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**From**: <vera.horvath AT eli-alps.hu>**To**: fizinfo AT lists.kfki.hu**Subject**: [Fizinfo] Meghívó az ELI ALPS márc. 9-i szemináriumára**Date**: Tue, 7 Mar 2023 09:03:01 +0100

Előadó: Varró Sándor (ELI ALPS, Szeged; ELKH Wigner FK, Budapest)

Cím: Quantum aberration in the phase space of entangled photons

Időpont: 2023. március 9. 9 óra

Helyszín: ELI ALPS konferenciaterme (Szeged, Wolfgang Sandner utca 3.)

Az előadás kivonata:

In the first part of the talk we attempt to give a brief exposition of the

scientific background of the subject we are discussing. The following points

will be highlighted: The coherent and squeezed states of a quantum-mechanical

harmonic oscillator (which may also represent a photon mode of the

electromagnetic radiation) have already been known immediately after the

invention of wave mechanics. Not much later, in 1935, Schrödinger introduced

the concept of entanglement (“Verschränkung”), when the quanta are distributed

coherently among several degrees of freedom. His analysis was motivated by the

critics due to Einstein, Podolsky and Rosen (EPR, 1935), of the quantum

description, in general. The experimental investigations of such fundamental

questions became possible after the invention of the laser. From the sixthies

of the last century the quantum states of light have played an important role

in the theory and practice of lasers and parametric processes in quantum

optics and quantum imaging [1], [2], [3]. The study and application of

entanglement have become one of the main ingredients of quantum information

science [4]. The non-classical states also naturally appear in the non-

perturbative description of the minimal coupling interaction of radiation

fields with charges, e.g. in the non-linear Compton process or in high-order

harmonic generation [5], [6], [7], so they have a role in attosecond physics,

too.

Recently we have derived the probability amplitudes of general squeezing

transitions, in terms of Gegenbauer polynomials [8]. On the basis of this

result we have also determined the photon statistics of thermal noise (black-

body radiation) amplification in a degenerate parametric amplifier. In the

meantime we have applied an analogous mathematical procedure for the non-

degenerate process producing EPR-type entangled photon pairs. In the second

half of the talk we shall discuss the results of the latter study. The photon

statistics of the entangled photon pairs have been calculated, in a close

connection with the quantum phase formalism, which we have already introduced

earlier [9]. It will be shown that in a special case, the derived probability

amplitudes reduce to the Zernike functions (polynomials), well-kown in the

classical theory of aberration in optical imaging. The quantum Zernike

polynomials depend on the phase-space variables, and they form a complete set

of orthogonal aberration functions. Thanks to these results, it is possible to

quantitatively assess the parametric photon sources, for example, in terms of

the corresponding Zernike moments.

References.

[1] Lugiato L A, Gatti A and Brambilla E, Quantum imaging. J. Opt. B: Quantum

Semiclass. Opt. 4 (2002) S176–S183.

[2] Dodonov V V, Nonclassical states in quantum optics: a squeezed review of

the first 75 years. J. Opt. B: Quantum Semiclass. Opt. 4, R1–R33 (2002).

[3] Andersen U L et al, 30 years of squeezed light generation. Phys. Scr. 91,

053001 (2016).

[4] > The Royal Swedish Academy of Sciences has decided to award the Nobel

Prize in Physics 2022 to Alain Aspect, John F. Clauser and Anton Zeilinger;

“for experiments with entangled photons, establishing the violation of Bell

inequalities and pioneering quantum information science”.

https://www.nobelprize.org/uploads/2022/10/press-physicsprize2022-2.pdf <

[5] Varró S : Entangled photon-electron states and the number-phase minimum

uncertainty states of the photon field. New Journal of Physics 10, 053028

(2008)

[6] Varró S : Entangled states and entropy remnants of a photon-electron

system. Physica Scripta T140, 014038 (2010).

[7] Varró S: Quantum optical aspects of high-harmonic generation. Photonics

2021, 8, 269 (2021).

[8] Varró S: Coherent and incoherent superposition of transition matrix

elements of the squeezing operator. New Journal of Physics 24, 053035 (2022).

[9] Varró S : Regular phase operator and SU(1,1) coherent states of the

harmonic oscillator. Physica Scripta 90 (7) 074053 (2015).

A szeminárium angol nyelvű,. Minden érdeklődőt szívesen látunk.

Horváth Vera

**[Fizinfo] Meghívó az ELI ALPS márc. 9-i szemináriumára**,*vera.horvath, 03/07/2023*

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