PRL95,133201(2005) PHYSICAL REVIEW LETTERS week ending 23 SEPTEMBER 2005 Observation of Atom Wave Phase Shifts Induced by Van Der Waals Atom-Surface Interactions John D.Perreault and Alexander D.Cronin University of Arizona,Tucson,Arizona 85721.USA (Received 29 March 2005;published 19 September 2005) 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. DOI:10.1103/PhysRevLett.95.133201 PACS numbers:34.50.Dy.03.75.Dg,34.20.Cf,42.30.Kg The generally accepted picture of the electromagnetic vdW potential and is of practical interest when designing vacuum suggests that there is no such thing as empty space. atom optics components on a chip [11,12]. Quantum electrodynamics tells us that even in the absence When an atom wave propagates through a cavity,it of any free charges or radiation the vacuum is actually accumulates a spatially varying phase due to its interaction permeated by fluctuating electromagnetic fields.An im- with the cavity walls,given by the WKB approximation portant physical consequence of this view is that the fluc- tuating fields can polarize atoms resulting in a long range attractive force between electrically neutral matter:the ()=。+6b()=-V(包 (1) van der Waals (vdw)interaction [1].This microscopic force is believed to be responsible for the cohesion of where is the position in the cavity,I is the interaction nonpolar liquids,the latent heat of many materials,and length,V()is the atom-surface potential within the cavity, deviations from the ideal gas law.The polarized atoms can h is Planck's constant,and v is the particle velocity [8]. also interact with their electrical image in a surface,result- Equation (1)also separates the induced phase (into ing in an atom-surface vdW force [2].For example,nearby constant中。and spatially varying 6中()parts.A plot of surfaces can distort the radial symmetry of carbon nano- the phase (from Eq.(1)is shown in Fig.I for the tubes [3]and deflect the probes of atomic force micro- cavity geometry and vdW interaction strength in our ex- scopes [4].Atom-surface interactions can also be a source periment.If these cavities have a width w and are oriented of quantum decoherence or uncontrolled phase shifts, in an array with spacing d,then the atom wave in the far which are important considerations when building practi- field will have spatially separated components(diffraction cal atom interferometers on a chip [5].For the case of an orders)with complex amplitudes atom near a surface the vdw potential takes the form V(r)=-C3r-3,where C3 describes the strength of the 1.0 interaction and r is the atom-surface distance [1].This form of the vdw potential is valid in the limit of atom- 0.8 surface distances smaller than the principle transition pe 0.6 wavelength of the atoms,typically 1 um. Previous experiments have shown how atom-surface 0.4 e interactions affect the intensity of atom waves transmitted 0.2 through cavities [6],diffracted from material gratings [7,8],and reflected from surfaces [9].However,as we shall 0.0 see,none of these experiments provide a complete charac- -30 -20-100 1020 30 terization of how atom-surface interactions alter the phase ξ[nm of atom waves.In order to monitor the phase of an atom wave,one must have access to the wave function itself(), FIG.1.Accumulated phase (of an atom wave as a func- not just the probability density for atoms(2).In this tion of cavity position due to a vdw interaction with C3= Letter an atom interferometer is used to directly observe 3 meV nm3.The atom wave has propagated through a 150 nm how atom-surface interactions affect the phase of atom long cavity at a velocity of 2 km/s.The gray rectangles indicate waves,as proposed in [10].This observation is significant the location of the cavity walls which are 50 nm apart.Notice because it offers a new measurement technique for the how there is a nonzero constant phase offset ~0.05 rad. 0031-9007/05/95(13)/133201(4)$23.00 133201-1 2005 The American Physical Society
