Quantized Ultracold Neutrons in Rough Waveguides: GRANIT Experiments and Beyond

Abstract

We apply our general theory of transport in systems with random rough boundaries to gravitationally quantized ultracold neutrons in rough waveguides as in GRANIT experiments (ILL, Grenoble). We consider waveguides with roughness in both two and one dimensions (2D and 1D). In the biased diffusion approximation the depletion times for the gravitational quantum states can be easily expressed via each other irrespective of the system parameters. The calculation of the exit neutron count reduces to evaluation of a single constant which contains a complicated integral of the correlation function of surface roughness. In the case of 1D roughness (random grating) this constant is calculated analytically for common types of the correlation functions. The results obey simple scaling relations which are slightly different in 1D and 2D. We predict the exit neutron count for the new GRANIT cell.

Rough Mirror as a Quantum State Selector: Analysis and Design

“…The 2D results (Table 4) are different because of different dimensionality and smaller linear sizes of our samples. Here as an observable, which is used to compare the results, we use Φ 2 which describes the neutron count in experiments with 2D roughness [38,41]. The generated rough surfaces are emulating the Gaussian roughness with the correlation function (|x|) = exp(−|x| 2 /8) (i.e., = 1, = 2) for which Φ 2 = 2.58 × 10 3 .…”