ELFT HÍRADÓ

[Zimányiné Horváth Vera <Vera.Horvath AT eli-alps.hu>]

Előadó:                Varró Sándor (ELI ALPS, Wigner FK)
Cím:                     From the figure-8 motion to the high-intensity 
Compton effect


Helyszín:             az ELI ALPS konferenciaterme (Szeged, Wolfgang Sandner 
utca 3.)
Időpont:             2023. június 15., 9 óra

Az előadás rövid összefoglalója:
We discuss the exact relativistic description of both the classical and the 
quantum mechanical motion of charged particles interacting with a laser field 
of arbitrary intensity. This subject gives us also a good opportunity to 
celebrate the centenary of Compton's discovery [1], which is an important 
ingredient of quantum electrodynamics (QED). First, in a brief historical 
overview we shall highlight the wave-particle duality and simultaneity in 
Compton scattering [2], [3].
The exact solutions of the Lorentz and Dirac equations of a charged particle 
in a plane electromagnetic wave in vacuum are represented by the well-known 
figure-8 motion and the Volkov states, respectively. These solutions have 
been extensively used in describing high-harmonic emission and attosecond 
pulse generation in the Compton or Thomson scattering processes [4]. They 
also have a role in the physics of free electron lasers [5]. Here we point 
out the surprising mathematical connection between the relativistic figure-8 
motion in a monochromatic radiation and the classical Kepler-Coulomb 
trajectories in a central field [6].
By going beyond the external field approximation, the Dirac (Klein-Gordon or 
Schrödinger) equation of the joint system of a charged particle interacting 
with quantized radiation modes in vacuum can also be solved exactly in 
various cases [7], [8]. The photon part of the single-mode stationary states 
are squeezed (coherent) number states. The photon statistics has been 
determined quite recently in terms of Gegenbauer polynomials [9], and this is 
now used for a refined analysis of high-harmonic generation in a quantized 
radiation field, which was first studied long ago [7].
Finally we discuss the interaction of a charged Dirac particle with two 
co-propagating circularly polarized quantized modes. On the basis of the 
recently found exact solutions, we shall see that entangled photon pairs 
naturally appear in this system, like in the quantum optical non-degenerate 
parametric down-conversion process. In a special case the probability 
amplitudes of the distribution of these photon pairs reduce to Zernike 
functions, which are well-kown in the theory of aberration in classical 
optical imaging. Accordingly, it is justified to introduce the concepts of 
aberration and Zernike moments on quantum phase space, which may give a new 
aspect in the theoretical study of high-order QED and parametric processes in 
laser-matter interactions.

References.
[1] Compton A H 1922 The spectrum of secondary X-rays. Phys. Rev. 19, 267-268 
(1922).
[2] Compton A H and Simon A W 1925 Directed quanta of scattered X-rays. Phys. 
Rev. 26, 289-299 (1925).
[3] Bay Z, Henri V P and Mc Lernon F 1955 Simultaneity in the Compton effect. 
Phys. Rev. 97, 1710-1712 (1955).
[4] Hack Sz, Varró S and Czirják A 2018 Carrier-envelope phase controlled 
isolated attosecond pulses in the nm wavelength range, based on coherent 
nonlinear Thomson back-scattering. New Journal of Physics 20, 073043 (2018).
[5] Varró S 2012 (Ed.) Free Electron Lasers.  (Rijeka, InTech, 2012).
[6] Varró S 2010 Intensity effects and absolute phase effects in nonlinear 
laser-matter interactions. In Laser Pulse Phenomena and Applications. (Duarte 
F J (Ed.); Rijeka, InTech, 2010). Chapter 12.
[7] Bergou J and Varró 1981 Nonlinear scattering processes in the presence of 
a quantised radiation field: II. Relativistic treatment. Journal of Physics 
A: Math. Gen. 14, 2281-2303 (1981).
[8] Varró S 2021 Quantum optical aspects of high-harmonic generation. 
Photonics 8, 269 (2021).
[9] Varró S 2022 Coherent and incoherent superposition of transition matrix 
elements of the squeezing operator. New Journal of Physics 24, 053035 (2022).


A szeminárium az alábbi link használatával online is meghallgatható:
https://teams.microsoft.com/l/meetup-join/19%3ameeting_MGFjM2M4NjItMWU4Zi00MzhkLThiZTYtN2ZhN2FlYjFjNTJi%40thread.v2/0?context=%7B%22Tid%22%3A%22b207389a-c5cb-4cb0-a1ad-227b94e96448%22%2C%22Oid%22%3A%22c993efcb-59ae-4652-9f68-d7a313727128%22%2C%22IsBroadcastMeeting%22%3Atrue%2C%22role%22%3A%22a%22%7D&btype=a&role=a

Minden érdeklődőt szívesen látunk.


ZIMÁNYINÉ HORVÁTH Vera
Látogatóközpont-vezető

ELI ALPS, ELI-HU Non-Profit Ltd.
H-6728 Szeged, Wolfgang Sandner utca 3.
Mobil: +36 70 491 14 12
E-mail: Vera.Horvath AT eli-alps.hu<http://Vera.Horvath AT eli-alps.hu/>
Honlap: www.eli-alps.hu<http://www.eli-alps.hu/>
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