Quantum theory of sticking

Orthogonality catastrophe in quantum sticking

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.

Dissipative effects on quantum sticking

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.

Low velocity quantum reflection of Bose-Einstein condensates

We study how interactions affect the quantum reflection of Bose-Einstein condensates. A patterned silicon surface with a square array of pillars resulted in high reflection probabilities. For incident velocities greater than 2.5 mm/s, our observations agreed with single-particle theory. At velocities below 2.5 mm/s, the measured reflection probability saturated near 60% rather than increasing towards unity as predicted by the accepted theoretical model. We extend the theory of quantum reflection to account for the mean-field interactions of a condensate which suppresses quantum reflection at low velocity. The reflected condensates show collective excitations as recently predicted.

Quantum reflection from a solid surface at normal incidence

We observed quantum reflection of ultracold atoms from the attractive potential of a solid surface. Extremely dilute Bose-Einstein condensates of 23Na, with peak density 10(11)-10(12) atoms/cm(3), confined in a weak gravitomagnetic trap were normally incident on a silicon surface. Reflection probabilities of up to 20% were observed for incident velocities of 1-8 mm/s. The velocity dependence agrees qualitatively with the prediction for quantum reflection from the attractive Casimir-Polder potential. Atoms confined in a harmonic trap divided in half by a solid surface exhibited extended lifetime due to quantum reflection from the surface, implying a reflection probability above 50%.

Quantum reflection times for attractive potential tails

When a wave packet with a narrow momentum distribution is quantum reflected in a purely attractive potential proportional to -1/r(alpha), alpha>2, it generally experiences a time gain compared to a free particle reflected at r=0; for alpha=3 and very low energies there are large time delays. In quantum reflection of an atomic beam by a surface, such a time gain (delay) represents an apparent plane of reflection which is shifted in front of (behind) the surface. The quantum reflected wave is always delayed with respect to the classical particle accelerated in the attractive potential.

Anomalous threshold laws in quantum sticking

It has been stated that for a short-ranged surface interaction, the probability of a low-energy particle sticking to a surface always vanishes as s approximately k with k-->0 where k=sqrt[E]. Deviations from this so-called universal threshold law are derived using a linear model of particle-surface scattering. The Fredholm theory of integral equations is used to find the global conditions necessary for a convergent solution. The exceptional case of a zero-energy resonance is considered in detail. Anomalous threshold laws, where s approximately k(1+alpha),alpha>0 as k-->0, are shown to arise from a soft gap in the weighted density of states of excitations; alpha is determined by the behavior of the weighted density of states near the binding energy.