1. An Extremely Brief Overview of the State of the Art of
Maxwell Gregoire
Atom Interferometer Gyroscopes
2. What is a gyroscope?
● A device for measuring the rotation rate (or any
time derivatives thereof) of its own reference
frame
3. Applications: Navigation
● Compare satellites to a drag-free test mass
– Solar wind, atmospheric drag
– Important for experiments that reference trajectories
● Submarines
– Cannot access GPS
– Less detectable if they
don't have to ping
● Aircraft and ships
(manned and unmanned)
– Not vulnerable to cyber
attack if they don't need GPS
4. Applications: Geophysics
● Measure wobble in Earth's rotation rate
due to
– Precession and nutation
– Lunar and solar tides
● Measure tidal drag:
– Earth's rotation causes tidal bulge to
“lead” the moon; moon pulls back on
tidal bulge, causes torque on Earth
opposite rotation vector
– Earth's rotation slows
– Moon's revolution slows, moon orbits
further away (Virial Thm: 2T = -V)
5. Applications: General Relativity
● Geodetic effect:
– A vector (ex. angular momentum of gyroscope on a satellite)
is affected by space-time curvature created by a nearby
massive body (ex. Earth).
● Lense-Thirring rotation a.k.a. gravitomagnetic frame-dragging:
– An object (ex. gyroscope on a satellite) rotates due to the
rotation of a nearby massive body (ex. Earth)
● Together, these effects predict
precession of a gyroscope on a
satellite that, classically, should not
happen
6. Applications and Figure of Merit
Sensitivity Quick
Response
Portability
Geodetic effect 10-8
ΩE
absolute X
Frame-dragging 10-10
ΩE
absolute X
ΩE
wobble 10-8
ΩE
change in ΩE
per day
Tidal drag 10-13
ΩE
change in ΩE
per year
Navigation 10-3
ΩE
absolute X X
Earth's rotation rate ΩE
= 7.3∙10-5
7. Polarizability Measurements
In our lab, the Earth's rotation...
● changes measured static polarizability by up to 1%
– Target accuracy is 0.2%
● changes measured magic zero wavelength by 200 pm
– Target accuracy is < 1 pm
E
d
valence electron cloud
nucleus
U = -α E2
/2
8. Atom Interferometer
L, T = L/v L, T = L/v
● Interference pattern forms at
position of 3rd grating
● Sweep 3rd grating in +/- x
direction: grating bars either
block or admit “bright spots”
area A
v, λdB
z
x
(not all diffraction orders are shown)
P
Detector
9. Atom Interferometer
L, T = L/v L, T = L/v
● Measure phase and contrast of
interference pattern
● Contrast = (max-min) / (max+min)
area A
v, λdB
z
x
(not all diffraction orders are shown)
P
Detector
max
min
phase
10. Atom Interferometer
phase Φ = k · [– 2Δx2(T) + Δx3(2T)]
L, T = L/v L, T = L/v
● k: grating “reciprocal lattice vector” a.k.a kx given to atom
in 1st order diffraction
● Δxi: how much grating i has moved since atom hit first
grating
area A
v, λdB
z
x
Detector
11. Atom Interferometer
phase Φ = (2π/d) · [– 2Δx2(T)+ Δx3(2T)]
L, T = L/v L, T = L/v
● d: grating period
● Δxi: how much grating i has moved (in x direction) since
atom hit first grating
area A
v, λdB
z
x
Detector
12. The Sagnac Effect
● grating period d
Φsag = (2π/d) · [0 – 0 + (ΩL)(2L/v)] = … = 4πΩA / λdBv
L, T = L/v L, T = L/v
phase Φ = (2π/d) · [– 2Δx2(T)+ Δx3(2T)]
area A
v, λdB
Ω
z
x
Detector
13. Atoms vs Light: response factor matters
● Response factor: Φsag/Ω
● In general, Φsag/Ω = 4πA / λv
● Φsag
atom = λlightc = mc2 ≈ 1011
Φsag
light λdBv ħv
That said, number of atoms matters
● In shot-noise limit: δΩ = δΦ = Ω
Φsag/Ω ΦsagC√N
When statistics are Gaussian
17. Dynamic range
With Sagnac shift...
● Sagnac shift is v-dependent:
– Atoms disperse in x
– Causes contrast loss
– Oh no! Whatever shall we
do?
P
x position along 3rd
grating
slow
fast
slow
fast
18. Dynamic range
With Sagnac shift, apply static,
non-uniform E
● Field pulls slower atoms more, in
opposite direction of Sagnac
shift
● Recovers contrast
● Measure Ω by maximizing
contrast
+
P
x position along 3rd
grating
cylinder, axis into page
