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APS

Using Atomic Diffraction to Measure the van der Waals Coefficient for Na and Silicon Nitride

John D. Perreault, Alex D. Cronin

Published May 1, 2003• 0 citations
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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. In this study a well collimated beam of Na atoms is used to illuminate a silicon nitride grating with a period of 100 nm. During passage through the grating slots atoms acquire a phase shift due to the van der Waals (vdW) interaction with the grating walls. This phase shift depends both on atom position and velocity. As a result the relative intensities of the matter-wave diffraction peaks deviate from optical theory and depend on the de Broglie wavelength of the atoms. The vdW coefficient C3 is determined by fitting a modified Fraunhoffer optical theory to the experimental data.

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Using atomic diffraction of Na from material gratings to measure atom-surface interactions

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In atom optics a material structure is commonly regarded as an amplitude mask for atom waves. However, atomic diffraction patterns formed using material gratings indicate that material structures also operate as phase masks. In this study a well collimated beam of sodium atoms is used to illuminate a silicon nitride grating with a period of 100 nm. 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 those expected for a purely absorbing grating. Thus a complex transmission function is required to explain the observed diffraction envelopes. An optics perspective to the theory of atomic diffraction from material gratings is put forth in the hopes of providing a more intuitive picture concerning the influence of the vdW potential. The van der Waals coefficient ${C}_{3}=2.7\ifmmode\pm\else\textpm\fi{}0.8\phantom{\rule{0.3em}{0ex}}\mathrm{meV}\phantom{\rule{0.3em}{0ex}}{\mathrm{nm}}^{3}$ is determined by fitting a modified Fresnel optical theory to the experimental data. This value of ${C}_{3}$ is consistent with a van der Waals interaction between atomic sodium and a silicon nitride surface.

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In atom optics a material structure is commonly regarded as an amplitude mask for atom waves. However, atomic diffraction patterns formed using material gratings indicate that material structures also operate as phase masks. In this study a well collimated beam of sodium atoms is used to illuminate a silicon nitride grating with a period of 100 nm. During passage through the grating slots atoms acquire a phase shift due to the van der Waals interaction with the grating walls. As a result the relative intensities of the matter-wave diffraction peaks deviate from those expected for a purely absorbing grating. Thus a complex transmission function is required to explain the observed diffraction envelopes. An optics perspective to the theory of atomic diffraction from material gratings is put forth in the hopes of providing a more intuitive picture concerning the influence of the vdW potential. The van der Waals coefficient $C_{3} = 2.7\\pm 0.8{meV nm}^{3}$ is determined by fitting a modified Fresnel optical theory to the experimental data. This value of $C_{3}$ is consistent with a van der Waals interaction between atomic sodium and a silicon nitride surface.

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Atom-surface interactions are becoming an integral part of the field of atom optics. Here the role of van der Waals atom-surface interactions in atom wave diffraction and interferometry are investigated. In particular, it is shown that van der Waals interactions influence the intensity and phase of atomic diffraction patterns obtained from material gratings. As a result the atomic diffraction patterns are utilized to make an accurate determination of the interaction strength and verify the spatial variation of the atom-surface potential. A theory for describing the modified atom wave diffraction patterns is developed through an analogy with optical waves. An atom interferometer is used to directly measure the de Broglie wave phase shift induced by atom-surface interactions. More specifically, the phases of the zeroth, first, and second diffraction orders are measured. A proposal for using electromagnetic fields to modify the van der Waals interaction is put forth. Several of the important experimental components for observing such an effect are also demonstrated.

