The g-factor of the electron bound in 28 Si 13+ : the most stringent test of bound-state quantum electrodynamics

This thesis describes the ultra-precise determination of the g-factor of the electron bound to hydrogenlike 28Si13+. The experiment is based on the simultaneous determination of the cyclotron- and Larmor frequency of a single ion, which is stored in a triple Penning-trap setup. The continuous Stern-Gerlach effect is used to couple the spin of the bound electron to the motional frequencies of the ion via a magnetic bottle, which allows the non-destructive determination of the spin state. To this end, a highly sensitive, cryogenic detection system was developed, which allowed the direct, non-destructive detection of the eigenfrequencies with the required precision.rnThe development of a novel, phase sensitive detection technique finally allowed the determination of the g-factor with a relative accuracy of 40 ppt, which was previously inconceivable. The comparison of the hereby determined value with the value predicted by quantumelectrodynamics (QED) allows the verification of the validity of this fundamental theory under the extreme conditions of the strong binding potential of a highly charged ion. The exact agreement of theory and experiment is an impressive demonstration of the exactness of QED. The experimental possibilities created in this work will allow in the near future not only further tests of theory, but also the determination of the mass of the electron with a precision that exceeds the current literature value by more than an order of magnitude.

Development of an experiment for ultrahigh-precision g-factor

Die vorliegende Arbeit befasst sich mit der Entwicklung und dem Aufbau eines Experiments zur hochpräzisen Bestimmung des g-Faktors gebundener Elektronen in hochgeladenen Ionen. Der g-Faktor eines Teilchens ist eine dimensionslose Konstante, die die Stärke der Wechselwirkung mit einem magnetischen Feld beschreibt. Im Falle eines an ein hochgeladenes Ion gebundenen Elektrons, dient es als einer der genausten Tests der Quantenelektrodynamik gebundener Zustande (BS-QED). Die Messung wird in einem dreifach Penning-Fallen System durchgeführt und basiert auf dem kontinuierlichen Stern-Gerlach-Effekt. Der erste Teil dieser Arbeit gibt den aktuellen Wissensstand über magnetische Momente wieder. Der hier gewählte experimentelle Aufbau wird begründet. Anschließend werden die experimentellen Anforderungen und die verwendeten Messtechniken erläutert. Das Ladungsbrüten der Ionen - einer der wichtigsten Aufgaben dieser Arbeit - ist dargestellt. Seine Realisierung basiert auf einer Feld-Emissions-Spitzen-Anordnung, die die Messung des Wirkungsquerschnitts für Elektronenstoßionisation ermöglicht. Der letzte Teil der Arbeit widmet sich der Entwicklung und dem Aufbau des Penning-Fallen Systems, sowie der Implementierung des Nachweisprozesses. Gegenwärtig ist der Aufbau zur Erzeugung hochgeladener Ionen und der dazugehörigen Messung des g-Faktors abgeschlossen, einschließlich des Steuerprogramms für die erste Datennahme. Die Ionenerzeugung und das Ladungsbrüten werden die nächsten Schritte sein.

Mode coupling for precise measurements of the electronic g-factor of hydrogen-like ions in Penning traps