Observation of Atom Wave Phase Shifts Induced by Van Der Waals Atom-Surface Interactions John D. Perreault and Alexander D. Cronin University of Arizona, Tucson, Arizona 85721, USA (Received 29 March 2005; published 19 September 2005) 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. DOI: 10.1103/PhysRevLett.95.133201 PACS numbers: 34.50.Dy, 03.75.Dg, 34.20.Cf, 42.30.Kq The generally accepted picture of the electromagnetic vacuum suggests that there is no such thing as empty space. Quantum electrodynamics tells us that even in the absence of any free charges or radiation the vacuum is actually permeated by fluctuating electromagnetic fields. An important physical consequence of this view is that the fluctuating fields can polarize atoms resulting in a long range attractive force between electrically neutral matter: the van der Waals (vdW) interaction [1]. This microscopic force is believed to be responsible for the cohesion of nonpolar liquids, the latent heat of many materials, and deviations from the ideal gas law. The polarized atoms can also interact with their electrical image in a surface, resulting in an atom-surface vdW force [2]. For example, nearby surfaces can distort the radial symmetry of carbon nanotubes [3] and deflect the probes of atomic force microscopes [4]. Atom-surface interactions can also be a source of quantum decoherence or uncontrolled phase shifts, which are important considerations when building practical atom interferometers on a chip [5]. For the case of an atom near a surface the vdW potential takes the form VrC3r3, where C3 describes the strength of the interaction and r is the atom-surface distance [1]. This form of the vdW potential is valid in the limit of atomsurface distances smaller than the principle transition wavelength of the atoms, typically &1 m. Previous experiments have shown how atom-surface interactions affect the intensity of atom waves transmitted through cavities [6], diffracted from material gratings [7,8], and reflected from surfaces [9]. However, as we shall see, none of these experiments provide a complete characterization of how atom-surface interactions alter the phase of atom waves. In order to monitor the phase of an atom wave, one must have access to the wave function itself ( ), not just the probability density for atoms (j j 2). In this Letter an atom interferometer is used to directly observe how atom-surface interactions affect the phase of atom waves, as proposed in [10]. This observation is significant because it offers a new measurement technique for the vdW potential and is of practical interest when designing atom optics components on a chip [11,12]. When an atom wave propagates through a cavity, it accumulates a spatially varying phase due to its interaction with the cavity walls, given by the WKB approximation o lV @v ; (1) where is the position in the cavity, l is the interaction length, V is the atom-surface potential within the cavity, @ is Planck’s constant, and v is the particle velocity [8]. Equation (1) also separates the induced phase into constant o and spatially varying parts. A plot of the phase from Eq. (1) is shown in Fig. 1 for the cavity geometry and vdW interaction strength in our experiment. If these cavities have a width w and are oriented in an array with spacing d, then the atom wave in the far field will have spatially separated components (diffraction orders) with complex amplitudes 1.0 0.8 0.6 0.4 0.2 0.0 φ(ξ) [rad] -30 -20 -10 0 10 20 30 ξ [nm] FIG. 1. Accumulated phase of an atom wave as a function of cavity position due to a vdW interaction with C3 3 meV nm3. The atom wave has propagated through a 150 nm long cavity at a velocity of 2 km=s. The gray rectangles indicate the location of the cavity walls which are 50 nm apart. Notice how there is a nonzero constant phase offset o 0:05 rad. PRL 95, 133201 (2005) PHYSICAL REVIEW LETTERS week ending 23 SEPTEMBER 2005 0031-9007=05=95(13)=133201(4)$23.00 133201-1 © 2005 The American Physical Society
week ending PRL95,133201(2005) PHYSICAL REVIEW LETTERS 23 SEPTEMBER 2005 中n=Anei地。a=e冲。 w/2 ei8o()ermen/ddE, form a spatial interference pattern I(x).with a 100 nm (2) -w/2 period,at the plane of G3.The phase and contrast of the interference pattern are measured by scanning Ga in the x direction with a piezoelectric stage and counting the trans- where A,and d are real numbers,and n is the diffraction mitted atoms with a detector.The detector ionizes the order number [8].For n =0 the second exponential in the transmitted atoms with a 60 um diameter hot Re wire, integrand is unity,.and to leading order in中()，Φo≈ and then counts the ions with a channel electron multiplier. (()is the average phase over the grating window. Experiments which measure the intensity of atom waves A copropagating laser interferometer(not shown in Fig.2) was used to monitor the positions of G1,G2,G3 and to (e.g.,atom wave diffraction)are only sensitive to2= compensate for mechanical vibrations.Since the optical IA2,which is in part influenced by ()However,it is interference fringe period is A=3 um,relative uncer- clear from Eq.