A lattice-induced opacity is identified in the scattering process of a normally-incident matter wave from a two dimensional lattice of atoms. This system can be treated as an analogue of a confinement induced resonance. Specifically by modifying the s-wave scattering length between atoms in the incident matter wave and the lattice-confined atoms, the transmission of the matter wave can be tuned controllably from zero to one. Based on this, we propose a possible scheme for a matter wave transistor. When the transmission of the matter wave is tuned to zero, a matter wave cavity can be formed by placing two such lattice planes of atoms parallel to one another. At higher kinetic energies, the two dimensional lattice of atoms can also serve as a matter wave beam splitter and a wave plate.
A lattice-induced opacity is identified in the scattering process of a normally incident matter wave colliding with a two dimensional lattice of atoms. This system can be treated as an analog of a confinement-induced resonance. Specifically, by modifying the
s-wave scattering length between atoms in the incident matter wave and the lattice-confined atoms, the transmission of the matter wave can be tuned controllably throughout the range from zero to one. The theoretical treatment shows how the mathematical description of confinement-induced resonances can be viewed as an extension of Bragg scattering theory, with alternate opportunities for transmission control.