_0.04Te thin film under different applied magnetic fields were performed. The measured data at 100 and 300 Oe applied magnetic fields show large bifurcations in the ZFC and FC curves while on the 5,000 Oe magnetic field there is no deviation.     

Umbesetzung der 2S 1/2-Hyperfeinstrukturniveaus im metastabilen Deuteriumatomstrahl einer Lambshift-Quelle durch Anwendung von statischen Magnetfeldern

Polarized deuteron beams may be obtained from metastable atomic beams by quenching three of the six hyperfinestructure levels. Using a field distribution which crosses zero on the beam axis the occupation numbers of the hyperfinestructure levels may be changed by a nonadiabatic process. The special conditions for this magnetic field are discussed by comparing the corresponding Larmor frequency of the metastable atoms with the angular frequency of the magnetic field vector. Experimental investigations were carried out for field gradients between 1.9 and 5.4 Oe/cm and for superposed homogeneous transverse fields of up to 6 Oe. With deuterons a tensorpolarization ofP ₃₃=?0.70±0.01 was obtained at a negative ion beam current of 42 nA.     

Characteristics of Level Anticrossing in Parallel Electric and Magnetic Fields

Using the matrix diagonalization method, we have studied two kinds of level anticrosing of Rydberg cesium atom in parallel electric and magnetic fields. Our numerical results reveal that in the vicinity position of level crossing between different parity states in a magnetic field, the energy levels and other behaviors of the states are quite sensitive to the electric field. We tabulate some features which may be as a guide in experimental verification.     

Axially symmetrical molecules in electric and magnetic fields: energy spectrum and selection rules

In this paper we investigate the effects of external electric and magnetic fields on a three-dimensional harmonic oscillator with axial symmetry. The energy spectrum of such a system is non-degenerate due to the presence of the magnetic field. The degeneracy of the energy spectrum in the absence of a magnetic field is discussed. The influence of electric and magnetic fields, as well as the frequencies of the oscillator on the probability distribution function is analyzed. Optical transition probabilities are examined by deriving the selection rules in dipole approximation for the quantum numbers n _p , m _l and n _z . Employing stationary perturbation theory, the effects of deformations of the potential energy function on the oscillatory states are analyzed. Such models have been used in literature in analysis of spectra of axially symmetrical molecules and cylindrical quantum dots.     

Tunable band structure effects on ballistic transport in graphene nanoribbons

Graphene nanoribbons (GNR) in mutually perpendicular electric and magnetic fields are shown to exhibit dramatic changes in their band structure and electron transport properties. A strong electric field across the ribbon induces multiple chiral Dirac points, closing the semiconducting gap in armchair GNRs. A perpendicular magnetic field induces partially formed Landau levels as well as dispersive surface-bound states. Each of the applied fields on its own preserves the even symmetry Ek=E−k of the subband dispersion. When applied together, they reverse the dispersion parity to be odd and gives Ee,k=−Eh,−k and mix the electron and hole subbands within the energy range corresponding to the change in potential across the ribbon. This leads to oscillations of the ballistic conductance within this energy range.     

Ionization of atoms in electric and magnetic fields and the imaginary time method

A semiclassical theory is developed for the ionization of atoms and negative ions in constant, uniform electric and magnetic fields, including the Coulomb interaction between the electron and the atomic core during tunneling. The case of crossed fields (Lorentz ionization) is examined specially, as well as the limit of a strong magnetic field. Analytic equations are derived for arbitrary fields ℰ and ℋ that are weak compared to the characteristic intraatomic fields. The major results of this paper are obtained using the “imaginary time” method (ITM), in which tunneling is described using the classical equations of motion but with purely imaginary “time.” The possibility of generalizing the ITM to the relativistic case, as well as to states with nonzero angular momentum, is pointed out. Zh. éksp. Teor. Fiz. 113, 1579–1605 (May 1998)     

Hyperfine interactions and electronic structures of BaFe 2 As 2 : a first-principles LDA+U study

The hyperfine parameters of hyperfine fields, electric field gradients and isomer shifts at the Fe site are investigated based on the first-principles calculations of the electronic structures using LDA (GGA)+U method in the low-temperature orthorhombic antiferromagnetic phase of undoped BaFe₂As₂. It is fond that the electric field gradient of Fe nucleus is highly related with the electronic structures close to the Fermi level. Though the addition of negative on-site Coulomb interaction to Fe-3d states improves the calculated magnetic moment of Fe atom and the hyperfine parameters of Fe nucleus when U = ?0.1 Ry (?0.08 Ry) for GGA+U (LDA+U) method, a negative U correction does not capture the right physics of this system. The calculations prove the strong coupling between the magnetic, structural and electronic properties in antiferromagnetic BaFe₂As₂ parent.     

Long-term drifts of stray electric fields in a Paul trap

We investigate the evolution of quasi-static stray electric fields in a linear Paul trap over a period of several months. Depending on how these electric fields are initially induced, we observe very different timescales for the field drifts. Photo-induced electric fields decay on timescales of days. We interpret this as photo-electrically generated charges on insulating materials which decay via discharge currents. In contrast, stray fields due to the exposure of the ion trap to a beam of Ba atoms mainly exhibit slow dynamics on the order of months. We explain this observation as a consequence of a coating of the trap electrodes by the atomic beam. This may lead to contact potentials which can slowly drift over time due to atomic diffusion and chemical processes on the surface. In order not to perturb the field evolutions, we suppress the generation of additional charges and atomic coatings in the Paul trap during the measurements. For this, we shield the ion trap from ambient light and only allow the use of near-infrared lasers. Furthermore, we minimize the flux of atoms into the ion trap chamber. Long-term operation of our shielded trap led us to a regime of very low residual electric field drifts of less than 0.03 V/m per day.     

Perturbative approach to the hydrogen atom in a strong magnetic field

We consider states of the hydrogen atom with the principal quantum number n≤3 and zero magnetic quantum number in a constant homogeneous magnetic field ?. The perturbation theory series is summed using the Borel transformation and conformal mapping of the Borel variable. Convergence of the approximate energy eigenvalues and their agreement with the corresponding existing results are observed for external fields up to n³?/?₀～5, where ?₀ is the atomic magnetic field. The possibility of restoring the asymptotic behavior of energy levels using perturbation theory coefficients is also discussed.     

Magnetovacs in gauged N = 4 supergravity

A two-parameter family of supersymmetric background field solutions of the recently formulated version of gauged N = 4 supergravity is found. This constitutes strong evidence that the theory has stable vacua, despite energy densities that are unbounded below. The background geometries are metric products of (AdS)₂ × S₂, and there are covariantly constant magnetic and electric fields. For a special choice of parameters the (AdS)₂ factor becomes a flat Minkowski space and electric fields vanish.     

Gauge-invariant charged,monopole and dyon fields in gauge theories

We propose explicit recipes to construct the Euclidean Green functions of gauge-invariant charged, monopole and dyon fields in four-dimensional gauge theories whose phase diagram contains phases with deconfined electric and/or magnetic charges. In theories with only either abelian electric or magnetic charges, our construction is an Euclidean version of Dirac's original proposal, the magnetic dual of his proposal, respectively. Rigorous mathematical control is achieved for a class of abelian lattice theories. In theories where electric and magnetic charges coexist, our construction of Green functions of electrically or magnetically charged fields involves taking an average over Mandelstam strings or the dual magnetic flux tubes, in accordance with Dirac's flux quantization condition. We apply our construction to 't Hooft-Polyakov monopoles and Julia-Zee dyons. Connections between our construction and the semiclassical approach are discussed.