de broglie wave phase shifts induced by surfaces 20 nm away
DESCRIPTION
de Broglie wave phase shifts induced by surfaces 20 nm away. Alex Cronin John Perreault Ben McMorran. University of Arizona, Tucson AZ, USA. NSF. Funding from: Research Corporation and NSF. Outline:. Nano-Structure Gratings. Coherent effects of V vdW (r)=C 3 /r 3 on Atom beams - PowerPoint PPT PresentationTRANSCRIPT
de Broglie wave phase shifts induced by surfaces
20 nm away
Alex CroninJohn PerreaultBen McMorran
Funding from: Research Corporation and NSFNSF
University of Arizona, Tucson AZ, USA
• Nano-Structure Gratings
• Coherent effects of VvdW(r)=C3/r3 on Atom beams
– Diffraction Intensities |An|2 depend on atom velocity
– No missing orders regardless of open fraction
– Interferometer measurement of phase shift in 0th order
– Measure of phase in 1st and 2nd orders
• Electron Optics Experiments on Vimage(r) = C1/r– Asymmetric Diffraction
– Depends on incident velocity and angle
Outline:
Na
z
x
supersonic source
.5 mm skimmer
10 μm collimating
slits
100 nm period diffraction
grating
60 μm diameter hot wiredetector
Atom Diffraction
1
2
4
10
2
4
100
2
4
Ato
m F
lux
( k
/sec
)
-1.0 -0.5 0.0 0.5 1.0detector position (mm)
0
1
3
4
2
6
5
7
Ato
m F
lux
(kC
/s)
Detector Position x (mm)
ninA e
2
nA
Na
z
x’
supersonic source
.5 mm skimmer
10 μm collimating
slits
100 nm period diffraction
grating
60 μm diameter hot wiredetector
Atom Interferometry
Ato
m F
lux
Ato
m F
lux
(kC
/s)
Grating Position x’ (nm)
n
Removable interaction grating
1 um
Nano-Structure Gratings
Nano-Structure Gratingsperiod d = 100 nm, 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 14 4167-4170 (1996)
•Start with Vvdw in all space •Compute phase shift just after the grating •Propagate to the detector plane
To understand the role of vdWforces on atom diffraction:
Atom-surface (and electron-surface) interactonscause phase shifts for de Broglie waves that aretransmitted through the grating channels.
At 10 nm, 3 eV and 0.3 eV but the same 0.3 rad
Far-Field Diffraction Envelopes for Intensity
Note: 2nd order would have phase shift if C3=0.
vdW Potential Atom phase
))
((
t
v
V
1.0
0.8
0.6
0.4
0.2
0.0
(r
ad)
50403020100position (nm)
gratingbar
-5
-4
-3
-2
-1
0
En
erg
y (
eV
)
50403020100position (nm)
[MDB97] [DJS99] [MDB97e] [SPT93] [ZhS95]
gratingbar
gratingbar
( )
r1 r2atom
( )V
t with
velocity v
Amplitude and phase of nth order change with C3/velocity
dnkiAiA incnn )(exp)exp(
Phase shift in nth order.
velocity = 3171 m/s
velocity = 2219 m/s
velocity = 1091 m/s
velocity = 662 m/s
1
10
100
Inte
nsity
[k/
s]
0.50.0Position [mm]
01
23
54
1
10
100
Inte
nsity
[k/
s]
3210Position [mm]
0
1
23
1
10
100In
tens
ity [
k/s]
210Position [mm]
0
1
2 3
54
1
10
100
Inte
nsity
[k/
s]
1.00.50.0Position [mm]
01
23
54
Best Fit to |An|2
4
6
0.01
2
4
6
0.1
2
4
6
1R
ela
tive
In
ten
sity
543210Diffraction Order
v = 662 m/s v = 1091 m/s v = 2219 m/s v = 3171 m/s vdW theory C3 = 0
with only one free parameter: C3
Rx to determine the strength of thevan der Waals potential V(r)=C3r -3:
1. Measure physical grating parameters: w, t, d
2. Fit diffraction pattern to determine flux in each order |An|2
3. Fit |An|2 to determine C3
Imperfect determination of grating geometry w, t and wedge angle. Uncertainty of 1 nm in w dominates the uncertainty in C3. Lineshape used to fit the raw diffraction pattern Gaussian works poorly, empirical lineshape works better.
