Analysis of a Material Phase Shifting Element in an Atom Interferometer

Abstract. The interaction of Na atoms with a surface was probed by inserting a nanofabricated material grating into one arm of an atom interferometer (IFM). This technique permits a direct measurement of the change in phase and coherence of matter waves as they pass within 25 nm of the grating bar surface. The practical concerns and challenges of making such a measurement are discussed here. Interference of spurious diffraction orders, IFM path overlap, and the partial obscuration of IFM beams are all important aspects of this experiment. The systematic effects that contribute to the measured phase shift and contrast are discussed. Atomic diffraction from material grating structures [1] has been used as a tool to measure atom-surface interactions for noble gases [2] and alkali atoms [3, 4]. In these experiments the van der Waals (vdW) interaction [5] changed the relative intensities of the diffraction orders. More recently the atom wave phase shift Φ0 induced by these grating structures1 was measured directly using a sodium atom beam interferometer (IFM) [6]. The experimental setup is shown in Fig. 1. An interaction grating (IG), comprised of an array of 50 nm wide channels, is inserted into one arm of the IFM. The vdW interaction between the sodium atoms and IG causes a phase shift of about Φ0 ∼ 0.3 radians. A number of systematic effects need to be understood before reporting this phase shift induced by the vdW interaction. This paper describes how the measured phase shift and contrast in [6] are influenced by these systematic effects and suggests some physical mechanisms for them. In general there is a non-trivial relationship between the measured phase shift Φmeas and induced phase shift Φ0, when the IFM paths are partially obscured by a phase shifting element. Therefore, care should be taken when interpreting the phase shift data. This notion of partial obscuration is shown in Fig. 2, which illustrates how the interference pattern can have different phases in different regions of space. The detected interference signal can be written as the average flux transmitted through each grating window of G3 in Fig. 1 S(θ) =