The g-factor is a constant which connects the magnetic moment $vec{mu}$ of a charged particle, of charge q and mass m, with its angular momentum $vec{J}$. Thus, the magnetic moment can be writen $ vec{mu}_J=g_Jfrac{q}{2m}vec{J}$. The g-factor for a free particle of spin s=1/2 should take the value g=2. But due to quantum electro-dynamical effects it deviates from this value by a small amount, the so called g-factor anomaly $a_e$, which is of the order of $10^{-3}$ for the free electron. This deviation is even bigger if the electron is exposed to high electric fields. Therefore highly charged ions, where electric field strength gets values on the order of $10^{13}-10^{16}$V/cm at the position of the bound electron, are an interesting field of investigations to test QED-calculations. In previous experiments [H"aff00,Ver04] using a single hydrogen-like ion confined in a Penning trap an accuracy of few parts in $10^{-9}$ was obtained. In the present work a new method for precise measurement of magnetic the electronic g-factor of hydrogen-like ions is discussed. Due to the unavoidable magnetic field inhomogeneity in a Penning trap, a very important contribution to the systematic uncertainty in the previous measurements arose from the elevated energy of the ion required for the measurement of its motional frequencies. Then it was necessary to extrapolate the result to vanishing energies. In the new method the energy in the cyclotron degree of freedom is reduced to the minimum attainable energy. This method consist in measuring the reduced cyclotron frequency $nu_{+}$ indirectly by coupling the axial to the reduced cyclotron motion by irradiation of the radio frequency $nu_{coup}=nu_{+}-nu_{ax}+delta$ where $delta$ is, in principle, an unknown detuning that can be obtained from the knowledge of the coupling process. Then the only unknown parameter is the desired value of $nu_+$. As a test, a measurement with, for simplicity, artificially increased axial energy was performed yielding the result $g_{exp}=2.000~047~020~8(24)(44)$. This is in perfect agreement with both the theoretical result $g_{theo}=2.000~047~020~2(6)$ and the previous experimental result $g_{exp1}=2.000~047~025~4(15)(44).$ In the experimental results the second error-bar is due to the uncertainty in the accepted value for the electron's mass. Thus, with the new method a higher accuracy in the g-factor could lead by comparison to the theoretical value to an improved value of the electron's mass. [H"af00] H. H"affner et al., Phys. Rev. Lett. 85 (2000) 5308 [Ver04] J. Verd'u et al., Phys. Rev. Lett. 92 (2004) 093002-1

Electron spin quantum beats and room temperature g factor in GaAsN

We report on the investigation of electron spin quantum beats at room temperature in GaAsN thin films by time-resolved Kerr rotation technique. The measurement of the quantum beats, which originate from the Larmor precession of electron spins in external transverse magnetic field, yields an accurate determination of the conduction electron g factor. We show that the g factor of GaAs1-xNx thin films is significantly changed by the introduction of a small nitrogen fraction.

Electric field tunable electron g factor and high asymmetrical Stark effect in InAs1-xNx quantum dots

The electronic structure, electron g factor, and Stark effect of InAs1-xNx quantum dots are studied by using the ten-band k center dot p model. It is found that the g factor can be tuned to be zero by the shape and size of quantum dots, nitrogen (N) doping, and the electric field. The N doping has two effects on the g factor: the direct effect increases the g factor and the indirect effect decreases it. The Stark effect in quantum ellipsoids is high asymmetrical and the asymmetry factor may be 319. (c) 2007 American Institute of Physics.

Effect of the Rashba and Dresselhaus spin-splitting terms on the electron g factor in semiconductor quantum wells under applied magnetic fields

We use the Ogg-McCombe Hamiltonian together with the Dresselhaus and Rashba spin-splitting terms to find the g factor of conduction electrons in GaAs-(Ga,Al)As semiconductor quantum wells (QWS) (either symmetric or asymmetric) under a magnetic field applied along the growth direction. The combined effects of non-parabolicity, anisotropy and spin-splitting terms are taken into account. Theoretical results are given as functions of the QW width and compared with available experimental data and previous theoretical works. © 2007 Elsevier B.V. All rights reserved.

Hole Rashba effect and g-factor in InP nanowires

The hole Rashba effect and g-factor in InP nanowires in the presence of electric and magnetic fields which bring spin splitting are investigated theoretically in the framework of eight-band effective-mass envelop function theory, by expanding the lateral wave function in Bessel functions. It is well known that the electron Rashba coefficient increases nearly linearly with the electric field. As the Rashba spin splitting is zero at zero k(z) ( the wave vector along the wire direction), the electron g-factor at k(z) = 0 changes little with the electric field. While we find that as the electric field increases, the hole Rashba coefficient increases at first, then decreases. It is noticed that the hole Rashba coefficient is zero at a critical electric field. The hole g-factor at k(z) = 0 changes obviously with the electric field.

