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Using Atomic Diffraction to Measure the van der Waals Coefficient for Na and Silicon Nitride J. D. Perreault1,2, A. D. Cronin2, H. Uys2 1Optical Sciences Center, University of Arizona, Tucson AZ, 85721 USA 2Physics Department, University of Arizona, Tucson AZ, 85721 USA Definitions van der Waals Diffraction Theory Abstract •The far-field diffraction pattern for a perfect grating is given by 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 C3 by fitting a modified Fraunhofer optical theory to the experimental data. i ξ ξ A n e rect w f n T ξ ξ 2 λ z Ix A n L x n dB n d lineshape d •The diffraction envelope amplitude An is just the scaled Fourier transform of the single slit transmission function T(ξ) I(x): atom intensity λdB: de Broglie wavelength An: diffractin envelope amplitude v: velocity |An|2: number of atoms in order n σv: velecity distribution T(ξ): single slit transmission function d: grating period V(ξ): vdW potential w: grating slit width φ(ξ): phase due to vdW interaction t: grating thickness ξ: grating coordinate •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 3.0 fξ: Fourier conjugate variable to ξ x: detector coordinate 3 3 tV ξ tC 3 w w ξ ξ v v 2 2 () [rad] z: grating-detector separation 2.0 L(x): lineshape function 1.0 n: diffraction order 0.0 -20 0 [nm] 10 20 Measured Grating Parameters Intuitive Picture Experiment Geometry •A grating rotation experiment along with an SEM image are used to independently determine w and t •As a consequence of the fact that matter propagates like a wave there exists a suggestive analogy •A supersonic Na atom beam is collimated and used to illuminate a diffraction grating index : light :: potential : atoms •A hot wire detector is scanned to measure the atom intensity as a function of x ξ -10 •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 x optical phase front z z grating rotation experiment SEM image Na w = 68.44 ± .0091 nm 100 nm period 60 μm diameter 10 μm diffraction hot wire collimating grating detector slits 2 10 4 2 -2 -1 0 1 6 4 v = 2109 m/s 2 (stat. only) v = 2109 m/s v = 1015 m/s 2 0.1 6 4 2 0 4 1 2 3 4 Diffraction Order C3 = 3.13 ± .04 meVnm3 5 1 v = 2109 m/s VDW Theory Optical Theory 0.1 0.01 0.001 0 1 2 3 Diffraction Order 4 5 •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 (stat. only) 1 v = 1015 m/s VDW Theory Optical Theory 0.1 0.01 0.001 0 1 2 3 4 Diffraction Order 5 1.0 0.8 0.6 0.4 th Intensity [kCounts/s] Position [mm] 2 C3 = 5.95 ± .45 meVnm3 1 10 0 4 2 •Free parameters: |An 1 4 2 -1 0 Position [mm] 1 |2, v, σv •The background and lineshape function L(x) are determined from an independent experiment Conclusions and Future Work •A preliminary determination of the van der Waals coefficient C3 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 C3 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 •The relative number of atoms in each diffraction order was fit with only one free parameter: C3 •Notice how optical theory (i.e. C3→0) fails to describe the diffraction envelope correctly for atoms 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. 83 1755 (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. 61 033608 (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 14 4167-4170 (1996) 0.6 0.4 0.2 th 4 Best Fit C3 – Preliminary Results 0 order intensity [arb. units] 100 Relative Number of Atoms Intensity [kCounts/s] v = 1015 m/s Using Zeroeth Order Diffraction to Measure C3 0 order phase [rad] 2 |An| Determining 2 negative lens Relative Number of Atoms .5 μm skimmer Relative Number of Atoms supersonic source 2 4 63 C3 [meVnm ] 8 •The ratio of the zeroeth order to the raw beam intensity could be used to measure C3 10 0.0 0 2 4 63 C3 [meVnm ] 8 •The phase shift could be measured in an interferometer to determine C3 10