PRL95,133201(2005) PHYSICAL REVIEW LETTERS week ending 23 SEPTEMBER 2005 interferometer paths should depend on the atom beam (2)is consistent with the data.This experiment has also velocity in the way described by Egs.(1)and(2).To test demonstrated the nonobvious result that atom waves can this prediction the experiment illustrated in Fig.3 was retain their coherence when passing within 25 nm of a repeated for several different atom beam velocities and surface.In the future,one could use this experiment to the data are shown in Fig.4.Systematic phase offsets of make a more precise measurement of C3 at the 10%level if ~30%caused by the overlap of the beams la)and |B)and the interference of unwanted diffraction orders are elimi- the detected interference of additional diffraction orders nated and the window size w of Ga is determined with a generated by Gi,G2,G3 in the atom interferometer (not precision of 3%.This level of precision in measuring w is shown in Fig.2)have been corrected for in Fig.4. possible with existing scanning electron microscopes. Uncertainty in the extent of beam overlap and amount of This work was supported by Research Corporation and signal from additional diffraction orders led to the uncer- the National Science Foundation Grant No.0354947 tainty of the phase measurements in Fig.4.A more de- tailed discussion of systematic effects can be found in [16]. The measured phase shift compares well to a prediction of the phase shift Po for the zeroth order of grating G4 [1]P.W.Milonni,The Quantum Vacuum (Academic Press, which includes the vdW interaction.The value of C3= New York.1994). 3 meV nm'used to generate the theoretical prediction in [2]J.E.Lennard-Jones,Trans.Faraday Soc.28.333(1932). Fig.4 is consistent with Lifshitz theory and previous [3]R.S.Ruoff,J.Tersoff,D.C.Lorents,S.Subramoney,and measurements based on diffraction experiments [8].It is C.Chan,Nature (London)364,514 (1993). important to note that if there was no interaction between [4]F.J.Giessibl,Rev.Mod.Phys.75,949(2003) the atom and the grating there would be zero observed [5]R.Folman and J.Schmiedmayer,Nature (London)413, phase shift. 466(2001). [6]A.Shih and V.A.Parsegian,Phys.Rev.A 12,835(1975); The confirmation of atom-surface induced phase shifts presented here can be extrapolated to the case of atoms A.Anderson,S.Haroche,E.A.Hinds,W.Jhe,and D.Meschede,Phys.Rev.A 37,3594 (1988):C.I. guided on a chip.Atoms traveling at I m/s over a distance Sukenik,M.G.Boshier,D.Cho,V.Sandoghdar,and of 1 cm will have an interaction time of 0.01 s.According E.A.Hinds,Phys.Rev.Lett.70,560(1993). to Eq.(1),if these atoms are 0.1 um from the surface they [7]R.E.Grisenti,W.Schollkopf,J.P.Toennies,G.C. will acquire a phase shift of 5 x 104 rad due to the vdw Hegerfeldt,and T.Kohler,Phys.Rev.Lett.83,1755 interaction.Similarly,if the atoms are 0.5 um from the (1999);A.D.Cronin and J.D.Perreault,Phys.Rev.A surface they will have a phase shift of 4 X 102 rad.There- 70,043607(2004);B.Brezger et al.,Phys.Rev.Lett.88 fore,a cloud of atoms 0.1 um from a surface will have a 100404(2002). rapidly varying phase profile which could severely reduce [8]J.D.Perreault,A.D.Cronin,and T.A.Savas,Phys.Rev.A 71.053612(2005) the contrast of an interference signal.At some atom- surface distance the vdW interaction will significantly alter [9]A.Anderson et al.,Phys.Rev.A 34,3513 (1986);J.J. Berkhout et al.,Phys.Rev.Lett.63,1689 (1989); atom-chip trapping potentials,resulting in the loss of F.Shimizu,Phys.Rev.Lett.86,987(2001) trapped atoms.Atom-chip magnetic traps are harmonic [10] D.W.Keith,M.L.Schattenburg,H.I.Smith,and D.E. near their center and can have a trap frequency of @ Pritchard,Phys.Rev.Lett.61,1580(1988);R.Bruhl et al., 2X 200 kHz [12].Given the vdW interaction we have Europhys.Lett.59,357 (2002). observed,such a magnetic trap would have no bound states C.Henkel and M.Wilkens,Europhys.Lett.47,414 for Na atoms if its center was closer than 220 nm from a (1999). surface.Therefore,the vdW interaction places a limit on [12]R.Folman,P.Kruger,J.Schmiedmayer,J.Denschlag,and the spatial scale of atom interferometers built on a chip C.Henkel,Adv.At.Mol.Opt.Phys.48,263(2002). because bringing the atoms too close to a surface can result [13]D.W.Keith,C.R.Ekstrom,Q.A.Turchette,and D.E. in poor contrast and atom intensity. Pritchard,Phys.Rev.Lett.66,2693 (1991);Atom Interferometry,edited by P.R.Berman (Academic Press, In conclusion.the affect of atom-surface interactions on New York,1997). the phase of a Na atom wave has been observed directly for [14]T.A.Savas,M.L.Schattenburg,J.M.Carter,and H.I. the first time.When the atom wave passes within 25 nm of Smith,J.Vac.Sci.Technol.B 14,4167(1996). a surface for 75 ps it accumulates a phase shift of Po [15]P.Meystre,Atom Optics (American Institute of Physics, 0.3 rad consistent with an attractive vdW interaction.The New York.2001). slight velocity dependence predicted for Po by Egs.(1)and [16]J.D.Perreault and A.D.Cronin,physics/0506090. 133201-4interferometer paths should depend on the atom beam velocity in the way described by Eqs. (1) and (2). To test this prediction the experiment illustrated in Fig. 3 was repeated for several different atom beam velocities and the data are shown in Fig. 4. Systematic phase offsets of 30% caused by the overlap of the beams ji and ji and the detected interference of additional diffraction orders generated by G1; G2; G3 in the atom interferometer (not shown in Fig. 2) have been corrected for in Fig. 4. Uncertainty in the extent of beam overlap and amount of signal from additional diffraction orders led to the uncer￾tainty of the phase measurements in Fig. 4. A more de￾tailed discussion of systematic effects can be found in [16]. The measured phase shift compares well to a prediction of the phase shift