Magnetic field tuning of the effective g factor in a diluted magnetic semiconductor quantum dot

The spin interaction and the effective g factor of a magnetic exciton (ME) are investigated theoretically in a diluted magnetic semiconductor (DMS) quantum dot (QD), including the Coulomb interaction and the sp-d exchange interaction. At low magnetic field, the ME energy decreases rapidly with increasing magnetic field and saturates at high magnetic field for high Mn concentration. The ground state of the ME exhibits an interesting crossing behavior between sigma(+)-ME and sigma(-)-ME for low Mn concentration. The g(ex) factor of the ME in a DMS QD displays a monotonic decrease with increasing magnetic field and can be tuned to zero by an external magnetic field. (C) 2003 American Institute of Physics.

Waveguide QED: Many-body bound-state effects in coherent and Fock-state scattering from a two-level system

Strong coupling between a two-level system (TLS) and bosonic modes produces dramatic quantum optics effects. We consider a one-dimensional continuum of bosons coupled to a single localized TLS, a system which may be realized in a variety of plasmonic, photonic, or electronic contexts. We present the exact many-body scattering eigenstate obtained by imposing open boundary conditions. Multiphoton bound states appear in the scattering of two or more photons due to the coupling between the photons and the TLS. Such bound states are shown to have a large effect on scattering of both Fock- and coherent-state wave packets, especially in the intermediate coupling-strength regime. We compare the statistics of the transmitted light with a coherent state having the same mean photon number: as the interaction strength increases, the one-photon probability is suppressed rapidly, and the two- and three-photon probabilities are greatly enhanced due to the many-body bound states. This results in non-Poissonian light. © 2010 The American Physical Society.

Two-electron QED contributions to the ground-state binding energy in He-like Kr34+ ions

The two-electron QED contributions to the ground-state binding energy of Kr34+ ions have been determined in two independent experiments performed with electron beam ion traps (EBIT) in Heidelberg (HD) and Tokyo (BT, Belfast-Tokyo collaboration). X rays arising from radiative recombination (RR) of free electrons to the ground state of initially bare Kr36+ and hydrogenlike Kr35+ ions were observed as a function of the interacting electron energy. The K edge absorption by thin Eu and W foils provided fixed photon energy references used to measure the difference in binding energy Delta E-2e between the H- and He-like Kr ions (Kr35+ and Kr34+, respectively). The two values agree well, yielding a final result of Delta E-2e=641.8 +/- 1.7 eV, confirming recent results of rigorous QED calculations. This accuracy is just of the order required to access screened radiative QED contributions.

QUANTUM HALL FERROMAGNET IN A DOUBLE WELL WITH VANISHING g-FACTOR.

We have studied the quantum Hall effect in Al(x)Ga(1-x)As-double well structure with vanishing g-factor. We determined the density-magnetic field n(s) - B diagrams for the longitudinal resistance R(xx). In spite of the fact that the n(s) - B diagram for conventional GaAs double wells shows a striking similarity with the theory, we observed the strong difference between these diagrams for double wells with vanishing g-factor. We argue that the electron-electron interaction is responsible for unusual behavior of the Landau levels in such a system.

Magnetic-field and confinement effects on the effective Land, g factor in AlxGa1-xAs parabolic quantum wells

The magnetic-field and confinement effects on the Land, factor in AlxGa1-xAs parabolic quantum wells under magnetic fields applied parallel or perpendicular to the growth direction are theoretically studied. Calculations are performed in the limit of low temperatures and low electron density in the heterostructure. The g factor is obtained by taking into account the effects of non-parabolicity and anisotropy of the conduction band through the 2 x 2 Ogg-McCombe Hamiltonian, and by including the cubic Dresselhaus spin-orbit term. A simple formula describing the magnetic-field dependence of the effective Land, factor is analytically derived by using the Rayleigh-Schrodinger perturbation theory, and it is found in good agreement with previous experimental studies devoted to understand the behavior of the g factor, as a function of an applied magnetic field, in semiconductor heterostructures. Present numerical results for the effective Land, factor are shown as functions of the quantum-well parameters and magnetic-field strength, and compared with available experimental measurements.