What is the potential V everywhere in and near the grating? structure is partially coated with sodium Slot walls are not semi-infinite planes NOT YET ADDRESSED
Systematic Uncertainties
Dirty Gratings
Have beenCleaned
(AFM images)
105
106
107
Inte
nsi
ty
-4 -3 -2 -1 0 1 2 3 4order
C3=0 C3=5 C2=1.2 C4=30 C5=1000
Computed usingPhasor method matching I1 / I0
Different power-law potentialsmake distinct diffraction envelopes.
V(r) = -Cn/rn
r=0n=2n=3n=4n=5
105
106
107
Inte
nsity
-4 -3 -2 -1 0 1 2 3 4order
C3=0 C3=5 C2=1.2 C4=30 C5=1000
Computed usingPhasor method matching I1 / I0
105
106
107
Inte
nsity
-4 -3 -2 -1 0 1 2 3 4order
C3=0 C3=5 C2=1.2 C4=30 C5=1000
Computed usingPhasor method matching I1 / I0
Cn chosen to match I1/I0
• Rotate the grating through “50% open fraction” and note second order is never suppressed.
• measure absolute transmission into zeroth order (it should change with C3/velocity)
• Use an interferometer to measure phase shift in 0th order
• Use different surface coating.
Next:
Missing orders would occur when zeros from single-slit diffraction coincide with constructive interference from many-slits.
missing orders ±3, ±6, ...
E.g. w/d = 1/3
0.10
0.08
0.06
0.04
0.02
0.00
Inte
nsity
[I 0
]-1
-10 -5 0 5 10sin() [d]
-1
0.10
0.08
0.06
0.04
0.02
0.00
Inte
nsity
[I 0
]-1
-10 -5 0 5 10sin() [d]
-1
detector
twist axis
atom beam
Experiment 2: Twist the grating to search for missing orders
Model parameters: d=100 nm, w=67 nm, t=116 nm, = 3.5o.
Dashed red lines C3=0 Solid black lines C3=5 meVnm3
Intensity in Each Order vs. Twist
angle (degrees)
1st order
2nd order
3rd order
4th order
0th order
Asymmetric +/- 1 orders
w
d
l
Blazed Gratings for Atom Waves
requirements:•van der Waals •Asymmetric channel walls
0.05
0.04
0.03
0.02
0.01
0.00
Inte
nsi
ty
[I 0]-1
1050-5-10sin() [d]
-1
0
1.00.80.60.40.20.0
Pha
se
-40 -20 0 20 40' (nm)
Region where d)/d = kj most strongly affects jth order
0.10
0.08
0.06
0.04
0.02
0.00
Inte
nsity
[I 0
]-1
-10 -5 0 5 10sin() [d]
-1
0.10
0.08
0.06
0.04
0.02
0.00
Inte
nsity
[I
0]-1
-10 -5 0 5 10sin() [d]
-1
Optical diffractionMuch more symmetric,missing orders possible
Atom diffractionAsymmetric,no missing orders - ever
0.04
0.02
0.00
Inte
nsity
[I 0
]-1
1050-5-10sin() [d]
-1
There are no missing orders in atom diffraction from a material grating.
Theorem:
Corollary:
Atom-surface interactions can be measuredby studying atom diffraction.
Vibration curves can prove “No Missing Orders” Thm
2nd
dw
1
2
2
vdWex (p )
w
w
n gi nk i d
A way to visualize the cumulative integral for n
Arrows from tail to tip represent amplitudes n. In =|n|2
Vibration Curves
(a) diffraction with absorption only
(b) Van der Waals included
Arrows from tail to tip represent amplitudes n. In =|n|2
2
2
Unless C3=0, endpoints of the spiral never overlap.
second diffraction orderw/d = 0.48C3 = 0, 1, 10, 100 meVnm3
Model shown for:
Thereforen is never zero, i.e., there are never missing orders. Q.E.D.
