Atom Interferometer Gyroscope

James GreenbergUniversity of Arizona Physics

Motivation: Precision Inertial Measurements

Test General RelativityNavigation

Reproduced from Jentsch et al. Gen. Relativ. Gravit. (2004)

From http://marsrover.nasa.gov/

From http://www.jhartfound.org/

http://www.nasa.gov/mission_pages/gpb/

Atom Interference Fringes

1G 2G 3G

Atom Beam

p = grating period =

Measurements: Phase and Contrast

ΔΦ

V

𝐶=max−minmax+min

Atom Beam

1G 2G 3G

1G 2G 3G

𝑣<𝑣0𝑣=𝑣0𝑣>𝑣0

Dispersion Contrast Loss𝑣0

large

𝜃∝ 1𝑣Velocity Distribution

𝜃

Dispersion Compensation

Φ𝐶𝑚𝑎𝑥≠0

Measured Contrast vs. Change in Phase

= Rotation RateL = grating separationp = grating period

Φ𝑆𝑎𝑔𝑛𝑎𝑐=4𝜋 𝐿2Ω𝑣𝑝

Reproduced from Lenef et al. PRL (1997)

Sagnac Phase (Shift)

Φ𝐶𝑚𝑎𝑥<0

From http://www.physicalgeography.net/

= 73rad/s 2.4rad shift

= Rotation RateL = grating separationp = grating period

Φ𝑆𝑎𝑔𝑛𝑎𝑐=4𝜋 𝐿2Ω𝑣𝑝

= 73rad/s 2.4rad shift

Reproduced from Lenef et al. PRL (1997)

Sagnac Phase (Shift)

From http://www.physicalgeography.net/

Acceleration Phase (Shift)Φ𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛=

2𝜋 𝐿2𝑔sin 𝜃𝑏𝑡  𝑣2𝑝

�⃗�𝜃𝑏𝑡

∆ 𝑥

1G

2G

3Gx

z

y

1 board tilt 4 radian phase shift

= Board tilt angleL = grating separationp = grating period

L

Model and Results

-20 mrad -1.15

10% uncertainty

Earth Rotation Rate

If board tilt assumed to be -20 mrad, then:

73 rad/s

13% Uncertainty

Summary of Work

• Determined inertial phase shifts from C() for multiple beam conditions

• Modeled C() data to fit measured • Measured board tilt and Earth rotation rate

codependently with 10% and 13% precision respectively

Thank You!

• Special thanks to:– Dr. Alex Cronin – Maxwell Gregoire– Raisa Trubko– Tyler St. Germaine– UA NASA Space Grant Staff

• Funding from:– NSF– NASA Space Grant