Quantum reflection by Casimir–van der Waals potential tails

Abstract

We study the reflectivity of Casimir-van der Waals potentials, which behave as ϪC 4 /r 4 at large distances and as ϪC 3 /r 3 at small distances. The overall behavior of the reflection amplitude R depends crucially on the parameter ϭͱ2MC 3 /(បͱC 4 ) which determines the relative importance of the Ϫ1/r 3 and the Ϫ1/r 4 parts of the potential. Near threshold, Eϭប 2 k 2 /(2M )→0, the reflectivity is given by ͉R͉ϳexp(Ϫ2bk), with b depending on and the shape of the potential at intermediate distances. In the limit of large energies, ln͉R͉ is proportional to Ϫk 1/3 with a known constant of proportionality depending only on C 3 . For small values of , the reflectivity behaves as for a homogeneous Ϫ1/r 3 potential in the whole range of energies and does not depend on C 4 or the shape of the potential beyond the Ϫ1/r 3 region. For moderate and large values of , the reflectivity depends on C 4 and on the potential shape. For sufficiently large values of , which are ubiquitous in realistic systems, there is a range of energies beyond the near-threshold region, where the reflectivity shows the high-energy behavior appropriate for a homogeneous Ϫ1/r 4 potential, i.e., ln͉R͉ is proportional to Ϫͱk with a proportionality constant depending only on C 4 . This conspicuous and model-independent signature of the Casimir effect is illustrated for the reflectivities of neon atoms scattered off a silicon surface, which were recently measured by Shimizu ͓Phys. Rev. Lett. 86, 987 ͑2001͔͒.

Comparison of hydrodynamic and Dirac models of dispersion interaction between graphene and H,He∗, or Na atoms

“…In almost all papers devoted to the experimental investigation of quantum reflection [6,7,11,13] the comparison of the measurement data with theory is performed with the use of a phenomenological potential for the atom-wall interaction. This simplifies the calculation of theoretical reflection amplitudes to be compared with the experimental ones.…”

“…The magnitude and the distance dependence of these forces were measured in several experiments [5]. In the last few years atom-wall interaction is being studied intensively in connection with the phenomenon of quantum-reflection [6][7][8][9][10][11][12][13]. Theoretical description of atom-wall interaction is given by the Lifshitz theory [1,2,4,5,14] which expresses the van der Waals and Casimir-Polder energy and force through the dynamic electric polarizability of an atom and the frequency-dependent dielectric permittivity of wall material.…”

Temperature and number evolution of cold cesium atoms inside a wall-coated glass cell

“…Quantum reflection is a reflection of matter waves from the attractive potential, happening when the atomsurface distance r is still beyond several atomic units. Near this region, the interaction can be described by the Casimir-van der Waals potential, which behaves as -C 4 /r 4 at large distances and as -C 3 /r 3 at small distances [22][23][24][25][26] . The coefficients C 3 and C 4 depend on the polarizability property of the cold cesium atoms and on the dielectric property of the cell surface.…”

Statistical approach to Casimir-Polder potentials in heterogeneous media

“…In strong contrast, at smaller distances fluctuations of the potential become larger than its mean, which is consequently no longer representative. In practice, this conclusion is crucial for measurements of quantum reflection [21,[31][32][33][34], and more generally for any measurement of the Casimir force involving heterogeneous materials.…”