1. Matter wave interferomery with poorly collimated beams
x [µm]
x [µm]
Ben McMorran, Alex Cronin
Department of Physics

2. 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

3. outline 1. partial coherence in grating interferometers
2. examples of grating matter wave interferometers
Mach-Zehnder atom interferometer
Talbot-Lau C60 interferometer
Lau electron interferometer
3. grating alignment sensitivity
4. ideas for g measurement using uncollimated beam

4. partially coherent optical field

5. partially coherent optical field

6. partially coherent optical field
complex degree of coherence µ(x)
intensity I(x)

7. A Model for Partial Coherence and Wavefront Curvature in Grating Interferometers
PRA (June 2008)
… We simulate
(1) the Talbot effect,
(2) far-field diffraction,
(3) Mach Zehnder interferometers
(4) Talbot-Lau Interferometers
(5) Lau interferometers …

8. Mutual Intensity Function:
(ρa ,z)
(ρb ,z)

9. Mutual Intensity Function:
GSM: ρa ρb σ0 w0

10. Mutual Intensity Function:
GSM:

11. Mutual Intensity Function:
GSM:
partially coherent Fresnel optics

15. a second grating in the far field

16. a second grating in the far field

17. 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 mm) path separation.
These are the notes that explain the vugraph. Please note that these vugraphs are much more generic and less technical than yours will be. But at the same time, realize that you can’t get too technical in a single vugraph.

18. gratings for matter waves
100nm

19. Optical
Grating
Second Grating

20. atom beam L = 1m skimmer Na α S1 = 10µm` S2 = 10µm
v = 1km/s  λ = 17pm
α = (S1+S2)/L ~ 10-5
θdiff = λ/d ~ 10-4
ℓ = λL/S1 ~ 1µm

21. atom beam L = 1m skimmer Na α S1 = 10µm` S2 = 10µm
ℓ > d  coherent diffraction
θdiff / α = 10  resolved diffraction
but
β = ℓ/S1 ~ 0.1  partially coherent
“Gaussian Schell Source as Model for Slit-Collimated Atomic and Molecular Beams”
McMorran, Cronin arXiv: (2008)

22. Atom Interference Fringes:1
Atom Diffraction: 3 2 5 4 6 7
Atom Interference Fringes:

23. Atom Interferometer

24. Atom fringes
intensity

26. add a second grating

27. “Talbot-Lau fringes”
add a second grating

28. “Matter-Wave Interferometer for Large Molecules”
Brezger, Hackermüller, Uttenthaler, Petschinka, Arndt, Zeilinger
Physical Review Letters (2002)
L = 1.38m
S2 = 0.5mm
S1 = 1.2mm
α ~ 10-3
θdiff ~ 10-6
ℓ ~ 10nm

29. add a second grating

30. coarse fringes in the far field:
“Lau fringes”
add a second grating

31. electron interferometery with two gratings
aperture
magnetic lens
grating 1
grating 2
stationary beam
1µm
imaging detector
α ~ θdiff ~ ℓ ~ 5nm
Cronin and McMorran, PRA 74 (2006) (R)

32. 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

33. Lau interferometer – fringe contrast vs. grating separationML S y G1 x A G2 z
CCD
z12 z

34. Lau interferometer – fringe contrast vs. grating separation
Cronin and McMorran, PRA (R) (2006)

35. Lau interferometer –twist gratings to measure coherencey G1 x G2 z
GSM source z0 z1 θ z2 z3
Lau fringe visibility

36. Lau interferometer – fringe contrast vs. grating rotation
alignment sensitivity depends on coherence parallel to grating slits
ℓ0 ≈ 10 nm

37. 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 < 80µm
v = 1 km/s: λ = 4.0Å S1 < 400µm
T = 4K  Δvx = 260m/s

39. position echo interferometer

40. position echo interferometer?
Mach-Zehnder
position echo

41. 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

42. position echo interferometer?

43. NEEDS FURTHER STUDY WITH REALISTIC PARAMETERS
position echo interferometer?
NEEDS FURTHER STUDY WITH REALISTIC PARAMETERS

44. matter wave fringes can be formed with uncollimated beams
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