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

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Presentation on theme: "Matter wave interferomery with poorly collimated beams x [µm] Ben McMorran, Alex Cronin Department of Physics x [µm]"— Presentation transcript:

1 Matter wave interferomery with poorly collimated beams x [µm] Ben McMorran, Alex Cronin Department of Physics 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 C 60 interferometer Lau electron interferometer 3. grating alignment sensitivity 4. ideas for g measurement using uncollimated beam

4 partially coherent optical field

5

6 intensity I(x) complex degree of coherence µ(x)

7 … 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)

8 Mutual Intensity Function: Intensity: (ρ a,z) (ρ b,z)

9 Mutual Intensity Function: Intensity: GSM: w0w0 σ0σ0 ρaρa ρbρb

10 Mutual Intensity Function: Intensity: GSM:

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

12

13

14

15 a second grating in the far field

16

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  m) path separation.

18 gratings for matter waves 100nm 1.5µm

19 Second Grating Optical Grating

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

21 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: (2008) ℓ > d  coherent diffraction θ diff / α = 10  resolved diffraction but β = ℓ/S1 ~ 0.1  partially coherent

22 Atom Diffraction: Atom Interference Fringes:

23 Atom Interferometer

24 Atom fringes intensity

25

26 add a second grating

27 “Talbot-Lau fringes”

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

29 add a second grating

30 coarse fringes in the far field: “Lau fringes”

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

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 z 12 A z ML S G1 G2 x y z CCD Lau interferometer – fringe contrast vs. grating separation

34 Cronin and McMorran, PRA (R) (2006)

35 Lau interferometer –twist gratings to measure coherence z0z0 G1 G2 x y z z1z1 z2z2 z3z3 θ GSM source  Lau fringe visibility

36 Lau interferometer – fringe contrast vs. grating rotation alignment sensitivity depends on coherence parallel to grating slits ℓ 0 ≈ 10 nm

37 some figures: antihydrogen incident on 1µm period gratings 1m from source: v = 10 km/s:λ = 0.4ÅS1 d) v = 5 km/s:λ = 0.8ÅS1 < 80µm v = 1 km/s:λ = 4.0ÅS1 < 400µm T = 4K  Δv x = 260m/s

38

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

44 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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