(2)that2 reveals no information about tainty in the optical interferometer output intensity of 中oorΦn.We have determined Ao andΦby placing this AlI~2Ax/A 1/1000 permits nanometer resolution array of cavities (grating)in one arm of an atom interfer- in the position of G3. ometer.This new technique is sensitive to the entire phase When grating G4 is inserted into the interferometer path shift ()induced by an atom-surface interaction,includ- a,the interference pattern I(x)shifts in space along the ing the constant offset中。 positive x direction.This can be understood by recalling The experimental setup for using an atom interferometer de Broglie's relation AdB =h/p [15].The atoms are sped to measure the phase shift Po induced by atom-surface up by the attractive vdW interaction between the Na atoms interactions is shown in Fig.2.The atom interferometer and the walls of grating G4.This causes AdB to be smaller used is similar to the type described in [13]and described in the region of G4,compressing the atom wave phase here briefly.A beam of Na atoms traveling at v =2 km/s fronts and retarding the phase of beam la)as it propagates (AdB =0.08 A)is generated from an oven,and a position along path a.One could also say that G4 effectively state of the atom wave is selected by two 10 um collima- increases the optical path length of path a.At G3 the tion slits spaced 1 m apart.A Mach-Zehnder-type inter- beams la)and IB)then have a relative phase between ferometer is formed using the zeroth and first order them leading to the state diffracted beams from three 100 nm period silicon nitride gratings [14].The three gratings G1,G2,G3 are spaced 1 m lx〉=Aneiola〉+ekB), (3) from each other and produce a first order diffraction angle of about 80 urad for 2 km/s sodium atoms.The grating where k=2/d is the grating wave number and d is the GI creates a superposition of position states la)and IB) grating period.The diffraction amplitude Ao reflects the which propagate along separated paths a and B,respec- fact that beam la)is also attenuated by G4.The state lx)in tively.The states are then recombined using grating G2 and Eg.(3)leads to an interference pattern which is shifted in space by an amount that depends on Po: G I(x)=(XlX〉x1+Ccos(kgx-Φo), (4) Aoeio） detector where C is the contrast of the interference pattern.Inserting ●I(X) G4 into path B will result in the same form of the interfer- ence pattern in Eq.(4),but with a phase shift of the opposite sign(i.e,Φo一-Φo). atom Grating G4 is an array of cavities 50 nm wide and beam ◆ 150 nm long which cause a potential well for the Na atoms eikgxβ> due to the vdW interaction.Atoms transmitted through G4 ◆ must pass within 25 nm of the silicon nitride cavity walls Iβ> G since the open slots of the grating are 50 nm wide.At this 1m 1m atom-surface distance the depth of the potential well is about 4X 10-7 eV.Therefore,as the atoms enter the FIG.2.Experimental setup for vdw induced phase measure- grating they are accelerated by the vdW interaction from ment.A Mach-Zhender atom interferometer with paths a and B 2000 m/s to at least 2000.001 m/s (depending on and is formed using the zeroth and first order diffracted beams of gratings Gi and G2 which have a period of 100 nm.The atom decelerated back to 2000 m/s as they leave the grating. wave interference pattern I(x)is read out using grating G3 as an This small change in velocity is enough to cause a phase amplitude mask.The phase fronts (groups of parallel lines) shift of o=0.3 rad according to Eqs.(1)and (2),which passing through grating G4 are compressed due to the attractive corresponds to a 5 nm displacement of the interference vdW interaction,resulting in a phase shift Po of beam la) pattern in the far field.It is quite remarkable to note that the relative to B).This causes the interference pattern I(x)to shift acceleration and deceleration happens over a time period in space at the plane defined by G3. of 75 ps,implying that the atoms experience an accelera- 133201-2
n Anein eio Z w=2 w=2 ei ei2n=dd; (2) where An and n are real numbers, and n is the diffraction order number [8]. For n 0 the second exponential in the integrand is unity, and to leading order in , 0 hi is the average phase over the grating window. Experiments which measure the intensity of atom waves (e.g., atom wave diffraction) are only sensitive to j nj 2 jAnj 2, which is in part influenced by . However, it is clear from Eq. (2) that j nj 2 reveals no information about o or n. We have determined A0 and 0 by placing this array of cavities (grating) in one arm of an atom interferometer. This new technique is sensitive to the entire phase shift induced by an atom-surface interaction, including the constant offset o. The experimental setup for using an atom interferometer to measure the phase shift 0 induced by atom-surface