ELFT HÍRADÓ

[<vera.horvath AT eli-alps.hu>]

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