matter wave interferomery with poorly collimated beams x [µm] ben mcmorran, alex cronin department...
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Matter wave interferomery with poorly collimated beams
x [µm]
Ben McMorran, Alex CroninDepartment of Physics
x [µm]
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main idea
can get matter wave interference fringes with uncollimated beams but:
• grating position matters
• spatial coherence matters
• beam divergence matters
• grating alignment matters
we’ve got a way to model this
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outline
1. partial coherence in grating interferometers
2. examples of grating matter wave interferometersMach-Zehnder atom interferometer
Talbot-Lau C60 interferometer
Lau electron interferometer
3. grating alignment sensitivity
4. ideas for g measurement using uncollimated beam
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partially coherent optical field
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partially coherent optical field
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partially coherent optical field
intensity I(x)
complex degree of coherence µ(x)
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… We simulate (1) the Talbot effect, (2) far-field diffraction, (3) Mach Zehnder interferometers(4) Talbot-Lau Interferometers(5) Lau interferometers …
A Model for Partial Coherence and Wavefront Curvature in Grating Interferometers
PRA (June 2008)
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Mutual Intensity Function:
Intensity:
z
(ρa ,z)
(ρb ,z)
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Mutual Intensity Function:
Intensity:
GSM:
w0
σ0
ρaρb
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Mutual Intensity Function:
Intensity:
GSM:
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Mutual Intensity Function:
Intensity:
GSM:
partially coherent Fresnel optics
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a second grating in the far field
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a second grating in the far field
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Atom Interferometer
Objective: Pioneer new techniques using matter-wave interference to make precision measurements.
• Study quantum decoherence,• Matter-wave index of refraction,• Atomic polarizability.
Approach: 3 nano-fabricated diffraction gratings.
• Mach-Zhender interferometer for atom-waves..
Interferometer Performance:
• Up to 50% contrast.• Small phase drift (< 2 rad / hr).• Layout is easily changed for new experiments.• Macroscopic (100 m) path separation.
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gratings for matter waves
100nm
1.5µm
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Second Grating
Optical Grating
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atom beam
Na
skimmer
S1 = 10µm`
L = 1m
S2 = 10µm
v = 1km/s λ = 17pm
α
α = (S1+S2)/L ~ 10-5
θdiff = λ/d ~ 10-4
ℓ = λL/S1 ~ 1µm
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atom beam
Na
skimmer
S1 = 10µm`
L = 1m
S2 = 10µm
α
“Gaussian Schell Source as Model for Slit-Collimated Atomic and Molecular Beams”
McMorran, Cronin arXiv:0804.1162 (2008)
ℓ > d coherent diffractionθdiff / α = 10 resolved diffraction
but
β = ℓ/S1 ~ 0.1 partially coherent
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1
2
4
10
2
4
100
2
4
Ato
m F
lux
( k
/se
c )
-1.0 -0.5 0.0 0.5 1.0detector position (mm)
Atom Diffraction:
Atom Interference Fringes:
01
3
42
6
5
7
100
80
60
40
20
0
inte
nsity
[kco
unts
/sec
]
4003002001000-100grating position [nm]
54
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22 cos( )gFlux U U L L U L ik x
( ) gik xi ky wte Upper Lower e
Atom Interferometer
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100
80
60
40
20
0inte
nsity
[kco
unts
/sec
]
4002000position [nm]
C = 24.7%
Atom fringes
inte
nsity
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add a second grating
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add a second grating
“Talbot-Lau fringes”
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“Matter-Wave Interferometer for Large Molecules”Brezger, Hackermüller, Uttenthaler, Petschinka, Arndt, Zeilinger
Physical Review Letters 88 100404-1 (2002)
S1 = 1.2mm
S2 = 0.5mmL = 1.38m
α ~ 10-3
θdiff ~ 10-6
ℓ ~ 10nm
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add a second grating
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add a second grating
coarse fringes in the far field:
“Lau fringes”
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1µm
electron interferometery with two gratings
aperture
magnetic lens
stationary beam
grating 1
imaging detector
grating 2
Cronin and McMorran, PRA 74 (2006) 061602(R)
α ~ 10-3 θdiff ~ 10-4 ℓ ~ 5nm
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Lau interferometer
G1 G2
incoherent source
• each opening of G1 acts as a point source for a diffraction pattern from G2
• at certain grating separations, diffraction patterns overlap
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z12
A
z
ML S
G1G2 x
y
z
CCD
Lau interferometer – fringe contrast vs. grating separation
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Lau interferometer – fringe contrast vs. grating separation
2.5
2.0
1.5
1.0
0.5
G1
-G2
se
pa
ratio
n (
mm
)
0.80.60.40.20.0CCD pixel location (mm) Cronin and McMorran, PRA 74 061602(R) (2006)
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Lau interferometer –twist gratings to measure coherence
z0
G1
G2
xy
z
z1
z2
z3
θ
GSM source
Lau fringe visibility
23
3max
sin
2
3
23
)(z
deV yd
z
y
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Lau interferometer – fringe contrast vs. grating rotation
alignment sensitivity depends on coherence parallel to grating slits
ℓ0 ≈ 10 nm
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some figures:
antihydrogen incident on 1µm period gratings 1m from source:
v = 10 km/s: λ = 0.4Å S1 < 40µm for coherent diffraction (ℓ > d) v = 5 km/s: λ = 0.8Å S1 < 80µmv = 1 km/s: λ = 4.0Å S1 < 400µm
T = 4K Δvx = 260m/s
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position echo interferometer
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position echo interferometer?
Mach-Zehnder position echo
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position echo interferometer?
• fine-spaced interference fringes
precision for measuring deflection
• uncollimated
more counts from wider slits
• integrate across w
more counts looking at all paths
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position echo interferometer?
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position echo interferometer?
NEEDS FURTHER STUDY WITH REALISTIC PARAMETERS
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conclusion
• simulations + experiments:
matter wave fringes can be formed with uncollimated beams
• necessary to think about partial coherence
• less coherence parallel to slits contrast sensitive to grating misalignment
• position echo behind 2 gratings useful for measure g?
• we have a tool to model this