Transcript Slide 1

Using Atomic Diffraction to Measure the van der
Waals Coefficient for Na and Silicon Nitride
J. D. Perreault1,2, A. D. Cronin2, H. Uys2
1Optical Sciences Center, University of Arizona, Tucson AZ, 85721 USA
2Physics Department, University of Arizona, Tucson AZ, 85721 USA
Definitions
van der Waals Diffraction Theory
Abstract
•The far-field diffraction pattern for a perfect grating is given by
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. During passage through the grating
slots atoms acquire a phase shift due to the van der Waals
(vdW) interaction with the grating walls. As a result the relative
intensities of the matter-wave diffraction peaks deviate from
optical theory. We present a preliminary measurement of the
vdW coefficient C3 by fitting a modified Fraunhofer optical
theory to the experimental data.


 i ξ 
 ξ 
A n  e rect 
w




 f  n
T ξ 
ξ
2

λ z

Ix    A n  L x  n dB 
n  
d

lineshape
d
•The diffraction envelope amplitude An is just the scaled Fourier transform of
the single slit transmission function T(ξ)
I(x): atom intensity
λdB: de Broglie wavelength
An: diffractin envelope amplitude
v: velocity
|An|2: number of atoms in order n
σv: velecity distribution
T(ξ): single slit transmission function
d: grating period
V(ξ): vdW potential
w: grating slit width
φ(ξ): phase due to vdW interaction
t: grating thickness
ξ: grating coordinate
•Notice that T(ξ) is complex when the van der Waals interaction is
incorporated and the phase following the WKB approximation to leading order
in V(ξ) is
3.0
fξ: Fourier conjugate variable to ξ
x: detector coordinate
3
3
tVξ  tC3 
w
w 

   

 ξ     ξ   
v
v 
2
2  

() [rad]
z: grating-detector separation
2.0
L(x): lineshape function
1.0
n: diffraction order
0.0
-20
0
 [nm]
10
20
Measured Grating Parameters
Intuitive Picture
Experiment Geometry
•A grating rotation experiment along with an SEM image are used
to independently determine w and t
•As a consequence of the fact that matter propagates like a wave there
exists a suggestive analogy
•A supersonic Na atom beam is collimated and used to illuminate a
diffraction grating
index : light :: potential: atoms
•A hot wire detector is scanned to measure the atom intensity as a
function of x
ξ
-10
•The van der Waals interaction acts as an effective negative lens that
fills each slit of the grating, adding curvature to the de Broglie wave
fronts and modifying the far-field diffraction pattern
x
optical phase front
z
z
grating rotation experiment
SEM image
Na
w = 68.44 ± .0091 nm
100 nm period 60 μm diameter
10 μm
diffraction
hot wire
collimating
grating
detector
slits
2
10
4
2
-2
-1
0
1
6
4
v = 2109 m/s
2
(stat. only)
v = 2109 m/s
v = 1015 m/s
2
0.1
6
4
2
0
4
1
2
3
4
Diffraction Order
C3 = 3.13 ± .04 meVnm3
5
1
v = 2109 m/s
VDW Theory
Optical Theory
0.1
0.01
0.001
0
1
2
3
Diffraction Order
4
5
•Using the previously mentioned theory one can see that the zeroth
order intensity and phase depend on the strength of the van der
Waals interaction
(stat. only)
1
v = 1015 m/s
VDW Theory
Optical Theory
0.1
0.01
0.001
0
1
2
3
4
Diffraction Order
5
1.0
0.8
0.6
0.4
th
Intensity [kCounts/s]
Position [mm]
2
C3 = 5.95 ± .45 meVnm3
1
10
0
4
2
•Free parameters: |An
1
4
2
-1
0
Position [mm]
1
|2,
v, σv
•The background and lineshape function
L(x) are determined from an independent
experiment
Conclusions and Future Work
•A preliminary determination of the van der Waals coefficient C3 is
presented here for two different atom beam velocities based on the
method of Grisenti et. al
•Using the phase and intensity dependence of the zeroeth
diffraction order on C3 we are pursuing novel methods for the
measurement of the van der Waals coefficient
•The van der Waals phase could be “tuned” by rotating the grating
about its k-vector, effectively changing the value of t by some
known amount
•The relative number of atoms in each diffraction order was fit with only one free
parameter: C3
•Notice how optical theory (i.e. C3→0) fails to describe the diffraction envelope
correctly for atoms
References
“Determination of Atom-Surface van der Waals Potentials from
Transmission-Grating Diffraction Intensities” R. E. Grisenti, W. Schollkopf,
and J. P. Toennies. Phys. Rev. Lett. 83 1755 (1999)
“He-atom diffraction from nanostructure transmission gratings: The role of
imperfections” R. E. Grisenti, W. Schollkopf, J. P. Toennies, J. R. Manson,
T. A. Savas and H. I. Smith. Phys. Rev A. 61 033608 (2000)
“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 14 4167-4170
(1996)
0.6
0.4
0.2
th
4
Best Fit C3 – Preliminary Results
0 order intensity [arb. units]
100
Relative Number of Atoms
Intensity [kCounts/s]
v = 1015 m/s
Using Zeroeth Order
Diffraction to Measure C3
0 order phase [rad]
2
|An|
Determining
2
negative lens
Relative Number of Atoms
.5 μm
skimmer
Relative Number of Atoms
supersonic
source
2
4
63
C3 [meVnm ]
8
•The ratio of the zeroeth order
to the raw beam intensity
could be used to measure C3
10
0.0
0
2
4
63
C3 [meVnm ]
8
•The phase shift could be
measured in an interferometer
to determine C3
10