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 1991-2004 group of David E. Pritchard at MIT 2004 - group of A. Cronin at Univ. of Arizona

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 ….

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.

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

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

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

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)

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

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

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

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

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, 180405, 2008) |k, g> |k + 4kL, g> kL Raman p>1 not directly possible without changing the frequency of the lasers or applying additional pulses

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

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

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  10-10 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 !

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

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 ?

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

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

H. Mueller et al (Phys. Rev. Lett. 100, 180405, 2008)

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