Speaker
Description
Landau–Zener-transitions are an essential tool in atom optics, and in particular, in accelerated optical lattices. It is amazing that despite its simplicity, the derivation of the well-known Landau-Zener-formula for the transition probability amplitude is rather involved, independent of the approach pursued. An integration in the complex plane, the asymptotic expansion of the parabolic cylinder function, or the introduction of a superadiabatic basis represent only a few of the many sophisticated techniques that eventually lead to the elementary result.
In the present talk, we employ the Markov approximation and the well-known Fresnel-integral to derive in ‘’one-line’’ the familiar expression for the Landau-Zener-formula. Moreover, we provide numerical as well as analytical justifications for our approach, and identify three characteristic motions of the probability amplitude in the complex plane.
In addition, we make the connection to Hawking radiation and report on a recent experiment [2], verifying key features of this unusual type of radiation. Our experiment is based on an analogy between quantum mechanics and surface gravity water waves.
References:
[1] E.P. Glasbrenner and W.P. Schleich, The Landau-Zener formula made simple, , J. Phys. B: At. Mol. Opt. Phys. 56, 104001 (2023)
[2] G.G. Rozenman, F. Ullinger, M. Zimmermann, M.A. Efremov, L. Shemer, W.P. Schleich and A. Arie, Observation of a phase space horizon with surface gravity water waves (to be published)
