Using Atomic Diffraction to Measure the van der Waals Coefficient for Na and Silicon Nitride J. D. Perreault 1,2, A. D. Cronin 2, H. Uys 2 1 Optical Sciences Center, University of Arizona, Tucson AZ, USA 2 Physics Department, University of Arizona, Tucson AZ, USA Abstract In atom optics a mechanical structure is commonly regarded as an amplitude mask for atom waves. However, atomic diffraction patterns indicate that mechanical structures also operate as phase masks. During passage through the grating slots atoms acquire a phase shift due to the van der Waals (vdW) interaction with the grating walls. As a result the relative intensities of the matter-wave diffraction peaks deviate from optical theory. We present a preliminary measurement of the vdW coefficient C 3 by fitting a modified Fraunhofer optical theory to the experimental data. Experiment Geometry Na ξ z x z supersonic source.5 μm skimmer 10 μm collimating slits 100 nm period diffraction grating 60 μm diameter hot wire detector A supersonic Na atom beam is collimated and used to illuminate a diffraction grating A hot wire detector is scanned to measure the atom intensity as a function of x Definitions λ dB : de Broglie wavelength v: velocity σ v : velecity distribution d: grating period w: grating slit width t: grating thickness I(x): atom intensity A n : diffractin envelope amplitude |A n | 2 : number of atoms in order n T(ξ): single slit transmission function V(ξ): vdW potential φ(ξ): phase due to vdW interaction ξ: grating coordinate f ξ : Fourier conjugate variable to ξ x: detector coordinate z: grating-detector separation L(x): lineshape function n: diffraction order Intuitive Picture As a consequence of the fact that matter propagates like a wave there exists a suggestive analogy The van der Waals interaction acts as an effective negative lens that fills each slit of the grating, adding curvature to the de Broglie wave fronts and modifying the far-field diffraction pattern optical phase front negative lens Measured Grating Parameters w = ±.0091 nm SEM image A grating rotation experiment along with an SEM image are used to independently determine w and t grating rotation experiment Determining |A n | 2 Free parameters: |A n | 2, v, σ v The background and lineshape function L(x) are determined from an independent experiment Using Zeroeth Order Diffraction to Measure C 3 Using the previously mentioned theory one can see that the zeroth order intensity and phase depend on the strength of the van der Waals interaction The ratio of the zeroeth order to the raw beam intensity could be used to measure C3 The phase shift could be measured in an interferometer to determine C3 Conclusions and Future Work A preliminary determination of the van der Waals coefficient C 3 is presented here for two different atom beam velocities based on the method of Grisenti et. al Using the phase and intensity dependence of the zeroeth diffraction order on C 3 we are pursuing novel methods for the measurement of the van der Waals coefficient The van der Waals phase could be “tuned” by rotating the grating about its k-vector, effectively changing the value of t by some known amount References “Determination of Atom-Surface van der Waals Potentials from Transmission-Grating Diffraction Intensities” R. E. Grisenti, W. Schollkopf, and J. P. Toennies. Phys. Rev. Lett (1999) “He-atom diffraction from nanostructure transmission gratings: The role of imperfections” R. E. Grisenti, W. Schollkopf, J. P. Toennies, J. R. Manson, T. A. Savas and H. I. Smith. Phys. Rev A (2000) “Large-area achromatic interferometric lithography for 100nm period gratings and grids” T. A. Savas, M. L. Schattenburg, J. M. Carter and H. I. Smith. Journal of Vacuum Science and Technology B (1996) van der Waals Diffraction Theory The far-field diffraction pattern for a perfect grating is given by The diffraction envelope amplitude A n is just the scaled Fourier transform of the single slit transmission function T( ξ ) Notice that T( ξ ) is complex when the van der Waals interaction is incorporated and the phase following the WKB approximation to leading order in V( ξ ) is Best Fit C 3 – Preliminary Results The relative number of atoms in each diffraction order was fit with only one free parameter: C 3 Notice how optical theory (i.e. C 3 →0) fails to describe the diffraction envelope correctly for atoms C 3 = 3.13 ±.04 meVnm 3 C 3 = 5.95 ±.45 meVnm 3 (stat. only)