interactions is shown in Fig. 2. The atom interferometer used is similar to the type described in [13] and described here briefly. A beam of Na atoms traveling at v 2 km=s (dB 0:08 A ) is generated from an oven, and a position state of the atom wave is selected by two 10 m collimation slits spaced 1 m apart. A Mach-Zehnder –type interferometer is formed using the zeroth and first order diffracted beams from three 100 nm period silicon nitride gratings [14]. The three gratings G1; G2; G3 are spaced 1 m from each other and produce a first order diffraction angle of about 80 rad for 2 km=s sodium atoms. The grating G1 creates a superposition of position states ji and ji which propagate along separated paths and , respectively. The states are then recombined using grating G2 and form a spatial interference pattern Ix, with a 100 nm period, at the plane of G3. The phase and contrast of the interference pattern are measured by scanning G3 in the x direction with a piezoelectric stage and counting the transmitted atoms with a detector. The detector ionizes the transmitted atoms with a 60 m diameter hot Re wire, and then counts the ions with a channel electron multiplier. A copropagating laser interferometer (not shown in Fig. 2) was used to monitor the positions of G1; G2; G3 and to compensate for mechanical vibrations. Since the optical interference fringe period is 3 m, relative uncertainty in the optical interferometer output intensity of I=I 2x= 1=1000 permits nanometer resolution in the position of G3. When grating G4 is inserted into the interferometer path , the interference pattern Ix shifts in space along the positive x direction. This can be understood by recalling de Broglie’s relation dB h=p [15]. The atoms are sped up by the attractive vdW interaction between the Na atoms and the walls of grating G4. This causes dB to be smaller in the region of G4, compressing the atom wave phase fronts and retarding the phase of beam ji as it propagates along path . One could also say that G4 effectively increases the optical path length of path . At G3 the beams ji and ji then have a relative phase between them leading to the state j i A0ei0 ji eikgxji; (3) where kg 2=d is the grating wave number and d is the grating period. The diffraction amplitude A0 reflects the fact that beam ji is also attenuated by G4. The state j i in Eq. (3) leads to an interference pattern which is shifted in space by an amount that depends on 0: Ixh j i / 1 Ccoskgx 0; (4) where C is the contrast of the interference pattern. Inserting G4 into path will result in the same form of the interference pattern in Eq. (4), but with a phase shift of the opposite sign (i.e., 0 ! 0). Grating G4 is an array of cavities 50 nm wide and 150 nm long which cause a potential well for the Na atoms due to the vdW interaction. Atoms transmitted through G4 must pass within 25 nm of the silicon nitride cavity walls since the open slots of the grating are 50 nm wide. At this atom-surface distance the depth of the potential well is about 4 107 eV. Therefore, as the atoms enter the grating they are accelerated by the vdW interaction from 2000 m=s to at least 2000:001 m=s (depending on ) and decelerated back to 2000 m=s as they leave the grating. This small change in velocity is enough to cause a phase shift of 0 0:3 rad according to Eqs. (1) and (2), which corresponds to a 5 nm displacement of the interference pattern in the far field. It is quite remarkable to note that the acceleration and deceleration happens over a time period of 75 ps, implying that the atoms experience an acceleraatom beam G1 G2 G3 G4 x I(x) detector eikgx A0eiΦ0 eikgx|α> |β> |α> |β> 1 m 1 m FIG. 2. Experimental setup for vdW induced phase measurement. A Mach-Zhender atom interferometer with paths and is formed using the zeroth and first order diffracted beams of gratings G1 and G2 which have a period of 100 nm. The atom wave interference pattern Ix is read out using grating G3 as an amplitude mask. The phase fronts (groups of parallel lines) passing through grating G4 are compressed due to the attractive vdW interaction, resulting in a phase shift 0 of beam ji relative to ji. This causes the interference pattern Ix to shift in space at the plane defined by G3. PRL 95, 133201 (2005) PHYSICAL REVIEW LETTERS week ending 23 SEPTEMBER 2005 133201-2
