Reciprocity and time-reversal symmetry in quantum reflection of atomic matter-waves from a diffraction grating

Abstract

The reciprocity theorem in wave optics states that the amplitude and phase of signal does not change if source and detector are interchanged in a given setup. We validate the reciprocity theorem in quantum reflection of helium atoms from a blazed diffraction grating. At grazing incidence conditions the helium atoms are quantum reflected tens of nanometer above the grating surface. We observe identical diffraction efficiencies of the nth order diffraction peaks at standard grating mount and of the -nth orders at reversed geometry when plotted as a function of deflection angle, thereby confirming reciprocity. For purely elastic scattering as in quantum reflection, observation of reciprocity implies time-reversal symmetry. Considering time-reversal invariance we discuss details of the quantum reflection process such as the distances above the surface where quantum reflection occurs for diffraction beams of different order n.