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Ulrich D. Jentschura

Publications and source records attributed to Ulrich D. Jentschura.

At least 55 records · Page 3Linked to original sources
arXiv2006

Nonrelativistic QED approach to the Lamb shift

We calculate the one- and two-loop corrections of order alpha(Zalpha)^6 and alpha^2(Zalpha)^6 respectively, to the Lamb shift in hydrogen-like systems using the formalism of nonrelativistic quantum electrodynamics. We obtain general results valid for all hydrogenic states with nonvanishing orbital angular momentum and for the normalized difference of S-states. These results involve the expectation value of local effective operators and relativistic corrections to Bethe logarithms. The one-loop correction is in agreement with previous calculations for the particular cases of S, P, and D states. The two-loop correction in the order alpha^2(Zalpha)^6 includes the pure two-loop self-energy and all diagrams with closed fermion loops. The obtained results allow one to obtain improved theoretical predictions for all excited hydrogenic states.

physics.atom-ph↗
arXiv2006

Calculation of the One- and Two-Loop Lamb Shift for Arbitrary Excited Hydrogenic States

General expressions for quantum electrodynamic corrections to the one-loop self-energy [of order alpha(Zalpha)^6] and for the two-loop Lamb shift [of order alpha^2(Zα)^] are derived. The latter includes all diagrams with closed fermion loops. The general results are valid for arbitrary excited non-S hydrogenic states and for the normalized Lamb shift difference of S states, defined as Delta_n = n^3 DeltaE(nS) - DeltaE(1S). We present numerical results for one-loop and two-loop corrections for excited S, P and D states. In particular, the normalized Lamb shift difference of S states is calculated with an uncertainty of order 0.1 kHz.

physics.atom-ph↗
arXiv2005

Complete two-loop correction to the bound-electron g factor

Within a systematic approach based on the dimensionally regularized nonrelativistic quantum electrodynamics, we derive the complete result for the two-loop correction to order $(α/π)^2 (Z α)^4$ for the $g$ factor of an electron bound in an $nS$ state of a hydrogenlike ion. The results obtained significantly improve the accuracy of the theoretical predictions for the hydrogenlike carbon and oxygen ions and influence the value of the electron mass inferred from $g$ factor measurements.

physics.atom-ph↗
arXiv2005

Calculation of Hydrogenic Bethe Logarithms for Rydberg States

We describe the calculation of hydrogenic (one-loop) Bethe logarithms for all states with principal quantum numbers n <= 200. While, in principle, the calculation of the Bethe logarithm is a rather easy computational problem involving only the nonrelativistic (Schroedinger) theory of the hydrogen atom, certain calculational difficulties affect highly excited states, and in particular states for which the principal quantum number is much larger than the orbital angular momentum quantum number. Two evaluation methods are contrasted. One of these is based on the calculation of the principal value of a specific integral over a virtual photon energy. The other method relies directly on the spectral representation of the Schroedinger-Coulomb propagator. Selected numerical results are presented. The full set of values is available at quant-ph/0504002.

quant-ph↗
arXiv2005

Multi-Instantons and Exact Results II: Specific Cases, Higher-Order Effects, and Numerical Calculations

In this second part of the treatment of instantons in quantum mechanics, the focus is on specific calculations related to a number of quantum mechanical potentials with degenerate minima. We calculate the leading multi-instanton constributions to the partition function, using the formalism introduced in the first part of the treatise [J. Zinn-Justin and U. D. Jentschura, e-print quant-ph/0501136]. The following potentials are considered: (i) asymmetric potentials with degenerate minima, (ii) the periodic cosine potential, (iii) anharmonic oscillators with radial symmetry, and (iv) a specific potential which bears an analogy with the Fokker-Planck equation. The latter potential has the peculiar property that the perturbation series for the ground-state energy vanishes to all orders and is thus formally convergent (the ground-state energy, however, is nonzero and positive). For the potentials (ii), (iii), and (iv), we calculate the perturbative B-function as well as the instanton A-function to fourth order in g. We also consider the double-well potential in detail, and present some higher-order analytic as well as numerical calculations to verify explicitly the related conjectures up to the order of three instantons. Strategies analogous to those outlined here could result in new conjectures for problems where our present understanding is more limited.

quant-ph↗
arXiv2005

Multi-Instantons and Exact Results I: Conjectures, WKB Expansions, and Instanton Interactions

