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.     

Quantum mechanics derived from stochastic electrodynamics

The connection between stochastic electrodynamics (SED) and the quantum theory of matter is further explored. The main result is that the Fokker-Planck-like equation of SED can be recast into the form of a Schrödinger equation with radiative corrections, when the system is close to a state of equilibrium. The phase-space distribution can be written as Wigner's pseudo-distribution plus corrections due to the nonlinearity of the external force and to radiative effects. The radiative corrections predicted by the theory, namely the Lamb shift and the decay of excited atomic states, coincide with those predicted by QED. Moreover, the theory offers a clear physical interpretation of these phenomena as due to the coupling of the electric dipole of the system with the zero-point radiation field and to radiation reaction, respectively.     

Giant lamb shift in photonic crystals

We obtain a general result for the Lamb shift of excited states of multilevel atoms in inhomogeneous electromagnetic structures and apply it to study atomic hydrogen in inverse-opal photonic crystals. We find that the photonic-crystal environment can lead to very large values of the Lamb shift, as compared to the case of vacuum. We also suggest that the position-dependent Lamb shift should extend from a single level to a miniband for an assembly of atoms with random distribution in space, similar to the velocity-dependent Doppler effect in atomic/molecular gases.     

Calculation of QED Effects in Hydrogen

Atomic mass differences are influenced by QED corrections, and a reliable understanding of these corrections is therefore of importance for the current and next generation of high-precision mass determinations based on Penning traps. We present a numerical evaluation of the self-energy correction, which is the dominant contribution to the Lamb shift, in the region of low nuclear charge. Our calculation is nonperturbative in the binding field and has a numerical uncertainty of 0.8Hz in atomic hydrogen for the ground state and of 1.0Hz for L-shell states (2S_1/2, 2P_1/2, and 2P_3/2). This revised version was published online in July 2006 with corrections to the Cover Date.     

Cooperative Lamb shift in an atomic vapor layer of nanometer thickness

We present an experimental measurement of the cooperative Lamb shift and the Lorentz shift using a nanothickness atomic vapor layer with tunable thickness and atomic density. The cooperative Lamb shift arises due to the exchange of virtual photons between identical atoms. The interference between the forward and backward propagating virtual fields is confirmed by the thickness dependence of the shift, which has a spatial frequency equal to twice that of the optical field. The demonstration of cooperative interactions in an easily scalable system opens the door to a new domain for nonlinear optics.     

光子晶体中巨Lamb移位

对非均匀电磁系统中原子的Lamb移位导出一个普适的理论公式，发现对Lamb移位的主要贡献来自实光子的吸收和再辐射过程，这打破了自1947年以来一直被人们所认同的传统概念，即在均匀空间中，Lamb移位主要来自虚光子的吸收和再辐射过程．对光子晶体，文章作者预言了巨Lamb移位效应．对原子集合，进一步发现依赖位置的Lamb移位将使一个能级扩展成一个能带，就像原子气体中依赖速度的多普勒效应一样．     

Lamb shift in atoms interacting with a strong laser field

Radiative corrections to the energy levels of an atom interacting with a strong laser field have been investigated. A formula for the Lamb shift of the laser-dressed states is derived, which makes it possible to calculate this shift with an error up to α². Original Russian Text ? R.Kh. Gainutdinov, A.A. Mutygullina, 2009, published in Izvestiya Rossiiskoi Akademii Nauk. Seriya Fizicheskaya, 2009, Vol. 73, No. 2, pp. 292–293.     

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).     

General theory of radiative corrections to atomic decay rates

A general expression is derived for the radiative corrections to the one-photon decay rates of hydrogen-like ions. Our approach is based on the evaluation of the imaginary part of the fourth-order Lamb shift for excited states. We thereby avoid the ambiguities connected with electron wave function renormalization. The result may be cast in a form which is manifestly gauge invariant. As an application, we show that the formulas used by Lin and Feinberg in their study of relativistic M1 transitions, obtained by heuristic arguments, are derivable from first principles.     

