Quantum reflection of rare-gas atoms and clusters from a grating

Quantum reflection is a universal property of atoms and molecules when scattered from surfaces in ultracold collisions. Recent experimental work has documented the quantum reflection and diffraction of He atoms, dimers, trimers, and neon atoms when reflected from a grating. Conditions for the observation of emerging beam resonances have been discussed and measured. In this paper, we provide a theoretical simulation of the quantum reflection from a grating for those systems. We confirm the universal dependence on the incident de Broglie wavelength with the threshold angles where the emerging beam resonances are observed. However, the angular dependence of the reflection efficiencies, that is, the ratio of scattered intensity into specific diffraction channels relative to the total intensity is found to be dependent on the details of the particle surface interaction.

Figure 1

Vertical interaction potentials $V\left(z\right)$ between the incident particles and the grating. The black dashed curve is the WS absorbing potential used. This potential is added as an imaginary part for all diffraction channels with slightly modified parameters (see text).

Figure 2

Theoretical (multichannel calculations) quantum reflection probabilities for He ($T_0=20$ K), ${\mathrm{He}}_2$ ($T_0=15$ K), ${\mathrm{He}}_3$ ($T_0=8.7$ K), and Ne ($T_0=40$ K) vs the perpendicular incident wave vector $k_{\mathrm{perp}}$ (in ${\mathrm{nm}}^{-1}$). The results for the He dimer are not compared with experiment since they have been measured only for scattering from a blazed grating rather than the regular grating used here. The experimental points have been provided by the authors of Refs. [4, 7].

Figure 3

Quantum reflection probabilities vs $k_{\mathrm{perp}}$ (in ${\mathrm{nm}}^{-1}$) for He, Ne, ${\mathrm{He}}_2$, and ${\mathrm{He}}_3$ at the same de Broglie wavelength, 0.179 nm. The source temperature $T_0$ used for each system is given in parentheses. Note that the reflection probabilities only display a universal linear behavior at very small $k_{\mathrm{perp}}$. At higher values of $k_{\mathrm{perp}}$, the behavior is quite similar for the heavier masses (${\mathrm{He}}_3$, Ne) and lighter particles (He, ${\mathrm{He}}_2$).

Figure 4

Diffraction efficiencies vs the incident angle (in mrad) for He, Ne, ${\mathrm{He}}_2$, and ${\mathrm{He}}_3$ at the same de Broglie wavelength of $\lambda =0.179$ nm. The Rayleigh angles are plotted as dashed vertical lines to indicate the opening or closing of a given diffraction channel.

Figure 5

Diffraction efficiencies of the open $n=-1$ diffraction channel vs the incident angle (in mrad) for He, Ne, ${\mathrm{He}}_2$, and ${\mathrm{He}}_3$ at the same de Broglie wavelength of $\lambda =0.179$ nm. The Rayleigh angles are plotted as dashed vertical lines to indicate the opening or closing of a given diffraction channel.