Triple Compton effect: a photon splitting into three upon collision with a free electron.

The process in which a photon splits into three after the collision with a free electron (triple Compton effect) is the most basic process for the generation of a high-energy multiparticle entangled state composed out of elementary quanta. The cross section of the process is evaluated in two experimentally realizable situations, one employing gamma photons and stationary electrons, and the other using keV photons and GeV electrons of an x-ray free electron laser. For the first case, our calculation is in agreement with the only available measurement of the differential cross section for the process under study. Our estimates indicate that the process should be readily measurable also in the second case. We quantify the polarization entanglement in the final state by a recently proposed multiparticle entanglement measure.

Precision measurement of the hydrogen-deuterium 1S-2S isotope shift.

Measuring the hydrogen-deuterium isotope shift via two-photon spectroscopy of the 1S-2S transition, we obtain 670,994,334,606(15) Hz. This is a 10-times improvement over the previous best measurement [A. Huber, Phys. Rev. Lett. 80, 468 (1998)] confirming its frequency value. A calculation of the difference of the mean square charge radii of deuterium and hydrogen results in d - p =3.82007(65) fm2, a more than twofold improvement compared to the former value.

Nonperturbative treatment of double compton backscattering in intense laser fields.

The emission of a pair of entangled photons by an electron in an intense laser field can be described by two-photon transitions of laser-dressed, relativistic Dirac-Volkov states. In the limit of a small laser field intensity, the two-photon transition amplitude approaches the result predicted by double Compton scattering theory. Multiexchange processes with the laser field, including a large number of exchanged laser photons, cannot be described without the fully relativistic Dirac-Volkov propagator. The nonperturbative treatment significantly alters theoretical predictions for future experiments of this kind. We quantify the degree of polarization correlation of the photons in the final state by employing the well-established concurrence as a measure of the entanglement.

Recursive algorithm for arrays of generalized Bessel functions: Numerical access to Dirac-Volkov solutions.

In the relativistic and the nonrelativistic theoretical treatment of moderate and high-power laser-matter interaction, the generalized Bessel function occurs naturally when a Schrödinger-Volkov and Dirac-Volkov solution is expanded into plane waves. For the evaluation of cross sections of quantum electrodynamic processes in a linearly polarized laser field, it is often necessary to evaluate large arrays of generalized Bessel functions, of arbitrary index but with fixed arguments. We show that the generalized Bessel function can be evaluated, in a numerically stable way, by utilizing a recurrence relation and a normalization condition only, without having to compute any initial value. We demonstrate the utility of the method by illustrating the quantum-classical correspondence of the Dirac-Volkov solutions via numerical calculations.

Unified treatment of even and odd anharmonic oscillators of arbitrary degree.

We present a unified treatment, including higher-order corrections, of anharmonic oscillators of arbitrary even and odd degree. Our approach is based on a dispersion relation which takes advantage of the PT symmetry of odd potentials for imaginary coupling parameter, and of generalized quantization conditions which take into account instanton contributions. We find a number of explicit new results, including the general behavior of large-order perturbation theory for arbitrary levels of odd anharmonic oscillators, and subleading corrections to the decay width of excited states for odd potentials, which are numerically significant.

Laser channeling of Bethe-Heitler pairs.

Electron-positron pair creation is analyzed for an arrangement involving three external fields: a high-frequency gamma photon, the Coulomb field of a nucleus, and a strong laser wave. The frequency of the incoming gamma photon is assumed to be larger than the threshold for pair production in the absence of a laser, and the peak electric field of the laser is assumed to be much weaker than Schwinger's critical field. The total number of pairs produced is found to be essentially unchanged by the laser field, while the differential cross section is drastically modified. We show that the laser can channel the angular distribution of electron-positron pairs into a narrow angular region, which also facilitates experimental observation.

Fundamental constants and tests of theory in Rydberg states of hydrogenlike ions.