真空中V型三能级原子的布居弛豫及其量子相干自发发射

本文研究了V型三能级原子与真空耦合构成光子-原子束缚态的布居弛豫及其量子相干现象,具体阐述了引起原子相干的必要条件、布居粒子数的交换过程、真空与原子耦合所产生的Lamb移动对自发发射光谱特性带来的影响.     

Relativistic and many-body effects in K, L, and M shell ionization energy for elements with and the determination of the 1s Lamb shift for heavy elements

We report on a calculation of K, L and M inner-shell ionization energy in atoms with atomic numbers in the range . Many-body effects are evaluated for all n =1, 2, and 3 hole states. Those include correlation and effects due to the auto-ionizing nature of the hole states (Auger shift). For high Z we add recent corrected nuclear polarization, and several second-order vacuum polarization corrections. K and L ionization energies are compared with experimental X-ray absorption edges measurements. Excellent agreement with rare gazes and metal vapor measurements is found. We also compare our calculations with X-ray transition energies for all K and L lines that involve K, L and M holes. Finally we use K X-ray lines to deduce an hydrogenlike 1 s Lamb shift for several heavy elements, with far better accuracy than has been obtained by direct measurements of hydrogenlike ions. Received: 25 February 1998 / Accepted: 31 March 1998     

The lamb shift in helium from a self-consistent field theory of electrodynamics

In this paper we present the results of an investigation of the finite self-consistent field theory of electrodynamics applied earlier to the calculation of the Lamb shift in hydrogen (Sachs & Schwebel, 1961; Sachs, 1972), now applied to the problem of the Lamb shift in the low-lying states of Helium. We construct the covariant nonlinear field equations of this theory for Helium, from the Lagrangian formalism. In the linear approximation, the Hamiltonian associated with this field theory for the two-electron atom is set up. It is equivalent to the Breit Hamiltonian plus two extra terms. This generalization is a direct consequence of the two-component spinor formalism of the factorization of the Maxwell theory of electromagnetism that is contained in this theory of electrodynamics (Sachs, 1971). Thus, the energy spectrum predicted for the Helium atom is the spectrum predicted by the Breit Hamiltonian, shifted by amounts in the different energy states according to the effects of the extra terms in the Hamiltonian. The latter can be associated with the corrections to the Helium spectrum that are conventionally attributed to the Lamb shift. The level shifts for the 1¹ S and 2³ S states are calculated using the Foldy-Wouthuysen transformation, with the generalization of Charplvy for the two-electron atom. The results are found to be in close agreement with the experimental values for the energy shifts not predicted by the Dirac theory, and with the theoretical values predicted by quantum electrodynamics.     

Reparameterization invariance of NRQED self-energy corrections and improved theory for excited D states in hydrogenlike systems

Canonically, the quantum electrodynamic radiative corrections in bound systems have been evaluated in photon energy regularization, i.e., using a noncovariant overlapping parameter that separates the high-energy relativistic scales of the virtual quanta from the nonrelativistic domain. Here, we calculate the higher-order corrections to the one-photon self-energy calculation with three different overlapping parameters (photon energy, photon mass and dimensional regularization) and demonstrate the reparameterization invariance of nonrelativistic quantum electrodynamics (NRQED) using this particular example. We also present new techniques for the calculation of the low-energy part of this correction, which lead to results for the Lamb shift of highly excited states that are important for high-precision spectroscopy.     

Influence of Lamb Shift Parameter on Dissipative Dynamics of the Phase Damped Jaynes–Cummings Model with Gravity Under Markovian Approximation

In this paper, we study the dissipative dynamics of the phase damped Jaynes–Cummings model with gravity under Markovian approximation in the presence of the Lamb shift parameter. The model consists of a moving two-level atom simultaneously exposed to the gravitational field and a single-mode traveling radiation field in the presence of a phase damping mechanism. We first present the master equation for the reduced density operator of the system under Markovian approximation in terms of a Hamiltonian describing the atom-field interaction with gravity in the presence of Lamb-shift parameter. Then, by making use of the super-operator technique, we obtain an exact solution of the master equation. Assuming that initially the radiation field is prepared in a Glauber coherent state and the two-level atom is in the excited state, we investigate the influence of Lamb shift parameter on the temporal evolution of collapses and revivals of the atomic population inversion, atomic dipole squeezing and atomic momentum diffusion in the presence of phase damping.     