Expt.#3: Use Diffraction Phase to Measure C3
1.0
0.8
0.6
0.4
0th o
rde
r in
ten
sity
[a
rb.
un
its]
1086420C3 [meVnm
3]
• Zeroth order intensity and phase depend on the strength of the van der Waals interaction with the grating bars.
0th order transmission vs. C3 phase shift vs. C3
0.6
0.4
0.2
0.0
0th
ord
er
ph
ase
[ra
d]
1086420C3 [meVnm
3]
Phase 0 due to Interaction Grating
Atom beam
Slits
Interaction Grating
Detector|a>
|b>
bea og xki
og xkCI cos1
140
120
100
80
60
40
20
0
-0.2 0.0 0.2
Preparing an interaction grating to act on one arm of the interferometer
Gap
In-tact Grating Position (mm)
1 um
gapgapgap
In tact grating
Measurement of Phase Shift Induced by the Interaction Grating
0.25
0.20
0.15
0.10
0.05
cont
rast
interaction grating position
4.2
4.0
3.8
3.6
3.4
3.2
3.0
phase [rad]
contrast phase
A B C B A B
A
B
C
Interaction grating position
(raw data 5 sec/ pt)
Phase Shift Induced by the Interaction Grating (averaged data)
• Phase shift induced by grating is φo=.22+/-.03 rad
• 90 seconds of data total• C3 = 4.0 +/- 1.0 meV nm3
60
50
40
30
Inte
nsity
[k/
sec]
-200 -100 0grating position (nm)
A
B
C
-0.2
-0.1
0.0
0.1
0.2
Pha
se
A B C
See talk byJohn Perreault
about theinterferometerexperiment.
L1 L2
-4-2024
200
150
100
500
-4 -2 0 2 4
200150
10050
0
A
B
C
D
Expt. #4: Measure the far-field 1 and 2
Four different interferometers:
Amplitude and phase of nth order change with C3/velocity
Velocity / [km/s] Velocity / [km/s]
Contrast from Four interferometers is resolved (thanks to 100 nm period gratings and 2 m IFM)
Predicted Phase shifts in red
Predicted Phase shifts in red
** *
* = preliminary data
Summary of4 Experiments Theory
velocity
twistInteraction grating
4-IFMs
Na + SiNx
Na + Na metal
Na valence + =∞Na with core + e=∞
10
8
6
4
2
0
C3
(meV
nm
3 )
No extra interaction needed to explain the data
Nano-Structure Grating in an Electron Microscope
twist lever
Grating
O. Lens
Grating
4 µm wire 4 µm wire
What About Electron Waves?
Images of a single wire with diffracted e-beam.
