Classical and Quantum Mechanics of the Driven Double Well

Akira Igarashi, Hiroaki S. Yamada

Akira Igarashi, Hiroaki S. Yamada

David Farrelly, John A. Milligan

The effect of two-frequency driving of a symmetric double well is investigated classically and quantum mechanically. By computing Husimi distributions it is shown that control and suppression of tunneling may be achieved by driving the system with two fields whose frequencies are in a 1:2 ratio. In particular, a second field of finite duration can be used to selectively trap the wave packet in either well.

Takeshi Matsuo, Yuhei Natsume, Takeo Kato

Giuseppe Della Valle, Marco Ornigotti, P. Laporta +3 more

In this contribution we report on a direct visualization of CDT using an optical realization of the quantum-mechanical driven double-well Hamiltonian based on two tunneling-coupled waveguides with a sinusoidally-curved axis. Our experimental implementation makes it possible for the first time to directly trace the wave function evolution in the driven double-well potential by exploiting the fluorescence pattern observed in an active erbium-ytterbium:glass waveguide.

Anders Andersen, Jacob Madsen, Christian Reichelt +5 more

In a thought-provoking paper, Couder and Fort [Phys. Rev. Lett. 97, 154101 (2006)] describe a version of the famous double-slit experiment performed with droplets bouncing on a vertically vibrated fluid surface. In the experiment, an interference pattern in the single-particle statistics is found even though it is possible to determine unambiguously which slit the walking droplet passes. Here we argue, however, that the single-particle statistics in such an experiment will be fundamentally different from the single-particle statistics of quantum mechanics. Quantum mechanical interference takes place between different classical paths with precise amplitude and phase relations. In the double-slit experiment with walking droplets, these relations are lost since one of the paths is singled out by the droplet. To support our conclusions, we have carried out our own double-slit experiment, and our results, in particular the long and variable slit passage times of the droplets, cast strong doubt on the feasibility of the interference claimed by Couder and Fort. To understand theoretically the limitations of wave-driven particle systems as analogs to quantum mechanics, we introduce a Schrödinger equation with a source term originating from a localized particle that generates a wave while being simultaneously guided by it. We show that the ensuing particle-wave dynamics can capture some characteristics of quantum mechanics such as orbital quantization. However, the particle-wave dynamics can not reproduce quantum mechanics in general, and we show that the single-particle statistics for our model in a double-slit experiment with an additional splitter plate differs qualitatively from that of quantum mechanics.