The collective Lamb shift in nuclear γ-ray superradiance

The electromagnetic transitions of M?ssbauer nuclei provide almost ideal two-level systems to transfer quantum optical concepts into the regime of hard x-rays. If many identical atoms collectively interact with a resonant radiation field, one observes (quantum) optical properties that are strongly different from those of a single atom. The most prominent effect is the broadening of the resonance line known as collective enhancement, resulting from multiple scattering of real photons within the atomic ensemble. On the other hand, the exchange of virtual photons within the ensemble leads to a tiny energy shift of the resonance line, the collective Lamb shift, that remained experimentally elusive for a long time after its prediction. Here we illustrate how highly brilliant synchrotron radiation allows one to prepare superradiant states of excited M?ssbauer nuclei, an important condition for observation of the collective Lamb shift.     

Effects of QED and Beyond from the Atomic Binding Energy

Atomic binding energies are calculated at utmost precision. A report on the current status of Lamb-shift predictions for hydrogenlike ions, including all quantum electrodynamical corrections to first and second order in the fine structure constant α is presented. All relevant nuclear effects are taken into account. High-precision calculations for the Lamb shift in hydrogen are presented. The hyperfine structure splitting and the g factor of a bound electron in the strong electromagnetic field of a heavy nucleus is considered. Special emphasis is also put on parity violation effects in atomic systems. For all systems possible investigations beyond precision tests of quantum electrodynamics are considered. This revised version was published online in July 2006 with corrections to the Cover Date.     

The shift of atomic ground state by a limited nonresonant moderately strong laser field

The shift of the atomic ground state due to the interaction with an external limited nonresonant laser field and vacuum fluctuation is calculated in resolvent formalism. The shift operator ¯R is taken to the fourth order of perturbation expansion. It is shown that the term which mixes these two interactions gives a slight correction to the total shift, which can be expressed by the Lamb shift of the excited state.     

The influence of nuclear structure on the Lamb shift in hydrogenlike heavy atoms

We evaluate and list the various contributions to the Lamb shift in hydrogenlike heavy atoms which arise from parameters describing shape, size and structure of the nucleus. We compare these contributions with those obtained from quantum electrodynamics. It is found that in heavy nuclei, nuclear contributions depending on experimental parameters and nuclear models are of the same size as QED contributions of order a². Therefore, in these systems the theoretical predictions for binding energies are limited by the exact knowledge of the nuclear parameters. In addition, we tabulate all corrections contributing to the 1s_1/2 Lamb shift in hydrogenlike Pb and U. This revised version was published online in August 2006 with corrections to the Cover Date.     

The muonium energy levels for n = 2

The initial results of a calculation of the muonium energy levels for n = 2 is reported. The results, which contain all recoil corrections through order α⁵ are combined with previously calculated higher-order binding corrections to yield 1047.03 MHz for the muonium Lamb shift and 10 921.50 for the $\text{2}\text{P}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{?2P}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ fine structure interval. A lower- order, quadratic recoil term, which is insignificant for the hydrogen Lamb shift, contributes ?0.17 MHz to the muonium Lamb shift.     

Cooperative single-photon subradiant states in a three-dimensional atomic array

We propose a complete superradiant and subradiant states that can be manipulated and prepared in a three-dimensional atomic array. These subradiant states can be realized by absorbing a single photon and imprinting the spatially-dependent phases on the atomic system. We find that the collective decay rates and associated cooperative Lamb shifts are highly dependent on the phases we manage to imprint, and the subradiant state of long lifetime can be found for various lattice spacings and atom numbers. We also investigate both optically thin and thick atomic arrays, which can serve for systematic studies of super- and sub-radiance. Our proposal offers an alternative scheme for quantum memory of light in a three-dimensional array of two-level atoms, which is applicable and potentially advantageous in quantum information processing.