0 for the zeroth order of grating G4 which includes the vdW interaction. The value of C3 3 meV nm3 used to generate the theoretical prediction in Fig. 4 is consistent with Lifshitz theory and previous measurements based on diffraction experiments [8]. It is important to note that if there was no interaction between the atom and the grating there would be zero observed phase shift. The confirmation of atom-surface induced phase shifts presented here can be extrapolated to the case of atoms guided on a chip. Atoms traveling at 1 m=s over a distance of 1 cm will have an interaction time of 0.01 s. According to Eq. (1), if these atoms are 0:1
m from the surface they will acquire a phase shift of 5 104 rad due to the vdW interaction. Similarly, if the atoms are 0:5
m from the surface they will have a phase shift of 4 102 rad. There￾fore, a cloud of atoms 0:1
m from a surface will have a rapidly varying phase profile which could severely reduce the contrast of an interference signal. At some atom￾surface distance the vdW interaction will significantly alter atom-chip trapping potentials, resulting in the loss of trapped atoms. Atom-chip magnetic traps are harmonic near their center and can have a trap frequency of ! 2 200 kHz [12]. Given the vdW interaction we have observed, such a magnetic trap would have no bound states for Na atoms if its center was closer than 220 nm from a surface. Therefore, the vdW interaction places a limit on the spatial scale of atom interferometers built on a chip because bringing the atoms too close to a surface can result in poor contrast and atom intensity. In conclusion, the affect of atom-surface interactions on the phase of a Na atom wave has been observed directly for the first time. When the atom wave passes within 25 nm of a surface for 75 ps it accumulates a phase shift of
0  0:3 rad consistent with an attractive vdW interaction. The slight velocity dependence predicted for
0 by Eqs. (1) and (2) is consistent with the data. This experiment has also demonstrated the nonobvious result that atom waves can retain their coherence when passing within 25 nm of a surface. In the future, one could use this experiment to make a more precise measurement of C3 at the 10% level if the interference of unwanted diffraction orders are elimi￾nated and the window size w of G4 is determined with a precision of 3%. This level of precision in measuring w is possible with existing scanning electron microscopes. This work was supported by Research Corporation and the National Science Foundation Grant No. 0354947. [1] P. W. Milonni, The Quantum Vacuum (Academic Press, New York, 1994). [2] J. E. Lennard-Jones, Trans. Faraday Soc. 28, 333 (1932). [3] R. S. Ruoff, J. Tersoff, D. C. Lorents, S. Subramoney, and C. Chan, Nature (London) 364, 514 (1993). [4] F. J. Giessibl, Rev. Mod. Phys. 75, 949 (2003). [5] R. Folman and J. Schmiedmayer, Nature (London) 413, 466 (2001). [6] A. Shih and V. A. Parsegian, Phys. Rev. A 12, 835 (1975); A. Anderson, S. Haroche, E. A. Hinds, W. Jhe, and D. Meschede, Phys. Rev. A 37, 3594 (1988); C. I. Sukenik, M. G. Boshier, D. Cho, V. Sandoghdar, and E. A. Hinds, Phys. Rev. Lett. 70, 560 (1993). [7] R. E. Grisenti, W. Schollkopf, J. P. Toennies, G. C. Hegerfeldt, and T. Kohler, Phys. Rev. Lett. 83, 1755 (1999); A. D. Cronin and J. D. Perreault, Phys. Rev. A 70, 043607 (2004); B. Brezger et al., Phys. Rev. Lett. 88, 100404 (2002). [8] J. D. Perreault, A. D. Cronin, and T. A. Savas, Phys. Rev. A 71, 053612 (2005). [9] A. Anderson et al., Phys. Rev. A 34, 3513 (1986); J. J. Berkhout et al., Phys. Rev. Lett. 63, 1689 (1989); F. Shimizu, Phys. Rev. Lett. 86, 987 (2001). [10] D. W. Keith, M. L. Schattenburg, H. I. Smith, and D. E. Pritchard, Phys. Rev. Lett. 61, 1580 (1988); R. Bruhl et al., Europhys. Lett. 59, 357 (2002). [11] C. Henkel and M. Wilkens, Europhys. Lett. 47, 414 (1999). [12] R. Folman, P. Kruger, J. Schmiedmayer, J. Denschlag, and C. Henkel, Adv. At. Mol. Opt. Phys. 48, 263 (2002). [13] D. W. Keith, C. R. Ekstrom, Q. A. Turchette, and D. E. Pritchard, Phys. Rev. Lett. 66, 2693 (1991); Atom Interferometry, edited by P. R. Berman (Academic Press, New York, 1997). [14] T. A. Savas, M. L. Schattenburg, J. M. Carter, and H. I. Smith, J. Vac. Sci. Technol. B 14, 4167 (1996). [15] P. Meystre, Atom Optics (American Institute of Physics, New York, 2001). [16] J. D. Perreault and A. D. Cronin, physics/0506090. PRL 95, 133201 (2005) PHYSICAL REVIEW LETTERS week ending 23 SEPTEMBER 2005 133201-4