week ending PRL95,133201(2005) PHYSICAL REVIEW LETTERS 23 SEPTEMBER 2005 tion of at least 106 g while passing through the grating. Grating G4 had to be prepared so that it was possible to Therefore,the vdW interaction is one of the most important obscure the test arm of the interferometer while leaving the forces at the nanometer length scale. reference arm unaffected.The grating is surrounded by a The experiment consists of measuring shifts in the po- silicon frame,making it necessary to perforate G4.A sition of the interference pattern I(x)when Ga is moved in scanning electron microscope image of G4 after it has and out of the interferometer paths.The interference data been perforated can be found in [16].The grating bars are shown in Fig.3.When G4 is placed in path a the themselves are stabilized by 1 um period support bars fringes shift in the positive x direction,whereas placing G4 running along the direction of k as described in [13,14]. in path B causes a shift in the negative x direction. The grating naturally fractured along these support struc- Therefore the absolute sign of the phase shift is consistent tures after applying pressure with a drawn glass capillary with an attractive force between the Na atoms and the walls tube.Using this preparation technique,G4 had a transition of grating G4.It is also observed that although the Na from intact grating to gap over a distance of about 3 um, atoms are passing within 25 nm of the grating the atom easily fitting inside our interferometer,which has a path waves retain their wavelike behavior (coherence),as evi- separation of about 80 um for atoms traveling at 2 km/s. dent by the nonzero contrast of the interference fringes. Because of the preparation technique,G4 was inserted The atom interferometer had a linear background phase into the test arm with kg orthogonal to the plane of the drift of approximately 2 rad/h and nonlinear excursions interferometer.This causes diffraction of the test arm out of ~1 rad over a period of 10 min,which were attributed to of the plane of the interferometer,in addition to the zeroth thermally induced position drift of the interferometer grat- order.However,the diffracted beams have an additional ings G,G2.G3 and phase instability of the vibration com- path length of approximately 2 nm due to geometry.Since pensating laser interferometer.The data were taken by our atom beam source has a coherence length of alternating between test (G4 in path a or B)and control (v/o)AaB =0.1 nm,the interference caused by the dif- (G4 out of the interferometer)conditions with a period of fracted beams will have negligible contrast.Therefore,the 50 s,so that the background phase drift was nearly linear between data collection cycles.A fifth order polynomial zeroth order of Ga will be the only significant contribution was fit to the phase time series for the control cases and to the interference signal. then subtracted from the test and control data.All of the In principle.the amount of phase shift o induced by the interference data were corrected in this way. vdw interaction should depend on how long the atom spends near the surface of the grating bars.Therefore the observed phase shift produced by placing G4 in one of the 0.6 36 34 0.5 0 0.4- 8 云 40 0.3 36 0.2 32 3 0.1 32 0.0 28 200022002400260028003000 24 50 50 100 atom velocity [m/s] Position [nm] FIG.4.Phase shift o induced by grating G4 for various atom FIG.3.Interference pattern observed when the grating G4 is beam velocities.The phase shift data have been corrected for inserted into path a or B of the atom interferometer.Each systematic offsets(~30%)caused by the interference of other interference pattern represents 5 s of data.The intensity error diffraction orders and beam overlap in the atom interferometer. bars are arrived at by assuming Poisson statistics for the number and the error bars reflect the uncertainty in the systematic of detected atoms.The dashed line in the plots is a visual aid to parameters.The solid line is a prediction of the induced phase help illustrate the measured phase shift of 0.3 rad.Notice how shift for vdw coefficient C3=3 meV nm3,grating thickness the phase shift induced by placing Ga in path a or B has opposite 150 nm,and grating open fraction 0.5.The data agree in sign.The sign of the phase shift is also consistent with the atom magnitude with the prediction and reproduce the slight trend experiencing an attractive potential as it passes through G4 of decreasing phase shift with increasing velocity. 133201-3
