ELFT HÍRADÓ

[Szeminárium koordinátor <szfi-seminar AT wigner.mta.hu>]

SZFI Seminar
Varró Sándor
(Wigner FK SZFI, ELI-ALPS)
Displacement and squeezing transitions in very-high-order multiphoton 
processes
In many recent investigations on light-matter interactions the theorist 
should possibly use exact solutions of the equations of motion, since 
perturbation theory does not give satisfactory agreement with the 
experiments. In quantum electrodynamics and in quantum optics, at the most 
fundamental level, the equations of motion contain linear and quadratic 
interaction terms. These terms can often be eliminated by performing the 
displacement and/or squeezing transformation. On the basis of such a 
technique, recently we have built up a general scheme for treating 
very-high-order multiphoton processes, like high-harmonic generation [1]. The 
transition probabilities are determined by the matrix elements (between 
photon number eigenstates) of the displacement and squeezing operators, which 
have to be superimposed according to the photon statistics of the inducing 
field. In the course of this study, it was a surprise for us that in the 
enormous literature on ‘non-classical states and squeezing’, which has 
accumulated during the last more than eight decades, the matrix elements of 
the squeezing operator (a special generator of Bogoliubov transformations) 
have not been published in a compact and usable, classical polynomial form. 
Recently, we have derived such a compact expression in terms of Gegenbauer 
polynomials [2], and we have used it to describe the effect of photon 
statistics on various quantum transitions. Among some illustrative 
applications of our analytical results, we shall discuss the multiphoton 
excitations in the field of a ‘pedestal’ (or ‘pre-pulse’) stemming from 
amplified spontaneous emission from a parametric amplifier.[1] Varró S, 
Quantum optical aspects of high-harmonic generation. Photonics 8, 269 (2021). 
[https://doi.org/10.3390/photonics8070269 ]. [2] Varró S, Coherent and 
incoherent superposition of transition matrix elements of the squeezing 
operator. J. Phys. Conf. Ser. (2022). E-print: arXiv: 2112.08430 
[quant-ph].Tuesday, 8 March 2022, 10:00
Bldg 1, auditorium, 
https://wigner-hu.zoom.us/j/92490328041?pwd=aW9tT005N3JDSWNXcFNrTUZHNUt5UT09  
 Meeting ID: 924 9032 8041  Passcode: 211664
Language of the talk: English
All interested are welcome!
Róbert Juhászszfi-seminar AT wigner.mta.hu