The use of the bi-factor model to test the uni-dimensionality of a battery of reasoning tests

Resumen tomado de la publicación

UNITARY POLE APPROXIMATION FOR THE COULOMB-PLUS-YAMAGUCHI POTENTIAL AND APPLICATION TO A 3-BODY BOUND-STATE CALCULATION

The unitary pole approximation is used to construct a separable representation for a potential U which consists of a Coulomb repulsion plus an attractive potential of the Yamaguchi type. The exact bound-state wave function is employed. U is chosen as the potential which binds the proton in the 1d5/2 single-particle orbit in F-17. Using the separable representation derived for U, and assuming a separable Yamaguchi potential to describe the 1d5/2 neutron in O-17, the energies and wave functions of the ground state (1+) and the lowest 0+ state of F-18 are calculated in the Gore-plus-two-nucleons model solving the Faddeev equations.

Influence of lower cutoff values for 100-g oral glucose tolerance test and glycemic profile for identification of pregnant women at excessive fetal growth risk

Objective: To evaluate data from patients with normal oral glucose tolerance test (OGTT) results and a normal or impaired glycemic profile (GP) to determine whether lower cutoff values for the OGTT and GP (alone or combined) could identify pregnant women at risk for excessive fetal growth. Methods: We classified 701 pregnant women with positive screening for gestational diabetes mellitus (GDM) into 2 categories - (1) normal 100-g OGTT and normal GP and (2) normal 100-g OGTT and impaired GP - to evaluate the influence of lower cutoff points in a 100-g OGTT and GP (alone or in combination) for identification of pregnant women at excessive fetal growth risk. The OGTT is considered impaired if 2 or more values are above the normal range, and the GP is impaired if the fasting glucose level or at least 1 postprandial glucose value is above the normal range. To establish the criteria for the OGTT (for fasting and 1, 2, and 3 hours after an oral glucose load, respectively), we considered the mean (75 mg/dL, 120 mg/dL, 113 mg/dL, and 97 mg/dL), mean plus 1 SD (85 mg/dL, 151 mg/dL, 133 mg/dL, and 118 mg/dL), and mean plus 2 SD (95 mg/dL, 182 mg/dL, 153 mg/dL, and 139 mg/dL); and for the GP, we considered the mean and mean plus 1 SD (78 mg/dL and 92 mg/dL for fasting glucose levels and 90 mg/dL and 130 mg/dL for 1- or 2-hour postprandial glucose levels, respectively). Results: Subsequently, the women were reclassified according to the new cutoff points for both tests (OGTT and GP). Consideration of values, in isolation or combination, yielded 6 new diagnostic criteria. Excessive fetal growth was the response variable for analysis of the new cutoff points. Odds ratios and their respective confidence intervals were estimated, as were the sensitivity and specificity related to diagnosis of excessive fetal growth for each criterion. The new cutoff points for the tests, when used independently rather than collectively, did not help to predict excessive fetal growth in the presence of mild hyperglycemia. Conclusion: Decreasing the cutoff point for the 100-g OGTT (for fasting and 1, 2, and 3 hours) to the mean (75 mg/dL, 120 mg/dL, 113 mg/dL, and 97 mg/dL) in association with the GP (mean or mean plus 1 SD-78 mg/dL and 92 mg/dL for the fasting state and 90 mg/dL and 130 mg/dL for 1- or 2-hour postprandial values-increased the sensitivity and specificity, and both criteria had statistically significant predictive power for detection of excessive fetal growth. © 2008 AACE.