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Europhysics Letters (EPL)

Dispersive atom interferometry phase shifts due to atom-surface interactions

S. Lepoutre, Haikel Jelassi, Vincent Lonij, G. Trénec, M Büchner, Alexander D. Cronin, J. Vigué

Published Oct 1, 2009• 28 citations
Publisher

Abstract

We used the Toulouse atom interferometer to study how Van der Waals (VdW) interactions between atoms and surfaces cause velocity-dependent phase shifts for atomic de Broglie waves. By introducing a thin nano-grating in one branch of this interferometer, we observed a phase shift that depends on velocity to the power −0.49. This dispersion serves to measure both the strength and the position dependence of the atom-surface potential in the range from 5 to 10 nm from the surface, and it can also set new limits on non-Newtonian gravity in the 2 nm range.

DOI
10.1209/0295-5075/88/20002

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We used the Toulouse atom interferometer to study how Van der Waals (VdW) interactions between atoms and surfaces cause velocity-dependent phase shifts for atomic de Broglie waves. By introducing a thin nano-grating in one branch of this interferometer, we observed a phase shift that depends on velocity to the power −0.49. This dispersion serves to measure both the strength and the position dependence of the atom-surface potential in the range from 5 to 10 nm from the surface, and it can also set new limits on non-Newtonian gravity in the 2 nm range.
The development of nanotechnology and atom optics relies on understanding how atoms behave and interact with their environment. Isolated atoms can exhibit wavelike (coherent) behavior with a corresponding de Broglie wavelength and phase which can be affected by nearby surfaces. Here an atom interferometer is used to measure the phase shift of Na atom waves induced by the walls of a 50 nm wide cavity. To our knowledge this is the first direct measurement of the de Broglie wave phase shift caused by atom-surface interactions. The magnitude of the phase shift is in agreement with that predicted by Lifshitz theory for a nonretarded van der Waals interaction. This experiment also demonstrates that atom waves can retain their coherence even when atom-surface distances are as small as 10 nm.
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.
This dissertation describes new measurements of the van der Waals (vdW) potential energy for atoms near a surface. The measurements presented here were accomplished by studying diffraction a beam of atoms transmitted through a nanograting. I will describe how we improved precision by a factor of 10 over previous diffraction measurements by studying how different types of atoms interact with the same surface. As a result of this new precision, we were able to show for the first time the contribution of atomic core electrons to the atom-surface potential, and experimentally test different atomic structure calculation methods.In addition, this dissertation will describe how changing the width of the grating bars to achieve a particular "magic" grating bar width or rotating a grating to a particular "magic" angle allows us to determine both the atom-surface potential strength and the geometry of the grating. This represents an improvement over several recent studies where uncertainties in the nanograting geometry limited precision in the measurements of the vdW potential.For a complementary measurement, also discussed in this dissertation, we collaborated with the Vigue group in Toulouse, France. In this collaboration we used an atom interferometer to measure the phase shift due to transmission through a nanograting. By combining diffraction data from Tucson with interferometry data from Toulouse we improved the precision of interferometry measurements of the atom-surface potential of a single atomic species by almost a factor of 10 over previous interferometric measurements of the vdW potential. These interferometry measurements also serve to measure the shape of the vdW potential and set a limit on non-Newtonian gravitational interactions at 1-2 nm length scales.Finally, this dissertation will discuss how nanogratings with optimized geometry can improve atom interferometers, for example, with blazed gratings. We discuss next generation atom-surface potential measurements and examine new ways of analyzing diffraction data.
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.
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.