We consider specific quantum mechanical model problems for which perturbation theory fails to explain physical properties like the eigenvalue spectrum even qualitatively, even if the asymptotic perturbation series is augmented by resummation prescriptions to "cure" the divergence in large orders of perturbation theory. Generalizations of perturbation theory are necessary which include instanton configurations, characterized by nonanalytic factors exp(-a/g) where a is a constant and g is the coupling. In the case of one-dimensional quantum mechanical potentials with two or more degenerate minima, the energy levels may be represented as an infinite sum of terms each of which involves a certain power of a nonanalytic factor and represents itself an infinite divergent series. We attempt to provide a unified representation of related derivations previously found scattered in the literature. For the considered quantum mechanical problems, we discuss the derivation of the instanton contributions from a semi-classical calculation of the corresponding partition function in the path integral formalism. We also explain the relation with the corresponding WKB expansion of the solutions of the Schroedinger equation, or alternatively of the Fredholm determinant det(H-E) (and some explicit calculations that verify this correspondence). We finally recall how these conjectures naturally emerge from a leading-order summation of multi-instanton contributions to the path integral representation of the partition function. The same strategy could result in new conjectures for problems where our present understanding is more limited.

quant-ph↗
arXiv2005

Radiative Corrections to Multi-Level Mollow-Type Spectra

This paper is concerned with two rather basic phenomena: the incoherent fluorescence spectrum of an atom driven by an intense laser field and the coupling of the atom to the (empty) modes of the radiation field. The sum of the many-photon processes gives rise to the inelastic part of the atomic fluorescence, which, for a two-level system, has a well-known characteristic three-peak structure known as the Mollow spectrum. From a theoretical point of view, the Mollow spectrum finds a natural interpretation in terms of transitions among laser-dressed states which are the energy eigenstates of a second-quantized two-level system strongly coupled to a driving laser field. As recently shown, the quasi-energies of the laser-dressed states receive radiative corrections which are nontrivially different from the results which one would expect from an investigation of the coupling of the bare states to the vacuum modes. In this article, we briefly review the basic elements required for the analysis of the dynamic radiative corrections, and we generalize the treatment of the radiative corrections to the incoherent part of the steady-state fluorescence to a three-level system consisting of 1S, 3P and 2S states.

quant-ph↗
arXiv2004

Relativistic and Radiative Corrections to the Mollow Spectrum

The incoherent, inelastic part of the resonance fluorescence spectrum of a laser-driven atom is known as the Mollow spectrum [B. R. Mollow, Phys. Rev. 188, 1969 (1969)]. Starting from this level of description, we discuss theoretical foundations of high-precision spectroscopy using the resonance fluorescence light of strongly laser-driven atoms. Specifically, we evaluate the leading relativistic and radiative corrections to the Mollow spectrum, up to the relative orders of (Z alpha)^2 and alpha(Z alpha)^2, respectively, and Bloch-Siegert shifts as well as stimulated radiative corrections involving off-resonant virtual states. Complete results are provided for the hydrogen 1S-2P_{1/2} and 1S-2P_{3/2} transitions; these include all relevant correction terms up to the specified order of approximation and could directly be compared to experimental data. As an application, the outcome of such experiments would allow for a sensitive test of the validity of the dressed-state basis as the natural description of the combined atom-laser system.

quant-ph↗
arXiv2004

Toward high-precision values of the self energy of non-S states in hydrogen and hydrogen-like ions

The method and status of a study to provide numerical, high-precision values of the self-energy level shift in hydrogen and hydrogen-like ions is described. Graphs of the self energy in hydrogen-like ions with nuclear charge number between 20 and 110 are given for a large number of states. The self-energy is the largest contribution of Quantum Electrodynamics (QED) to the energy levels of these atomic systems. These results greatly expand the number of levels for which the self energy is known with a controlled and high precision. Applications include the adjustment of the Rydberg constant and atomic calculations that take into account QED effects.

quant-ph↗
arXiv2004

Two-Loop Bethe Logarithms for Higher Excited S Levels

Processes mediated by two virtual low-energy photons contribute quite significantly to the energy of hydrogenic S states. The corresponding level shift is of the order of (alpha/pi)^2 (Zalpha)^6 m_e c^2 and may be ascribed to a two-loop generalization of the Bethe logarithm. For 1S and 2S states, the correction has recently been evaluated by Pachucki and Jentschura [Phys. Rev. Lett. vol. 91, 113005 (2003)]. Here, we generalize the approach to higher excited S states, which in contrast to the 1S and 2S states can decay to P states via the electric-dipole (E1) channel. The more complex structure of the excited-state wave functions and the necessity to subtract P-state poles lead to additional calculational problems. In addition to the calculation of the excited-state two-loop energy shift, we investigate the ambiguity in the energy level definition due to squared decay rates.

