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arXiv:1112.4544 · Physical Review Letters

Orthogonality Catastrophe in Quantum Sticking

Dennis P. Clougherty, Yanting Zhang

Published Sep 18, 2012• 13 citations
arXivHTMLPDF

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.

DOI
10.1103/physrevlett.109.120401

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•Jan 1, 2010•0 citations
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.
A continuum model for low-energy physisorption on a membrane under tension is proposed and studied with variational mean-field theory. A discontinuous change in the energy-dependent sticking coefficient is predicted under certain conditions. This singularity is a result of the bosonic orthogonality catastrophe of the vibrational states of the membrane. The energy-dependent sticking coefficient is predicted to have exponential scaling in 1/E1/E1/E at energies above the singularity. The application of this model to the quantum sticking of cold hydrogen to suspended graphene is discussed. The model predicts that a beam of atomic hydrogen can be completely reflected by suspended graphene at ultralow energies.
Using variational mean-field theory, many-body dissipative effects on the threshold law for quantum sticking and reflection of neutral and charged particles are examined. For the case of an Ohmic bosonic bath, we study the effects of the infrared divergence on the probability of sticking and obtain a nonperturbative expression for the sticking rate. We find that for weak dissipative coupling α, the low-energy threshold laws for quantum sticking are modified by an infrared singularity in the bath. The sticking probability for a neutral particle with incident energy E→0 behaves asymptotically as s~E((1+α)/2(1-α)); for a charged particle, we obtain s~E(α/2(1-α)). Thus, "quantum mirrors"-surfaces that become perfectly reflective to particles with incident energies asymptotically approaching zero-can also exist for charged particles. We provide a numerical example of the effects for electrons sticking to porous silicon via the emission of a Rayleigh phonon.
The role of shape resonances and many-body effects on universal quantum sticking of ultracold atoms onto solid surfaces is examined analytically and computationally using an exactly solvable representation of the Dyson equation. We derive the self-energy renormalization of the transition amplitude between an ultracold scattering atom and the bound states on the surface in order to elucidate the role of virtual phonon exchanges in the limiting behavior of the sticking probability. We demonstrate that, to first order in the interactions for finite ranged atom–surface potentials, virtual phonons can only rescale the strength of the atom–surface coupling and do not rescale the range of the coupling. Thus, universal sticking behavior at ultralow energies is to be expected for all finite ranged potentials. We demonstrate that the onset of the universal sticking behavior depends greatly on the position of the shape resonance of the renormalized potential and for sufficiently low energy shape resonances, deviations from the universal s(E)∝√E can occur near these energies. We believe that this accounts for many of the low energy sticking trends observed in the scattering of submillikelvin H atoms from superfluid 4He films.
We provide a general and nonperturbative theoretical basis for quantum reflection of an ultracold atom incident on a cold or warm surface. Sticking is identified with the formation of a long-lived resonance, from which it emerges that the physical reason for not sticking is that the many internal degrees of freedom of the target serve to decohere the incident one body wave function, thereby upsetting the delicate interference process necessary to form a resonance. We then explore the transition to the post-threshold behavior, when sticking prevails at higher incident energies. Studying the WKB wave functions of the atom provides a quick understanding of our results even in the ultracold regime where WKB is not applicable. Explicit examples are examined in detail and we predict the temperatures required to reach the various regimes.
In paper I (physics/0010068) entitled "The No-sticking Effect in Ultra-cold Collisions", we showed that under very general circumstances, atoms approaching a surface will not stick as its incoming energy approaches zero. This is true of either warm or cold surfaces. Here we explore the transition region from non sticking to sticking as energy is increased. The key to understanding the transition region is the WKB approximation and the nature of its breakdown. Simple rules for understanding the rollover to higher energy, post-threshold behavior, including analytical formulae for some asymptotic forms of the attractive potential are presented. We discuss a practical example of atom-surface pair in various substrate geometries. We also discuss the case of low energy scattering from clusters.
A study is made of the interaction between hydrogen atoms and the surface elementary excitations of superfluid "He. Calculations for the sticking probability and for the energy and effective mass of a hydrogen atom bound to the surface are presented. As a first step in the calculations, we formulate the Hamiltonian describing a hydrogen atom interacting with the surface of "He in its ground state together with the interaction coupling to the surface elementary excitations (the ripplons). The derivation is based on the association of the surface ground state with a flat surface and the excited states with a sinusoidally varying height of the surface. The interaction potential is derived by summing a *He-H atom-atom pair potential over helium atoms below the surface. The atom-atom pair potential is chosen so that the derived surface potential is a Morse potential with parameters which are fitted to the effective surface potential derived by Mantz and Edwards for a hydrogen atom interacting with N-1 helium atoms. The energy and angle dependent sticking probability, S(E,θ), and the thermally averaged sticking probability, S(T), are calculated. Results are compared with the experimental value of S(T), S(T)=0.035±0.005, measured for the temperature range 0.18<T<0.27K. The possibility that a hydrogen atom bound above the surface may exhibit polaronic behaviour is investigated. The energy of the hydrogen surface "polaron" and its effective mass are calculated using perturbation theory. The hydrogen atom is found to be weakly coupled to the surface elementary excitations, and therefore the polaronic effects are weak. The contribution to these results from virtual transition to free states is emphasized.