1. Mach-Zehnder atom interferometer with nanogratings
Front View
Support
bars
Period = 100 nm
The mirrors and beam-splitters of the Mach-Zehnder optical interferometers are replaced by nanograting diffraction
group of David E. Pritchard at MIT
group of A. Cronin at Univ. of Arizona

2. I=I0[1+V sin(+ interaction)] V= 42 %, I0=190 kc/s
PhD Perreault (2005)
This interferometer has been applied to measure:
polarisability of Na
decoherence effects
refraction index of gases for sodium waves
atom – surface van der Waals interaction ….

3. Atomic interferometer with Bragg phase gratings
collimated
atomic beam
exit 1
exit 2
detector
3 laser standing waves L
L= 0.6 m
Beam separation: 100 µm
The mirrors and beam-splitters of the Mach-Zehnder optical interferometers are replaced by Bragg diffraction on laser standing waves
In the Bragg regime, diffraction of order p>1 can be used.

4. Atom interference fringes with 7Li
diffraction order p = 1
counting time = 0.1 s/point
fringe visibility V = 84 %
mean output flux I0 = 24 k c/s
This interferometer has been applied to measure
- electric polarisability of 7Li
- refraction index of gases for lithium waves
- atom – surface van der Waals interaction

5. Mesure de l’interaction de Van der Waals
window
A: both beams pass through the grating
B: one beam pass the grating
C: both beams pass through the window

6. A, E: both beams pass through the grating
B, D: one beam passes through
the grating
C: both beams pass through the window

7. Vary the atom velocity (750 – 3500 m/s)
Interpretation not simple:
for high atom velocities, the atom contributing
to the fringes probes smaller atom- surface
distances
The connection of the phase shift to C3
depends on grating dimensions
(analysis under progress)

8. Atomic interferometer as a gyrometer/accelerometer
T: time of flight between 2 laser beams
kG: grating vector
a: acceleration or Coriolis term 2Wv
f= p kG a T2
f Sagnac = 2 p kG W v T2
facceleration = p kG a|| T2
(kG≈4p/lres)
lres is the first resonance line:
No dependence on the atomic mass
dependence on the atoms only through lres
He* Li
Ne* Na K
87Rb Cs
lres (nm)
1083
671
640
589
770
780
850

9. Spatial/temporal interferometers
f= p kG a W|| v T2
Spatial interferometers: vT= L
(Kasevich, Rasel, )
f L2/v
Temporal interferometers:
(Landragin, Rasel, …)
f v
In both cases, similar dispersion of the
phase with atom velocity

10. Sensitivity to acceleration
acc p kG a T2 a = =
rot p kG W v T2 W v
The use of very slow atoms enhances dramatically the sensitivity to accelerations
 double interferometer with counterpropagating atoms
cancellation of the acceleration phase

11. Raman versus Bragg diffraction
h0
hL
|k, g>
|k + 2kL, g> kL
|k, g>
|k, g1>  |k + k1 + k2, g2>
|k, g>  |k + 2kL, g>
Coupling depends on laser power, detuning … p/2 and p pulses

12. Bragg Raman f= p kG a T2 p=2 or larger |k + 4kL, g> |e> h0 hL
Siu Au Lee’s group and our group: p=3
and H. Mueller et al p=1,..,12
(Phys. Rev. Lett. 100, , 2008)
|k, g>
|k + 4kL, g> kL
Raman
p>1 not directly possible
without changing the
frequency of the lasers
or applying additional pulses

13. Raman
Bragg
(p= 1)
p> 1
Collimation/cooling
to v < vrecoil not really needed
very high flux, but low visibility
Low phase noise (lasers) are needed
Two internal states
Space for improvements ?
Collimation/cooling to
v < vrecoil needed so that interferometer output ports can be separated  low flux
Only one internal state
Several improvements possible
present performance for inertial
measurements much lower than the ones
of Raman interferometers

14. Bragg diffraction based atom interferometer as inertial sensor: State of the art:
The existing interferometers (thermal atoms) with separated beams were not planned for inertial measurements :
Pritchard/Cronin interferometer (Na, material gratings)
Toulouse interferometer (Li, Bragg laser diffraction)
Sensitivity (v= 1000 m/s):
Interferometer
Material gratings
Phase gratings
Rotation
f/p = 4.4 104 W s
f/p = 1.3 104 W s
acceleration
f/p = 22.0 a rad s2 m-1
f/p = 6.7 a rad s2 m-1
Phase sensitivity
Fmin 1/(V I)
4 mrad / Hz
4 mrad/  Hz

15. Be aware of seismic noise ! interferometer stabilisation needed !
What can we do ?
(1) Slow down the atoms:
for v= 10 m/s and L=0.6 m
h= 1.7 cm
Under construction
standing waves h
(2) Increase the atomic flux: x10 (x100 hopefully)
(laser cooling, …) (planned)
Fmin ≈ 0.4 mrad / Hz
 Rotation: f/p = 1.3  106 W s
Acceleration: f/p = 6.7  104 a rad s2 m-1
 Fmin ≈ 0.4 mrad / Hz
p dW  3.1  s-1 Hz-0.5
p da  6.0  10-9 m s-2 Hz-0.5
Be aware of seismic noise !
interferometer stabilisation needed !

16. Interferometer suspension under progress
Suspension by 3 wires under vacuum M3 M2 M1 Li
D.B Newell et al
Rev.Sci.Intr. 68,
3211 (1997)
Horizontal isolation
performance
First measurements
with our pendulum

17. Conclusion How far can we go ?
High precision measurement of the phase induced by
atom-surface van der Waals interaction
We are building:
a new Mach-Zehnder interferometer with a slow and intense beam of lithium,
suspension of the interferometer with servo loops to strongly reduce the seismic noise
Interferometers with separated arms (Bragg diffraction) are interesting for inertial measurements
How far can we go ?

18. Nanograting interferometer
Atomic Interferences
C= 41.6 %, I0= 186 kc/s (PhD Perreault)

19. Bragg Raman p=2 p=2 ? ? f= p kG a T2 |k + 4kL, g> |e> |e> h1
hL
h0
p=2 ? ?
|g2>
|g1>
|k, g>
|k + 4kL, g> kL
f= p kG a T2

20. H. Mueller et al
(Phys. Rev. Lett. 100, , 2008)

22. Mesure de l’interaction de Van der Waals
window
A: both beams pass through the grating
B: one beam pass the grating
C: both beams pass through the window