hep-ph↗
arXiv2004

Instantons in Quantum Mechanics and Resurgent Expansions

Certain quantum mechanical potentials give rise to a vanishing perturbation series for at least one energy level (which as we here assume is the ground state), but the true ground-state energy is positive. We show here that in a typical case, the eigenvalue may be expressed in terms of a generalized perturbative expansion (resurgent expansion). Modified Bohr-Sommerfeld quantization conditions lead to generalized perturbative expansions which may be expressed in terms of nonanalytic factors of the form exp(-a/g), where a > 0 is the instanton action, and power series in the coupling g, as well as logarithmic factors. The ground-state energy, for the specific Hamiltonians, is shown to be dominated by instanton effects, and we provide numerical evidence for the validity of the related conjectures.

hep-ph↗
arXiv2004

Electron Self Energy for Higher Excited S Levels

A nonperturbative numerical evaluation of the one-photon electron self energy for the 3S and 4S states with charge numbers Z=1 to 5 is described. The numerical results are in agreement with known terms in the expansion of the self energy in powers of Zalpha.

hep-ph↗
arXiv2003

Two-Loop Bethe Logarithms

We calculate the two-loop Bethe logarithm correction to atomic energy levels in hydrogen-like systems. The two-loop Bethe logarithm is a low-energy quantum electrodynamic (QED) effect involving multiple summations over virtual excited atomic states. Although much smaller in absolute magnitude than the well-known one-loop Bethe logarithm, the two-loop analog is quite significant when compared to the current experimental accuracy of the 1S-2S transition: it contributes -8.19 and -0.84 kHz for the 1S and the 2S state, respectively. The two-loop Bethe logarithm has been the largest unknown correction to the hydrogen Lamb shift to date. Together with the ongoing measurement of the proton charge radius at the Paul Scherrer Institute its calculation will bring theoretical and experimental accuracy for the Lamb shift in atomic hydrogen to the level of 10^(-7).

hep-ph↗
arXiv2003

Two-Loop QED Bound-State Calculations and Squared Decay Rates

We discuss the epsilon-method as used in various recent QED bound-state calculations by considering mathematical model examples. Recently obtained results for higher-order self-energy binding corrections at the two-loop level are reviewed. Problems associated with the interpretation of squared decay rates as radiative bound-state energy level shifts are discussed. We briefly expand on the relation of squared decay rates to nonresonant and radiative corrections to the Lorentzian line shape, including their dependence on the experimental process under study.

hep-ph↗
arXiv2003

Perturbation Approach to the Self Energy of non-S Hydrogenic States

We present results on the self-energy correction to the energy levels of hydrogen and hydrogenlike ions. The self energy represents the largest QED correction to the relativistic (Dirac-Coulomb) energy of a bound electron. We focus on the perturbation expansion of the self energy of non-S states, and provide estimates of the so-called A60 perturbative coefficient, which can be considered as a relativistic Bethe logarithm. Precise values of A60 are given for many P, D, F and G states, while estimates are given for other electronic states. These results can be used in high-precision spectroscopy experiments in hydrogen and hydrogenlike ions. They yield the best available estimate of the self-energy correction of many atomic states.

physics.atom-ph↗
arXiv2003

Theory of the Lamb Shift in Hydrogenlike Systems

Analytic calculations of the Lamb shift represent a considerable challenge due to the size and the complexity of the expressions that occur in intermediate steps. In the current work, we present a method for the treatment of the bound-state self-energy in higher orders. Advantage is taken of computer algebra systems. The method is applied to the 2P-states, and the (one-loop) self-energy is calculated up to the order of alpha (Zalpha)^6. The calculation leads to improved predictions for the in atomic hydrogen. In particular, the focus of the current work is the calculation of the so-called A_60-coefficient with improved accuracy. A_60-coefficients for 2P states are calculated with an accuracy of less than 1 Hz in frequency units. An account of the contributions to the Lamb shift of 2P states is given [status of 1996 when this thesis was completed]. Bound-state quantum electrodynamics combines the complexity of modern quantum field theory, including renormalization, augmented by the structure of bound states and the inherent relativistic corrections with the experimental possibilities of modern high-resolution laser spectroscopy.

hep-ph↗