z. Phys. B. 98, 319-321 (1995) ZEITSCHRIFT FORPHYSIK B 9 Springer-Verlag 1995 Quantum reflection Carlo Carraro 1'*, Milton W. Cole 2 1Lyman Laboratory of Physics, Harvard University, Cambridge, MA 02138, USA 2104 Davey Laboratory, Department of Physics and Center for Materials Physics,Pennsylvania State University,University Park, PA 16802, USA (e-mail: mwc@psuvm.psu.edu., Fax: (814)865-3604) Abstract. Recent experimental and theoretical results concerning the sticking coefficient at ultralow energy are described. The need for an accurate treatment of long range forces, including retardation, is emphasized. The system involving H atoms incident on liquid helium pro- vides the first clear evidence of quantum reflection. New results are reported for the sticking of D atoms incident on helium. The energy upper bound for the regime of quan- tum reflection for alkali atoms is found to be extremely low, but ultimately achievable. PACS: 34.50.Dy; 82.20.Tr; 67.65.Tz 1. Introduction In the low energy (E) regime, many physical phenomena exhibit behavior which is qualitatively distinct from that seen at higher energies. The problem of sticking provides one example. It has long been realized that quantum mechanics affects the sticking coefficient, s, in a dramatic way at low energy [1]. More recently, it has been found that long range forces play a particularly important role in determining s at low E. This situation has allowed us to demonstrate that the (usually elusive) effects of retardation on these forces are clearly manifested in recent sticking experiments [2, 3]. The present paper describes the basic ideas and results, with special emphasis provided for the case of hydrogen atoms incident on liquid helium. This focus is due to the relative ease of the calculations and the fact that only this system has been explored to date in the extreme quantum regime. The basic concepts are more general, however, and have relevance to eventual measurements of the sticking of very cold alkali atoms. The basic physics of low E sticking is straightforward. An atom, incident at low E has a wave length 2 which is * Present address: Department of Chemistry, University of California, Berkeley,CA 94720, USA long compared to the characteristic distance scale of the gas-surface interaction V(r). The general theory of waves yields the expectation in this limit that the wave/particle is likely to be reflected long before the atom arrives at the attractive well. Hence s falls to zero; the specific prediction is that s is proportional to the amplitude for the impinging wave within close proximity to the surface. This leads to a dependence, s ~ ~/E (1) This so-called quantum reflection behavior differs dramati- cally from the classical expectation that s ought to ap- proach unity at low E for the case of a very cold surface. The latter belief is intuitively obvious because the ap- proach to the surface takes infinite time, during which the particle exerts a nonzero force on the surface. This guarantees that there will ensue some excitation of the solid, resulting in energy loss and hence s = 1. There have been many studies of the specific case of H/He because of both an experimental relevance and the theoretical convenience of this system (a well known force law and the existence of only one bound state [4]). Inter- est in this field exponentiated in 1991 when data of Doyle et al. I-5] implied that s approaches 0.3 for ultralow energy (10 .4 K) H atoms incident on liquid helium, in marked contrast to the prediction of equation (1). This apparent discrepancy was tentatively resolved by the hypothesis that the experiment actually involved a helium film, of thickness d ~ 50 A [2, 6]. Since 2 > d, the underlying sub- strate strongly alters the long range potential experienced by the impinging atom, drastically modifying s. The pre- dictions of the most recent version of the theory [7] and its subsequent confirmation [3] are discussed below. We also describe here new theoretical predictions of quantum reflection of D atoms incident on liquid helium and dis- cuss the possibility of seeing quantum reflection with ultracold alkali atoms. Since rather complete reports of the general theory have been published recently, we shall only sketch the basic ideas of the calculation and its relation to the recent experiments. We shall mention also some intriguing results obtained [8,9] for ultralong range potentials