Orthogonality Catastrophe in Quantum Sticking

Abstract

We show that the orthogonality catastrophe can dramatically affect the probability with which an ultralow energy atom or ion will stick to a surface. We predict new energy-dependent scaling laws for the sticking probability in this low-energy regime. We provide numerical results of this theory for the case of ultracold electrons sticking to the surface of highly porous silicon and show that the sticking probability can differ substantially from that calculated with perturbation theory. We then generalize our results for finite surface temperatures and find surprisingly that the sticking probability can change sharply, vanishing below a critical incident energy that varies with the surface temperature. We describe in detail this superreflective surface phase for ultralow energy matter waves where the reflection coefficient is strictly equal to one.