Hawking radiation, the logarithmic phase singularity, and the inverted harmonic oscillator

by Mr. Matthias Zimmermann

University of ULM and German Space Agency
at Quantum optics seminar

Wed, 01 Jun 2022, 15:00
ZOOM only


Zoom Link: https://us02web.zoom.us/j/85244607029

Some of the most intriguing, but so far unobserved quantum effects are Hawking [1]
and Unruh [2] radiation. At the very heart of both phenomena lies a logarithmic phase
singularity that manifests itself at a horizon in spacetime. A very similar singularity is
present in the elementary quantum system of an inverted harmonic oscillator when
viewed in rotated quadratures of phase space [3,4].
In this talk, we establish the astonishing resemblance [5] between these systems on
a theoretical level. Moreover, we demonstrate that the Fourier transform of a
logarithmic phase is the key element that governs both the Bose-Einstein and the
Fermi-Dirac statistics. This feature determines not only the spectrum of the emitted
particles at an event horizon in spacetime, but also the transmission and reflection
coefficients of the inverted harmonic oscillator.
Finally, we present different possible ways to reveal the logarithmic phase singularity
intrinsic to the energy eigenstates of the inverted harmonic oscillator by applying
appropriate transformations in phase space.

[1] S.W. Hakwing, Nature 248, 30 (1974).
[2] W.G. Unruh, Phys. Rev. D 14, 870 (1976).
[3] N.L. Balazs and A. Voros, Ann. Phys. (N.Y.) 119, 123 (1990).
[4] D.M. Heim, W.P. Schleich, P.M. Alsing, J.P. Dahl, and S. Varro, Phys. Lett. A
377, 1822 (2013).
[5] F. Ullinger, M. Zimmermann, and W.P. Schleich, AVS Quantum Sci. 4,
024402 (2022)

Created on 29-05-2022 by Folman, Ron (folman)
Updaded on 29-05-2022 by Folman, Ron (folman)