de Broglie wave phase shifts induced by surfaces closer than 25 nm

Abstract

Abstract. 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 coefficient C3 = 2.7±0.8 meVnm 3 , and one atom interferometer experiment determines C3 = 4±1 meVnm 3 . The results of all four experiments are consistent with the Lifshitz prediction that is explicitly calculated here for Nasilicon nitride to be C3 = 3.25 meVnm 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. IntroductionTen nm away from a surface the potential energy for an atom is approximately 3 µeV, and for an electron it is about 10,000 times larger. More precisely, the van der Waals potential for sodium atoms and the image-charge potential for electrons both depend on the permittivity of the surface material; both potentials are also affected by surface charges, surface coatings, and surface geometry. Precise knowledge of the potential close to real surfaces is now needed for understanding atom optics experiments and nanotechnology devices, yet measurements of atomsurface interaction strengths have only been made for a few systems so far. Here we present four atom optics experiments that serve to measure the potential energy for atoms due to a surface located within 25 nm. Comparison to theoretical values of the non-retarded atom-surface van der Waals interaction will be made in the discussion.Our experiments are based on coherent transmission of sodium atom de Broglie waves through an array of 50 nm wide channels in a silicon nitride nanostructure grating. Transmitted atoms pass within 25 nm to a grating bar surface, and remain this close for only 10 −10 sec. Even in this short time, interactions with the channel walls modify the phase of the atom waves. Phase front curvature on the nanometer scale has the observed effect of modifying the phase Φ n and amplitude |A n | in each far-field diffraction order. We measured atom diffraction intensities and atom interferometer fringe phase shifts in order to determine the potential for sodium atoms induced by surfaces of silicon nitride.For comparison we used the same nanostructure gratings to diffract electron beams. Despite the 10,000 times larger potential energy (at 10 nm) due to image-charge effects, electron diffraction shows similar features to atom diffraction as a result of stronger interactions with the surface over shorter time scales.

Comment on ``Ramsey spectroscopy, matter-wave interferometry, and the microwave-lensing frequency shift''

“…Any differential phase shift of the wave functions occurring during the clipping could easily and grossly change the size of the frequency shift or even its sign. We note that radian level phase shifts are observed in similar systems as a result of wall interactions [9]. We also note that this defect (no discussion of the nature of the clipping) is shared by our investigations into lensing [5], however, we do not use our theory to calculate numerical corrections to be applied to PFS measurements.…”

Impact of Casimir-Polder interaction on Poisson-spot diffraction at a dielectric sphere

“…The disturbance A(P ) at a point P in the detection plane can be expressed by Eq. 19, which makes use of the Fresnel approximation and already incorporates the phase shift expected from the Casimir-Polder interaction [27].…”

“…The dispersion forces can exhibit intricate spatial dependence in complex geometries (see, for example, [16][17][18][19][20][21]), but in many far-field diffraction experiments the effect is reduced to an effective slit-narrowing fitted to the data after the experiment [22]. Dispersion forces near gratings are extremely difficult to model accurately [12,[16][17][18][19][20][21][23][24][25][26][27][28][29][30], especially when sharp edges are involved [31]. This, coupled to the fact that gratings necessarily have a large number of sharp edges spaced closely together, means that progress in detailed accounts of this effect has stalled.…”

Reply to ``Comment on `Ramsey spectroscopy, matter-wave interferometry, and the microwave-lensing frequency shift' ''

“…While this shift is distinct from the microwave lensing frequency shifts that are treated in [2,4,[5][6][7][8][9][10][11], it might nonetheless be useful to offer some quantitative analysis. Jefferts' et al statement that "radian level phase shifts are observed in similar systems as a result of wall interactions" at distances of 25 nm [12] is injudicious. The wall interactions are governed by the static polarizability α(0) =401 a.u.…”