Remarks on quantum mechanics on surfaces

Alberto Benvegnù, Nicola Sansonetto, Mauro Spera

充宏 池上

F.W. Wiegel

We study the simplest possible example of a topological quantum phenomenon: the movement of a free quantum mechanical particle on a Riemann surface with infinitely many sheets. The propagator is given, in the exact form as well as in a semiclassical approximation. It is shown that the semiclassical treatment of this topological model differs slightly from the usual WICB treatment which applies to situations in which topology plays no role; the difference is caused by the presence of the Edwards-Gulyaev term in the path integral in polar coordinates. Finally, we suggest that the Edwards-Gulyaev term sheds some light on the remarkable accuracy of the Geometric Theory of Diffraction.

F.W. Wiegel

James S. Fakonas, Anya Mitskovets, Harry A. Atwater

Metals can sustain traveling electromagnetic waves at their surfaces supported by the collective oscillations of their free electrons in unison. Remarkably, classical electromagnetism captures the essential physics of these 'surface plasma' waves using simple models with only macroscopic features, accounting for microscopic electron–electron and electron–phonon interactions with a single, semi-empirical damping parameter. Nevertheless, in quantum theory these microscopic interactions could be important, as any substantial environmental interactions could decohere quantum superpositions of surface plasmons, the quanta of these waves. Here we report a measurement of path entanglement between surface plasmons with 95% contrast, confirming that a path-entangled state can indeed survive without measurable decoherence. Our measurement suggests that elastic scattering mechanisms of the type that might cause pure dephasing in plasmonic systems must be weak enough not to significantly perturb the state of the metal under the experimental conditions we investigated.

David Avisar, A. Eilam, A. D. Wilson‐Gordon

The question of whether sunlight induces coherent dynamics in biological systems is under debate. Here we show, on the basis of an exact fully quantum mechanical treatment, that thermal light induces excited-state coherences in matter similar to those induced by a coherent state. We demonstrate the phenomenon on a V-type model system and a two-state Born-Oppenheimer molecular system. Remarkably, wavepacket-like dynamics is induced in the excited molecular potential-energy surface.