Beams of gravitationally bound ultracold neutrons in rough waveguides

Abstract

of gravitationally bound ultracold neutrons in rough waveguides. Phys. Rev. A, 83, 033618 1-9 (2011 We investigate the propagation of ultracold neutrons through a rough waveguide in conjunction with recent experiments in which the ultracold neutrons were beamed between a perfect mirror and a rough scatterer and absorber. The main goal is to find a way to resolve the lowest gravitationally quantized discrete states in the peV range. We compare the neutron count for various types of mirrors with Gaussian, power-law, and exponential correlation functions of surface inhomogeneities. The main conclusion is that all the information about inhomogeneities, including their amplitude, correlation radius, and the rate of decay of the correlation function, enter the exit neutron count via just a single constant , which effectively renormalizes the amplitude of roughness. To observe well-defined quantum steps, one should have an experimental setup with > 40. For a wide variety of correlation functions, the constant is proportional to the square of the amplitude of the surface roughness and is inversely proportional to the square root of the correlation radius. The strong dependence of on roughness parameters and the shape of the correlation function opens a novel way for improving the resolution of gravitationally bound states by optimizing the roughness pattern without reverting to an undesirable strong roughness. We discuss how to optimize the scatterer and absorber by first generating numerically the desired roughness profile and then transferring it to the mirror. We also study the effect of beam preparation on the initial occupancies of gravitational states before the beam enters the waveguide. It turns out that there are simple ways to manipulate the beam in front of the waveguide that can help to resolve the gravitationally bound quantum states. Our results are in good agreement with available experimental data.

Quantized Ultracold Neutrons in Rough Waveguides: GRANIT Experiments and Beyond

“…The neutrons are sensitive only to geometrical and statistical properties of random surface inhomogeneities and their behavior in the rough waveguide can serve as a perfect application of our transport theory including a model-free description of the GRANIT experiments which is the main goal of this paper. Some of our earlier results for a neutron waveguide with 1D roughness (a mirror with random grating) can be found in [25,26].…”

“…The value of the dimensionless constant Φ depends on the properties of the waveguide, but the moment we calculate Φ we know the dependence of the exit neutron count on the waveguide width ℎ, Figure 2, irrespective of the origin of these particular values of Φ. In Figure 2 taken from [26] we plot the exit neutron count (ℎ)/ 0 (11) for several values of Φ. The noticeable quantum steps on the curves start appearing for Φ > 40.…”

“…This equation has been used in [26] when fitting the experimental data from [1][2][3][4] (see Figure 2). The only information we have about the mirror roughness in those earlier experiments is that the average lateral size of inhomogeneities is of the order 1.19 and the average amplitude is approximately 0.119.…”

Rough Mirror as a Quantum State Selector: Analysis and Design

“…For each fitting function the table shows the correlation radii , ,PL and the quality of the fits , (7). The last column shows the calculated parameter Φ , ,PL [37] responsible for the exit neutron count. as measured by difference in the correlation radii , in and directions is of the order of several percent and is small, smaller than the difference between the patches which is rather pronounced.…”

Shaping the distribution of vertical velocities of antihydrogen in GBAR

“…In the sequel of this section, a simple analysis of the problem is presented in terms of quasi-classical arguments, to be confirmed in the next sections. A more complete quantum-mechanical description is also available in papers devoted to ultracold neutrons [15,[17][18][19][20].…”