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.Comment: Dedicated to Prof. H. Walther on the occasion of his 70th birthda

Comparison of classical and second quantized description of the dynamic Stark shift

We compare the derivation of the dynamic Stark shift of hydrogenic energy levels in a classical framework with an adiabatically damped laser-atom interaction, which is equivalent to the Gell-Mann-Low-Sucher formula, and a treatment based on time-independent perturbation theory, with a second-quantized laser-atom dipole interaction Hamiltonian. Our analysis applies to a laser that excites a two-photon transition in atomic hydrogen or in a hydrogenlike ion with low nuclear charge number. Our comparisons serve to demonstrate why the dynamic Stark shift may be interpreted as a stimulated radiative correction and illustrates connections between the two derivations. The simplest of the derivations is the fully quantized approach. The classical and the second-quantized treatment are shown to be equivalent in the limit of large photon numbers.Comment: 5 page

Determining the carrier-envelope phase of intense few-cycle laser pulses

The electromagnetic radiation emitted by an ultra-relativistic accelerated electron is extremely sensitive to the precise shape of the field driving the electron. We show that the angular distribution of the photons emitted by an electron via multiphoton Compton scattering off an intense (I>10^{20}\;\text{W/cm^2}), few-cycle laser pulse provides a direct way of determining the carrier-envelope phase of the driving laser field. Our calculations take into account exactly the laser field, include relativistic and quantum effects and are in principle applicable to presently available and future foreseen ultra-strong laser facilities.Comment: 4 pages, 2 figure

Nonsequential Double Recombination in Intense Laser Fields

A second plateau in the harmonic spectra of laser-driven two-electron atoms is observed both in the numerical solution of a low-dimensional model helium atom and using an extended strong field approximation. It is shown that the harmonics well beyond the usual cut-off are due to the simultaneous recombination of the two electrons, which were emitted during different, previous half-cycles. The new cut-off is explained in terms of classical trajectories. Classical predictions and the time-frequency analysis of the ab initio quantum results are in excellent agreement. The mechanism corresponds to the inverse single photon double ionization process in the presence of a (low frequency) laser field.Comment: 4 pages, RevTeX, v2 with an extended strong field approximation treatment of the process; instead, v1 describes an attosecond control scheme to enhance the proces

Constrained probability distributions of correlation functions

Context: Two-point correlation functions are used throughout cosmology as a measure for the statistics of random fields. When used in Bayesian parameter estimation, their likelihood function is usually replaced by a Gaussian approximation. However, this has been shown to be insufficient. Aims: For the case of Gaussian random fields, we search for an exact probability distribution of correlation functions, which could improve the accuracy of future data analyses. Methods: We use a fully analytic approach, first expanding the random field in its Fourier modes, and then calculating the characteristic function. Finally, we derive the probability distribution function using integration by residues. We use a numerical implementation of the full analytic formula to discuss the behaviour of this function. Results: We derive the univariate and bivariate probability distribution function of the correlation functions of a Gaussian random field, and outline how higher joint distributions could be calculated. We give the results in the form of mode expansions, but in one special case we also find a closed-form expression. We calculate the moments of the distribution and, in the univariate case, we discuss the Edgeworth expansion approximation. We also comment on the difficulties in a fast and exact numerical implementation of our results, and on possible future applications.Comment: 13 pages, 5 figures, updated to match version published in A&A (slightly expanded Sects. 5.3 and 6

Polarization operator approach to electron-positron pair production in combined laser and Coulomb fields

The optical theorem is applied to the process of electron-positron pair creation in the superposition of a nuclear Coulomb and a strong laser field. We derive new representations for the total production rate as two-fold integrals, both for circular laser polarization and for the general case of elliptic polarization, which has not been treated before. Our approach allows us to obtain by analytical means the asymptotic behaviour of the pair creation rate for various limits of interest. In particular, we consider pair production by two-photon absorption and show that, close to the energetic threshold of this process, the rate obeys a power law in the laser frequency with different exponents for linear and circular laser polarization. With the help of the upcoming x-ray laser sources our results could be tested experimentally.Comment: 10 pages, 3 figure

Strong-field spatial interference in a tailored electromagnetic bath

Light scattered by a regular structure of atoms can exhibit interference signatures, similar to the classical double-slit. These first-order interferences, however, vanish for strong light intensities, restricting potential applications. Here, we show how to overcome these limitations to quantum interference in strong fields. First, we recover the first-order interference in strong fields via a tailored electromagnetic bath with a suitable frequency dependence. At strong driving, the optical properties for different spectral bands are distinct, thus extending the set of observables. We further show that for a two-photon detector as, e.g., in lithography, increasing the field intensity leads to twice the spatial resolution of the second-order interference pattern compared to the weak-field case.Comment: final versio