Quantum reflection and interference of matter waves from periodically doped surfaces

We show that periodically doped, flat surfaces can act as reflective diffraction gratings for atomic and molecular matter waves. The diffraction element is realized by exploiting the fact that charged dopants locally suppress quantum reflection from the Casimir-Polder potential. We present a general quantum scattering theory for reflection off periodically charged surfaces and discuss the requirements for the observation of multiple diffraction peaks.

Figure 1

Schematic of the reflection problem. The incident wave vector $\mathbf{k}$ impinges with angle $\theta$ at the surface, and $\phi$ is the azimuthal angle with respect to the in-plane orientation.

Figure 2

Probabilities of reflection into different diffraction orders for a doping profile $\Delta \left(z\right)$ given by (a) Eq. (28) and (b) Eq. (32). In (a) the numerically obtained values (red diamonds) compare well with the analytical result (black squares) given by Eq. (30).