•Jan 1, 2005•0 citations
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. In this study a well collimated beam of Na atoms is used to illuminate a silicon nitride grating with a period of 100 nm. During passage through the grating slots atoms acquire a phase shift due to the van der Waals (vdW) interaction with the grating walls. This phase shift depends both on atom position and velocity. As a result the relative intensities of the matter-wave diffraction peaks deviate from optical theory and depend on the de Broglie wavelength of the atoms. The vdW coefficient C3 is determined by fitting a modified Fraunhoffer optical theory to the experimental data.
In atom optics a material structure is commonly regarded as an amplitude mask for atom waves. However, atomic diffraction patterns formed using material gratings indicate that material structures also operate as phase masks. In this study a well collimated beam of sodium atoms is used to illuminate a silicon nitride grating with a period of 100 nm. 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 those expected for a purely absorbing grating. Thus a complex transmission function is required to explain the observed diffraction envelopes. An optics perspective to the theory of atomic diffraction from material gratings is put forth in the hopes of providing a more intuitive picture concerning the influence of the vdW potential. The van der Waals coefficient ${C}_{3}=2.7\ifmmode\pm\else\textpm\fi{}0.8\phantom{\rule{0.3em}{0ex}}\mathrm{meV}\phantom{\rule{0.3em}{0ex}}{\mathrm{nm}}^{3}$ is determined by fitting a modified Fresnel optical theory to the experimental data. This value of C3{C}_{3}C3​ is consistent with a van der Waals interaction between atomic sodium and a silicon nitride surface.
In atom optics a material structure is commonly regarded as an amplitude mask for atom waves. However, atomic diffraction patterns formed using material gratings indicate that material structures also operate as phase masks. In this study a well collimated beam of sodium atoms is used to illuminate a silicon nitride grating with a period of 100 nm. During passage through the grating slots atoms acquire a phase shift due to the van der Waals interaction with the grating walls. As a result the relative intensities of the matter-wave diffraction peaks deviate from those expected for a purely absorbing grating. Thus a complex transmission function is required to explain the observed diffraction envelopes. An optics perspective to the theory of atomic diffraction from material gratings is put forth in the hopes of providing a more intuitive picture concerning the influence of the vdW potential. The van der Waals coefficient C3=2.7±0.8meVnm3C_{3} = 2.7\pm 0.8{meV nm}^{3}C3​=2.7±0.8meVnm3 is determined by fitting a modified Fresnel optical theory to the experimental data. This value of C3C_{3}C3​ is consistent with a van der Waals interaction between atomic sodium and a silicon nitride surface.
In atom optics a material structure is commonly regarded as an amplitude mask for atom waves. However, atomic diffraction patterns formed using material gratings indicate that material structures also operate as phase masks. In this study a well collimated beam of sodium atoms is used to illuminate a silicon nitride grating with a period of 100 nm. During passage through the grating slots atoms acquire a phase shift due to the van der Waals interaction with the grating walls. As a result the relative intensities of the matter-wave diffraction peaks deviate from those expected for a purely absorbing grating. Thus a complex transmission function is required to explain the observed diffraction envelopes. An optics perspective to the theory of atomic diffraction from material gratings is put forth in the hopes of providing a more intuitive picture concerning the influence of the vdW potential. The van der Waals coefficient C3=2.7pm0.8meVnm3C_{3} = 2.7\\pm 0.8{meV nm}^{3}C3​=2.7pm0.8meVnm3 is determined by fitting a modified Fresnel optical theory to the experimental data. This value of C3C_{3}C3​ is consistent with a van der Waals interaction between atomic sodium and a silicon nitride surface.
Atom-surface interactions can significantly modify the intensity and phase of atom de Broglie waves diffracted by a silicon nitride grating. This affects the operation of a material grating as a coherent beam splitter. The phase shifts induced by diffraction are measured by comparing the relative phases of several interfering paths in a Mach-Zehnder Na atom interferometer formed by three material gratings. The values of the diffraction phases are consistent with a simple model which includes a van der Waals atom-surface interaction between the Na atoms and the silicon nitride grating bars.
Four atom optics experiments that each serve to measure atom-surface interactions near nanofabricated gratings are presented here. In these experiments atoms in a beam travel within 25 nm of a material grating bar, and the analysis incorporates phase shifts for the atomic de Broglie waves due to interactions betwen Na atoms and silicon nitride surfaces. One atom diffraction experiment determines the van der Waals coeficient C 3 = 2.7 ± 0.8 meV nm 3 , and one atom interferometer experiment determines C 3 = 4 ± 1 meV nm 3 . The results of all four experiments are consistent with the Lifshitz prediction that is explicitly calculated here for Nasilicon nitride to be C 3 = 3.25 meV nm 3 . The four atom optics experiments and review of van der Waals theory are complemented by similar experiments using electron beams and analysis of image-charge effects.
Atom-surface interactions are becoming an integral part of the field of atom optics. Here the role of van der Waals atom-surface interactions in atom wave diffraction and interferometry are investigated. In particular, it is shown that van der Waals interactions influence the intensity and phase of atomic diffraction patterns obtained from material gratings. As a result the atomic diffraction patterns are utilized to make an accurate determination of the interaction strength and verify the spatial variation of the atom-surface potential. A theory for describing the modified atom wave diffraction patterns is developed through an analogy with optical waves. An atom interferometer is used to directly measure the de Broglie wave phase shift induced by atom-surface interactions. More specifically, the phases of the zeroth, first, and second diffraction orders are measured. A proposal for using electromagnetic fields to modify the van der Waals interaction is put forth. Several of the important experimental components for observing such an effect are also demonstrated.