Absolute gravity measurements with a cold atom gravimeter

Transcription

1 Absolute gravity measurements with a cold atom gravimeter Anne Louchet-Chauvet, Sébastien Merlet, Quentin Bodart, Tristan Farah, Arnaud Landragin, Franck Pereira Dos Santos LNE-SYRTE Observatoire de Paris

2 Outline Introduction to Raman interferometry Principle of the cold atom gravimeter Systematic effects Coriolis acceleration Optical wavefront aberrations Test of accuracy: comparison

3 Mach-Zehnder atomic interferometer mirrors and beam splitters for matter waves: a,p a,p b,p+ћk eff T T π/2 π/2 π Optical interferometer: Intensity modulation Atomic interferometer: Quantum state at the output Pp p + = 1 1 C cos Φ k eff 2 h ( )

4 Stimulated Raman transitions 87 Rb simplified atomic level scheme 87 Rb 5P 3/2 i> Example: beam splitter for matter waves, with a π/2 Raman transition k nm 5S 1/2 k 1, ω 1 k 2, ω 2 F=2 = b GHz F=1 = a a, p hk eff =h(k 1 -k 2 ) 2-level system Rabi oscillations Transition probability Pulse duration (µs) k 2 Two-photon Raman transition: Momentum state is labeled by quantum state Contra-propagating Raman transition separates the two wavepackets of each atom

5 Outline Introduction to Raman interferometry Principle of the cold atom gravimeter Systematic effects Coriolis acceleration Optical wavefront aberrations Test of accuracy: comparison

6 p z 0 T 2T π/2 p A p+ ħ k eff II C D Sensitivity to acceleration I π π/2 B t α p β p+ ħ k eff Phase difference of lasers imprinted onto the atomic wave during Raman transitions: φ ( t) = ω eff t k z( t) + ϕ ( t) eff eff Pulse 1 Pulse 2 Pulse 3 z = 0 1 z( T ) = gt 2 z( 2T ) = 2gT 2 2 Interferometer phase shift : Φ Φ = Φ = = k Φ II I ( φ φ A C B D eff gt 2 + φ ) ( φ ) + δφ noise + δφ systematics

7 Experimental setup Raman 1 Raman 2 Seismometer v(t) φ vib S 2D-MOT 3D-MOT 10 7 Rb atoms T atoms ~2 µk PC k eff gt² π/2 Output state detection π π/2 atom interferometer Mirror Passive isolation platform Interferometer Typical sensitivity: 6x10-8 1s k eff gt² + φ vib S Best sensitivity, at night: 1.4x10-8 1s displacement of mirror induces a displacement of the equiphase planes

8 2 nd generation drop chamber 1.4m Goal: relative accuracy of 10-9 g = 1µGal Gravimeter transportable (invert North-South orientation in 2 hours) Back-reflecting mirror inside the chamber and of better quality

9 Outline Introduction to Raman interferometry Principle of the cold atom gravimeter Systematic effects Coriolis acceleration Optical wavefront aberrations Test of accuracy: comparison

10 Coriolis acceleration Ω k eff g v Optical molasses power imbalance defines initial transverse speed Non zero transverse velocity sensitivity to the Sagnac effect g (µgal) g = 10-9 g for v 0 = 100 µm.s -1 For T = 2 µk, σ v ~ 1 cm.s -1 = 100 v 0!!! Cloud expansion symmetric around the vertical axis averages Coriolis shift to zero Bias: -1,5 +- 0,5 µgal Normalized molasses power difference (1-R)/(1+R) Invert North South orientation reverses the Coriolis dependence

11 Wavefront aberrations Wavefronts are not flat: gaussian beams, quality of the optics t = 0 δϕ 1 = δϕ(v r =0) v r 0 R Simple case of a curved wavefront δφ = K.r 2 (with K = k 1 /2R) δϕ 2 > δϕ 1 t = T t = 2T δϕ 3 > δϕ 2 ϕ 0 ϕ = 0 δϕ (v = 0) δϕ (v = 0) g < 10-9 g with T = 2 µk R > 10 km! flatness better thanλ/300!!!

12 Wavefront aberrations 300 Old Gravimeter New Gravimeter g (µgal) Temperature (µk) Large reduction of the aberration shift with respect to the first generation experiment

13 Wavefront aberrations 5 22/03 25/05 5 Simulation of the wavefront profile: g (µgal) 0 δg (m.s -2 ) Temperature (µk) Temperature (µk) Fluctuation of the aberration pattern between displacements of the experiment or displacement of the initial position of the cloud Bias: µgal

14 Exploring systematic effects Fluorescence imaging monitoring atomic initial position Selection of horizontal velocity classes Lower atomic temperature (evaporative cooling) Reduced sensitivity to optical wavefront aberrations

15 Outline Introduction to Raman interferometry Gravimeter principle Systematic effects Coriolis acceleration Optical wavefront aberrations Test of accuracy: comparisons

16 Comparison April 2010 in Trappes FG5#209 g (µgal) CAG IMGC µgal MJD

17 Comparison April 2010 in Trappes 00:30 00:35 00:40 FG5#209 Earthquake in China (6.9) on April 13th δg (µ Gal) g (µgal) CAG MJD IMGC µgal MJD

18 Results of the comparison 880 Reproducible differences g (µgal) FG5#209 IMGC-02 CAG GR40 GR8 GR26 GR29 Point on pillar GR Limit of agreement Some systematics not well controlled Accuracy (µgal) s gm (µgal) U (k=2) (µgal) FG5# IMGC CAG

19 Conclusion Cold atom gravimeter, designed for 10-9 g accuracy Good stability over a few days Fluctuations on the long term Some biases are not yet well understood Prospects Control the atomic initial position and velocity by imaging Act on the transverse trajectories by selecting velocity class Cool down the cloud (evaporative cooling)

20 Thanks PhD students Patrick Cheinet Julien Le Gouët Torsten Petelski (UNIFI) Quentin Bodart Post docs Jaewan Kim Tanja Mehlstaubler Nicola Malossi Anne Chauvet Permanent members Sébastien Merlet Arnaud Landragin Franck Pereira Dos Santos