4 keV beam
twist = -10±2°
1.5 keV beam
twist = 5±3°
w
d
l
140
120
100
80
60
40
20
0
-50 0 50
120
100
80
60
40
20
0
-50 0 50
=5.4o
=-2o
500 eV electron beam
w
d
l
140
120
100
80
60
40
20
0
-50 0 50
120
100
80
60
40
20
0
-50 0 50
=5.4o
=-2o
500 eV electron beam Envelope from same theory (image chg)
diffraction profiles - comparison
120
100
80
60
40
20
0
-60 -40 -20 0 20 40 60
twist = 5±3°, 500 eV
100
80
60
40
20
0
-60 -40 -20 0 20 40 60
twist = 10±2°, 500 eV
60
40
20
0
-60 -40 -20 0 20 40 60
twist = -10±2°, 500 eV
140
120
100
80
60
40
20
0
-60 -40 -20 0 20 40 60
twist = 0±2°, 500 eV
200
150
100
50
0
-60 -40 -20 0 20 40 60
twist = 5±3°, 1.5 keV
140
120
100
80
60
40
20
0
-60 -40 -20 0 20 40 60
twist = 10±2°, 1.5 keV
100
80
60
40
20
0
-60 -40 -20 0 20 40 60
twist = -10±2°, 1.5 keV
150
100
50
0
-60 -40 -20 0 20 40 60
twist = 0±2°, 1.5 keV
140
120
100
80
60
40
20
0
-40 -20 0 20 40
twist = 10±2°, 4 keV
150
100
50
0
-40 -20 0 20 40
twist = 5±3°, 4 keV
160
140
120
100
80
60
40
20
0
-40 -20 0 20 40
twist = -10±2°, 4 keV
160
140
120
100
80
60
40
20
0
-40 -20 0 20 40
twist = 0±2°, 4 keV
11°:
5°:
-2°:
-12°:
500 eV 1.5 keV 4 keV
Electron Diffraction Results
• Asymmetric due to grating tilt• More symmetric at higher energy
• Both explained by diffraction theory with image charge potential and = 4
V(r) = e2 (1-)/(1+) r = 1 eV nm / r
Impact of atom-surface & electron-surface V(r)
• measured C3 = 3 (1) meVnm3 four different ways
• Flux is diverted from 0th order• no missing orders• blazed gratings• similar effects for 500 eV electron beams
• power law of potential can be tested• limitations for smaller gratings / slower atoms.
• Decoherence? Retardation?
105
106
107
Inte
nsi
ty
-4 -3 -2 -1 0 1 2 3 4order
C3=0 C3=5 C2=1.2 C4=30 C5=1000
Computed usingPhasor method matching I1 / I0
Different power-law potentialsmake distinct diffraction envelopes.
V(r) = -Cn/rn
r=0n=2n=3n=4n=5
105
106
107
Inte
nsity
-4 -3 -2 -1 0 1 2 3 4order
C3=0 C3=5 C2=1.2 C4=30 C5=1000
Computed usingPhasor method matching I1 / I0
105
106
107
Inte
nsity
-4 -3 -2 -1 0 1 2 3 4order
C3=0 C3=5 C2=1.2 C4=30 C5=1000
Computed usingPhasor method matching I1 / I0
Cn chosen to match I1/I0
Impact: Performance of interferometer.Figure of Merit = C sqrt(N).
0.015
0.010
0.005
0.000
C (
I/Io
)1/2
20151050C3
w1 = .56w2 = .50w3 = .37
w1 = .70w2 = .80w3 = .37
• Thank you
40 45 50 55 60 65 70 75 800
1
2
3
4
5
6
w
4050
6070
80
10001500
20002500
30000
2
4
6
wv
C3 = 5
Student Version of MATLAB
Model of I2/I3
I2/I3
different velocities
W
Atom Interferometer
)cos(|2|| vdW
)()( vdW
xkLULLUUFlux
eLowerUppere
g
xkitkyi g
Calculation Ref Predicted Phase Shift (radians)
Short-range van der Waals and ideal surface
DJS99 0.45
Long-range C4 and ideal surface
MDB97 0.80
Casimir Polder (C.P.) and ideal surface, 1 electron only
MDB97 0.36
C.P. and Dielectric half- sapce
SpT93 0.29
C.P. and thin dielectric walls
ZhS95 0.25
C.P. for a grating bar
*theory not yet available
• 0.22 radobserved
Measurement of C3 Using an Atom Interferometer
• Measured C3 consistent with vdW for Na and silicon nitride.
• Stat. Uncertainty in φo can be reduced to 2% in 1 hr.
• Uncertainty in grating geometry will permit 5% level for C3.
φo = .22 +/- .03 rad
C3 = 4.0 +/- 1.0 meV nm3
0.30
0.20
0.10 vdW
[rad
]
86420C3 [meV nm
3]
Questions:
• What about far field phase shifts?
• Can we detect electron-surface interactions?
• is 20% of C3 from core electrons correct?
• What is UvdW for a structure?
• How does radiation modify UvdW ?
• Can there be vdW friction?