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 Schr\"odinger-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.Comment: 14 pages, 5 figure

Laser-assisted second-order relativistic QED processes : Bremsstrahlung and pair creation modified by a strong electromagnetic wave field

The primary aim of this thesis is to advance the understanding of higher-order laser-assisted relativistic processes within quantum electrodynamics (QED), which necessitates a formulation using fully laser-dressed fermion propagators. This study is motivated by presently available laser sources which routinely produce electromagnetic fields strong enough to accelerate the electron to velocities close to the speed of light. %The light-matter interaction therefore has to be treated by the theory of quantum electrodynamics (QED). The strong laser-matter interaction requires an all-order treatment, different from the perturbative expansion of the usual QED. In this thesis, the influence of a strong laser field on two fundamental processes of QED is studied theoretically. The first process, bremsstrahlung from an electron scattered at the Coulomb potential of a nucleus, is found to show a resonant behavior in the presence of the laser. The cross section is numerically evaluated from the formula resulting from applying the strong-field Feynman rules. The second process, electron-positron pair creation by a gamma photon and a Coulomb field is studied in the case when the laser field strength is below the critical field. Here the total cross section is unchanged by the laser, while the differential cross section is drastically modified. Finally, a detailed study and a novel evaluation algorithm of the generalized Bessel function, a special function occurring naturally in laser-modified QED, is presented

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 multi-particle 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 multi-particle entanglement measure.Comment: 5 pages; RevTeX; to be published in Phys.Rev.Let

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. Multi-exchange 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.Comment: 4 pages, 4 figure

Sub-10-fs population inversion in N2+ in air lasing through multiple state coupling

Laser filamentation generated when intense laser pulses propagate in air has been an attractive phenomenon having a variety of potential applications such as detection and spectroscopy of gases at far distant places. It was discovered recently that the filamentation in air induces ‘lasing’, showing that electronically excited N2+ is population-inverted, exhibiting marked contrast to the common understanding that molecular ions generated by intense laser fields are prepared mostly in their electronic ground states. Here, to clarify the mechanism of the population inversion, we adopt few-cycle laser pulses, and experimentally demonstrate that the lasing at 391 nm occurs instantaneously after N2+ is produced. Numerical simulations clarify that the population inversion is realized by the post-ionization couplings among the lowest three electronic states of N2+. Our results shed light on the controversy over the mechanism of the air lasing, and show that this post-ionization coupling can be a general mechanism of the atmospheric lasing.UTokyo Research掲載「レーザーが空気中で増幅される機構を解明」 URI: http://www.u-tokyo.ac.jp/ja/utokyo-research/research-news/mechanism-of-air-lasing.htmlUTokyo Research "Mechanism of air lasing" URI: http://www.u-tokyo.ac.jp/en/utokyo-research/research-news/mechanism-of-air-lasing.htm

Correlated two-photon emission by transitions of Dirac-Volkov states in intense laser fields: QED predictions

In an intense laser field, an electron may decay by emitting a pair of photons. The two photons emitted during the process, which can be interpreted as a laser-dressed double Compton scattering, remain entangled in a quantifiable way: namely, the so-called concurrence of the photon polarizations gives a gauge-invariant measure of the correlation of the hard gamma rays. We calculate the differential rate and concurrence for a backscattering setup of the electron and photon beam, employing Volkov states and propagators for the electron lines, thus accounting nonperturbatively for the electron-laser interaction. The nonperturbative results are shown to differ significantly compared to those obtained from the usual double Compton scattering.Comment: 32 pages, 12 figure