Using an Atom Interferometer to Measure Atom Wave Phase Shifts Induced by Atom-Surface Interactions John D. Perreault and Alexander D. Cronin Supported by a grant from Research Corporation and the National Science Foundation

Talk Outline Intro to van der Waals (vdW) atom surface interactions: motivation, physical origin, previous data vdW interaction causes an atom wave phase shift Measurement of vdW induced phase shift with an atom interferometer Preparation of a suitable IG Phase stability of atom interferometer (IFM) Relationship between the measured and induced phase shift Surprises: two phase humps, anomalous contrast reduction Velocity dependence of vdW induced phase shift Conclusions and future work

Atom-Surface Interactions are Important in Atom Optics Nano-fabricated material gratings are a relatively cheap and reliable way to create a coherent superposition state diffraction pattern atom beam material grating

Atom-Surface Interactions are Important in Atom Optics Nano-fabricated material gratings are a relatively cheap and reliable way to create a coherent superposition state Manipulating atoms on a chip is an important step in making atom optics applications more practical atoms magnetic waveguide chip

Atom-Surface Interactions are Important in Atom Optics Nano-fabricated material gratings are a relatively cheap and reliable way to create a coherent superposition state Manipulating atoms on a chip is an important step in making atom optics applications more practical Quantum reflection from a surface may lead to a simple mirror for matter-waves

Atom-Surface Interactions are Important in Atom Optics Nano-fabricated material gratings are a relatively cheap and reliable way to create a coherent superposition state Manipulating atoms on a chip is an important step in making atom optics applications more practical Quantum reflection from a surface may lead to a simple mirror for matter-waves In all of the above one must understand how atom- surface interactions affect the intensity, phase and coherence of matter waves Atom-surface interactions may lead to quantum decoherence for matter waves on a chip and/or limit the use of material gratings with cold atoms

Physical Origin of the Atom- Surface vdW Interaction An atom will be attracted to a perfectly conducting surface even though it has no permanent dipole: How can this be? Vacuum field fluctuations induce a dipole in the atom which interacts with its image dipole in the surface x induced dipole image dipole r

Previous Experimental Schemes for Measuring vdW Atom-Surface Interaction Early experiments were based on the deflection of atom beams by surfaces (Shih et al.) More accurate measurements were made by measuring the energy shift of excitation spectra for atoms in a micro-cavity (Sandoghdar et al.) Recently it has been discovered that atomic diffraction patterns from material gratings show evidence of atom-surface interaction (Grisenti et al. using noble gases) Material gratings can be used as a tool for studying atom-surface interactions

Nano-structure Gratings Gratings have a period d = 100 nm and window size w ~ 50 nm “Large-area achromatic interferometric lithography for 100nm period gratings and grids” T. A. Savas, M. L. Schattenburg, J. M. Carter and H. I. Smith. Journal of Vacuum Science and Technology B (1996) 200 nm The grating dimensions are determined using SEM

Where to Look for Evidence of Atom- Surface Interaction? Atomic diffraction patterns obtained from material gratings show evidence of atom-surface interactions Atom-surface interactions between the grating and the atom beam will manifest itself as a change in the relative heights of the diffraction orders and as an atom-wave phase shift v = 1 km/s v = 3 km/s

Phase Profile Between the Grating Bars The wave function accumulates a phase after passing through the grating slots, due to atom-surface interactions The grey regions indicate the space occupied by the grating bars

An Atom-Surface Interaction Leads to a Matter-Wave Phase Shift mechanical grating bar de Broglie wave phase front phase shift Φ 0 reference wave test wave The zeroeth diffraction order of the interaction grating has a phase Φ 0 that depends on the atom-surface interaction and causes the interference fringes to shift Φ 0 is arrived at by calculating the phase of the diffraction amplitude with n=0

Using an Atom Interferometer to Measure Atom-Surface Induced Phase Shifts Atom beam Slits Interaction Grating Detector x

Observation of Phase Shift Induced by the Interaction Grating Each interference pattern corresponds to 5 seconds of data Notice how putting the interaction grating in either IFM arm causes the opposite sign phase shift which is also consistent with an attractive interaction x

Atom Optics Lab

Mach-Zehnder Atom Interferometer A Mach-Zehnder Atom interferometer is formed using the zeroeth and first orders of two diffraction gratings Note that the interferometer paths are spatially separated Atom fringes Atom beam intensity

Preparation of Interaction Grating Since the IG is surrounded by a silicon frame a hole had to be made in the grating to allow the reference arm to pass unaffected However, the transition from grating to gap must be <50 micrometers to fit between the IFM arms A glass capillary tube was drawn to a ~10 micrometer diameter and used as a perforation tool grating capillary tube microscope stage

Preparation of IG The grating naturally fractured along the 1  m period support structures The SEM image shows that the transition from gap to intact grating is < 2  m, easily fitting inside our 50  m wide IFM Perforating grating Perparing a clean gap 1  m 100  m

Interferometer Phase Stability The IFM had a background phase drift of about 2π rad/hr with occational non- linear excursions of 1 rad/10 min Data was taken by alternating between test (IG in path  or  ) and control (IG out of the IFM) conditions with a period of 50 s = 10 files A fifth order polynomial was fit only to the control cases and subtracted from all the data

Relationship Between Measured and Observed Phase Shift interaction grating plane: IG interference pattern:  There is a non-trivial relationship between measured and induced phase when the beams are partially obscured

Surprising Features in the Phase Profile extra hump unexpected dip

Surprising Features in the Contrast Profile One would expect the contrast to return to the nominal value when both of the arms are blocked by the IG

Reason for Anomolous Phase Profile Features Extra phase hump: Unexpected phase dip and contrast reduction: detector shifted unshifted Detected interference of other diffraction orders can can create additional phase humps IG IG support structure The support structure masks off the two IFM beams with a pattern of different phases In the worst case, the amplitude of the two beams do not overlap when they are recombined, inhibiting interference

Resolution of Suprising Features

v = 2110 m/s v = 2380 m/s v = 2490 m/s v = 2740 m/s Phase Profile as a Function of Atom Beam Velocity

Induced Phase Shift as a Function of Atom Beam Velocity The solid line represents a prediction for the zeroeth order phase shift induced by the grating assuming: w=50 nm, t=150 nm, C 3 =3 meVnm 3 This value of C 3 is consistent with previous measurements of 2.7 +/- 0.8 meV nm 3 from previous diffraction experiments (arXiv:physics/ )

Conclusions Measured atom-surface induced phase shift of 0.3 rad consistent with the vdW interaction strength of C 3 = 3 meV nm 3 Explored velocity dependence of the vdW induced phase shift Demonstrated that atom waves can retain their coherence even when passing within 25 nm of a surface

Future Work Explore non-retarded (1/r 3 ) to retarded transition (1/r 4 ) of the vdW atom-surface interaction Measure phase of higher diffraction orders with n>0 Coat gratings with various materials to look for surface dependence