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Matter wave interferomery with poorly collimated beams

This study explores matter wave interference fringes using uncollimated beams in grating interferometers. It highlights the importance of grating position, spatial coherence, and beam divergence for successful interference. The paper presents a model for partial coherence and wavefront curvature in grating interferometers, along with examples of grating matter wave interferometers.

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Matter wave interferomery with poorly collimated beams

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

  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: Intensity: (ρa ,z) (ρb ,z)

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

  10. Mutual Intensity Function: Intensity: GSM:

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

  12. a second grating in the far field

  13. a second grating in the far field

  14. AtomInterferometer • 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.

  15. gratings for matter waves 1.5µm 100nm

  16. Optical Grating Second Grating

  17. 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

  18. 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:0804.1162 (2008)

  19. 0 1 Atom Diffraction: 3 2 5 4 6 7 Atom Interference Fringes:

  20. Atom Interferometer

  21. Atom fringes intensity

  22. add a second grating

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

  24. “Matter-Wave Interferometer for Large Molecules” Brezger, Hackermüller, Uttenthaler, Petschinka, Arndt, Zeilinger Physical Review Letters 88 100404-1 (2002) L = 1.38m S2 = 0.5mm S1 = 1.2mm α ~ 10-3 θdiff ~ 10-6 ℓ~ 10nm

  25. add a second grating

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

  27. electron interferometery with two gratings aperture magnetic lens grating 1 grating 2 stationary beam 1µm imaging detector α ~ 10-3 θdiff ~ 10-4ℓ~ 5nm Cronin and McMorran, PRA 74 (2006) 061602(R)

  28. Lau interferometer G2 G1 incoherent source • each opening of G1 acts as a point source for a diffraction pattern from G2 • at certain grating separations, diffraction patterns overlap

  29. Lau interferometer – fringe contrast vs. grating separation S ML y G1 x A G2 z CCD z12 z

  30. Lau interferometer – fringe contrast vs. grating separation Cronin and McMorran, PRA 74 061602(R) (2006)

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

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

  33. 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

  34. position echo interferometer

  35. position echo interferometer? position echo Mach-Zehnder

  36. 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

  37. position echo interferometer?

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

  39. 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

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