tion of at least 106 g while passing through the grating. Therefore, the vdW interaction is one of the most important forces at the nanometer length scale. The experiment consists of measuring shifts in the position of the interference pattern Ix when G4 is moved in and out of the interferometer paths. The interference data are shown in Fig. 3. When G4 is placed in path the fringes shift in the positive x direction, whereas placing G4 in path causes a shift in the negative x direction. Therefore the absolute sign of the phase shift is consistent with an attractive force between the Na atoms and the walls of grating G4. It is also observed that although the Na atoms are passing within 25 nm of the grating the atom waves retain their wavelike behavior (coherence), as evident by the nonzero contrast of the interference fringes. The atom interferometer had a linear background phase drift of approximately 2 rad=h and nonlinear excursions of 1 rad over a period of 10 min, which were attributed to thermally induced position drift of the interferometer gratings G1; G2; G3 and phase instability of the vibration compensating laser interferometer. The data were taken by alternating between test (G4 in path or ) and control (G4 out of the interferometer) conditions with a period of 50 s, so that the background phase drift was nearly linear between data collection cycles. A fifth order polynomial was fit to the phase time series for the control cases and then subtracted from the test and control data. All of the interference data were corrected in this way. Grating G4 had to be prepared so that it was possible to obscure the test arm of the interferometer while leaving the reference arm unaffected. The grating is surrounded by a silicon frame, making it necessary to perforate G4. A scanning electron microscope image of G4 after it has been perforated can be found in [16]. The grating bars themselves are stabilized by 1 m period support bars running along the direction of kg as described in [13,14]. The grating naturally fractured along these support structures after applying pressure with a drawn glass capillary tube. Using this preparation technique, G4 had a transition from intact grating to gap over a distance of about 3 m, easily fitting inside our interferometer, which has a path separation of about 80 m for atoms traveling at 2 km=s. Because of the preparation technique, G4 was inserted into the test arm with kg orthogonal to the plane of the interferometer. This causes diffraction of the test arm out of the plane of the interferometer, in addition to the zeroth order. However, the diffracted beams have an additional path length of approximately 2 nm due to geometry. Since our atom beam source has a coherence length of v= vdB 0:1 nm, the interference caused by the diffracted beams will have negligible contrast. Therefore, the zeroth order of G4 will be the only significant contribution to the interference signal. In principle, the amount of phase shift 0 induced by the vdW interaction should depend on how long the atom spends near the surface of the grating bars. Therefore the observed phase shift produced by placing G4 in one of the 36 32 28 24 -50 0 50 100 Position [nm] 44 40 36 32 Intensity [kCounts/s] 38 36 34 32 30 α β α α β β FIG. 3. Interference pattern observed when the grating G4 is inserted into path or of the atom interferometer. Each interference pattern represents 5 s of data. The intensity error bars are arrived at by assuming Poisson statistics for the number of detected atoms. The dashed line in the plots is a visual aid to help illustrate the measured phase shift of 0.3 rad. Notice how the phase shift induced by placing G4 in path or has opposite sign. The sign of the phase shift is also consistent with the atom experiencing an attractive potential as it passes through G4. 0.6 0.5 0.4 0.3 0.2 0.1 0.0 Φ0 [rad] 2000 2200 2400 2600 2800 3000 atom velocity [m/s] FIG. 4. Phase shift 0 induced by grating G4 for various atom beam velocities. The phase shift data have been corrected for systematic offsets (30%) caused by the interference of other diffraction orders and beam overlap in the atom interferometer, and the error bars reflect the uncertainty in the systematic parameters. The solid line is a prediction of the induced phase shift for vdW coefficient C3 3 meV nm3, grating thickness 150 nm, and grating open fraction 0.5. The data agree in magnitude with the prediction and reproduce the slight trend of decreasing phase shift with increasing velocity. PRL 95, 133201 (2005) PHYSICAL REVIEW LETTERS week ending 23 SEPTEMBER 2005 133201-3
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. 133201-4
interferometer 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 uncertainty of the phase measurements in Fig. 4. A more detailed 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. Therefore, 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 atomsurface 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 eliminated 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