Particle diffraction studied using quantum trajectories

Abstract

Diffraction and interference of matter waves are key phenomena in quantum mechanics. Here we present some results on particle diffraction in a wide variety of situations, ranging from simple slit experiments to more complicated cases such as atom scattering by corrugated metal surfaces and metal surfaces with simple and isolated adsorbates. The principal novelty of our study is the use of the so-called Bohmian formalism of quantum trajectories. These trajectories are able to satisfactorily reproduce the main features of the experimental results and, more importantly, they provide a causal intuitive interpretation of the underlying dynamics. In particular, we will focus our attention on: (a) a revision of the concepts of near and far field in undulatory optics; (b) the transition to the classical limit, where it is found that although the quantum and classical diffraction patterns tend to be quite similar, some quantum features are maintained even when the quantum potential goes to zero; and (c) a qualitative description of the scattering of atoms by metal surfaces in the presence of a single adsorbate.

Role of quantum vortices in atomic scattering from single adsorbates

“…Actually, it can be said that the latter corresponds to a laminar regime, while the former is turbulent, with a smooth transition between them in close analogy with classical fluid dynamics. 8,9 Second, and more importantly, we see in ͑a͒ and ͑b͒ that the complex dynamics mentioned above is not completely chaotic, but gets highly organized around a number of points avoided by the trajectories. These points constitute centers around which trajectories loop ͓see inset to Fig.…”

“…In order to simulate with good accuracy the scattering process, we use an initial incoming plane wave, approximated as a linear superposition of 250 Gaussian wave packets, 9 homogeneously distributed along a distance of 100 bohr. The width parameters of each wave packet are taken as x ϭ1.58 bohr and z ϭ5 bohr, respectively.…”

“…First, these trajectories do not get so close to the interaction region due to the existence of an effective barrier, that can be alternatively interpreted as a quantum pressure caused by other trajectories in the ensemble. 9 This implies a weaker interaction acting on the incoming particles, and thus simpler dynamics. As a result, the regime is not so turbulent, and a wide region of laminar flow is appreciated.…”

“…8,9 For example, Lopreore and Wyatt 10 have analyzed wave packets tunneling through barriers, nicely elucidating the corresponding mechanism in terms of quantum trajectories; a portion of them, in the foremost part of the initial packet, overcomes the barrier because they acquire some kinetic energy during a boost phase, shortly after the launching. With a similar analysis in mixed quantum-classical simulations, Prezhdo and Brooksby 11 have solved the quantum back reaction problem for the reaction of O 2 with Pt, and Gindensperger et al have reported a study including continuum states, 12 and a description of rotational diffractive scattering.…”

Probability and complex quantum trajectories

“…Later, a complex trajectory approach for solving the QHJE was developed by Tannor and co-workers [13]. The QHJE was derived independently by Sanz and Miret-Artes [14], who also found the complex trajectory representation useful in better understanding the nonlocality in quantum mechanics [15,16].…”