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

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

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

partially coherent optical field

partially coherent optical field

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

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 …

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

Mutual Intensity Function: GSM: ρa ρb σ0 w0

Mutual Intensity Function: GSM:

Mutual Intensity Function: GSM: partially coherent Fresnel optics

a second grating in the far field

a second grating in the far field

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.

gratings for matter waves 100nm

Optical Grating Second Grating

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

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)

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

Atom Interferometer

Atom fringes intensity

add a second grating

“Talbot-Lau fringes” add a second grating

“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

add a second grating

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

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

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

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

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

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

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

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

position echo interferometer

position echo interferometer? Mach-Zehnder position echo

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

position echo interferometer?

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

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