A comparison of precision frequency measurements to quantum electrodynamics (QED) predictions for Rydberg states of hydrogenlike ions can yield information on values of fundamental constants and test theory. With the results of a calculation of a key QED contribution reported here, the uncertainty in the theory of the energy levels is reduced to a level where such a comparison can yield an improved value of the Rydberg constant.

Electron self-energy in the presence of a magnetic field: hyperfine splitting and g factor.

A high-precision numerical calculation is reported for the self-energy correction to the hyperfine splitting and to the bound-electron g factor in hydrogenlike ions with low nuclear charge numbers. The binding nuclear Coulomb field is treated to all orders, and the nonperturbative remainder beyond the known Zalpha-expansion coefficients is determined. For the 3He+ ion, the nonperturbative remainder yields a contribution of -450 Hz to the normalized difference of the 1S and 2S hyperfine-structure intervals, to be compared with the experimental uncertainty of 71 Hz and with the theoretical error of 50 Hz due to other contributions. In the case of the g factor, the calculation provides the most stringent test of equivalence of the perturbative and nonperturbative approaches reported so far in the bound-state QED calculations.

Evaluation of laser-assisted bremsstrahlung with Dirac-Volkov propagators.

We study spontaneous bremsstrahlung emission in a highly intense laser field. In this regime the interaction with the laser field has to be treated nonperturbatively by using the relativistic formalism including Dirac-Volkov propagators, while the interaction with the Coulomb field and the bremsstrahlung radiation can be treated in first-order perturbation theory. For the intermediate electron state a fully laser-dressed propagator is used, including radiative corrections to avoid singularities on the mass shell. We find that the use of the Dirac-Volkov propagator is crucial to obtain correct numerical results. The cross section of the process is evaluated for laser intensities of order 10(20) W/cm(2) and relativistic energies of the initial electron.

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 alpha2(Zalpha)6] 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 states, defined as Delta N = n3deltaE(nS) - delta E(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 states is calculated with an uncertainty of order 0.1 kHz.

Precise calculation of transition frequencies of hydrogen and deuterium based on a least-squares analysis.

We combine a limited number of accurately measured transition frequencies in hydrogen and deuterium, recent quantum electrodynamics (QED) calculations, and, as an essential additional ingredient, a generalized least-squares analysis, to obtain precise and optimal predictions for hydrogen and deuterium transition frequencies. Some of the predicted transition frequencies have relative uncertainties more than an order of magnitude smaller than that of the g factor of the electron, which was previously the most accurate prediction of QED.

Nonrelativistic QED approach to the bound-electron g factor.

Within a systematic approach based on nonrelativistic quantum electrodynamics, we derive the one-loop self-energy correction of order alpha(Z alpha)(4) to the bound-electron g factor. In combination with numerical data, this analytic result improves theoretical predictions for the self-energy correction for carbon and oxygen by an order of magnitude. Basing on one-loop calculations, we obtain the logarithmic two-loop contribution of order alpha(2)(Z alpha)(4)ln([(Z alpha)(-2)] and the dominant part of the corresponding constant term. The results obtained improve the accuracy of the theoretical predictions for the 1S bound-electron g factor and influence the value of the electron mass determined from g-factor measurements.

Two-loop Bethe-logarithm correction in hydrogenlike atoms.

We calculate the two-loop Bethe logarithm correction to atomic energy levels in hydrogenlike 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).

Asymptotic properties of self-energy coefficients.

We investigate the asymptotic properties of higher-order binding corrections to the one-loop self-energy of excited states in atomic hydrogen. We evaluate the historically problematic A60 coefficient for all P states with principal quantum numbers n

Lamb shift of laser-dressed atomic states.

We discuss radiative corrections to an atomic two-level system subject to an intense driving laser field. It is shown that the Lamb shift of the laser-dressed states, which are the natural state basis of the combined atom-laser system, cannot be explained in terms of the Lamb shift received by the atomic bare states which is usually observed in spectroscopic experiments. In the final part, we propose an experimental scheme to measure these corrections based on the incoherent resonance fluorescence spectrum of the driven atom.