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Q: Fachverband Quantenoptik und Photonik
Q 58: Matter Wave Optics
Q 58.6: Poster
Donnerstag, 17. März 2022, 16:30–18:30, P
The logarithmic phase singularity in the inverted harmonic oscillator — •Freyja Ullinger1,2, Matthias Zimmermann2, and Wolfgang P. Schleich1,2 — 1Institut für Quantenphysik and Center for Integrated Quantum Science and Technology (IQST), Universität Ulm, 89081 Ulm, Germany — 2Institute of Quantum Technologies, German Aerospace Center (DLR), 89081 Ulm, Germany
Relevant phenomena in quantum field theory, such as Hawking radiation and acceleration radiation [1,2], are based on a logarithmic phase singularity and the presence of an event horizon in spacetime.
In this poster, we show that related effects emerge in the simple quantum system of a one-dimensional inverted harmonic oscillator. In fact, the Wigner function corresponding to an energy eigenfunction of this system [3,4] clearly displays a horizon in phase space. Although usually hidden, even a logarithmic phase singularity in combination with an amplitude singularity emerges with the help of a suitable coordinate transformation.
Our insights into this simple quantum system lay the foundation for future applications in the field of matter wave optics.
[1] S. W. Hawking, Nature 248, 30 (1974)
[2] M. O. Scully, S. Fulling, D. M. Lee, D. N. Page, W. P. Schleich, and A. A. Svidzinsky, Proc. Natl. Acad. Sci. U.S.A. 115, 8131 (2018)
[3] N. L. Balazs and A. Voros, Ann. Phys. (N. Y.) 199, 123 (1990)
[4] D. M. Heim, W. P. Schleich, P. M. Alsing, J. P. Dahl, and S. Varro, Phys. Lett. A 377, 1822 (2013)