Construction of an absolute gravimeter using atom interferometry with cold 87. Rb atoms

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1 Construction of an absolute gravimeter using atom interferometry with cold 87 Rb atoms Patrick Cheinet Julien Le Gouët Kasper Therkildsen Franck Pereira Dos Santos Arnaud Landragin David Holleville André Clairon

2 Summary Use of the gravimeter: The Watt Balance Principle of our gravimeter, atom interferometry Lasers frequency locks Sensitivity to phase noise Sensitivity to vibrations and rejection method Advancement : the traps Conclusion

3 The Watt Balance project Objective : Why : Mass metrology: Principle : replace the standard Kg with a definition linked to the Planck s constant h the standard Kg is the last artifact of the international system, observed drift on the primary and secondary standards of Kg over 3 years goal of 1-8 of relative precision Balance a mechanical power with an electrical power BIPM standard Kg

4 The Watt Balance project L F Laplace = i L B statical Phase i B F g = m g B i L = m g Dynamical Phase constant speed motion v L E = B L v m g v = E i m Planck s B Constant Josephson Frequency = k f g J v h Necessity of a precise g mesurement

5 General Principle Raman laser Beams 87 Rb atoms cooled In a D-MOT 1 9 to 1 1 atoms.s atoms trapped in 1 ms Cooled to a few µk In a 3D-MOT State selection 5S 1/, F=1, m F = > Push beam π/ Detection π π/ Raman laser Beams Raman pulses T=1 ms Total interaction time = interferometer Φ = k eff.g.t

6 5P 3/ > GHz 5S 1/ > e 3 > e > e 1 > e > virtual state i > 78 nm Stimulated Raman Transitions 87 Rb f > 6.8 GHz δ => Doppler cooling Detection k k 1 p = k k 1 - k k 1 k opt Transition Probability During the transition, the atom takes two photon recoils and change its trajectory π/ pulse : Atomic beam Splitter The lasers couple the f 1 > and f > states in a quantum superposition => Rabi oscillations π/ π Ω Rabi τ π pulse : Atomic mirror f 1 > Raman Trapping same lasers for trapping and Raman

7 Optical Bench 1 single bench for cooling and Raman pulses F or φ-lock ECL3 MOPA 1 F-LOCK ECL MOPA 6.8 GHz Réf HYPER 4.8 à 6.8 GHz (YIG) ECL1 DETECTION AOM Locked on spectroscopy line TRAPS RAMANS

8 Transition to φ-lock Error Signal (MHz) GHz Sweep in 8µs, lasers unlocked Master Repumper YIG Frequency change (MHz) Fixed ramps applied on lasers controls Error Signal (MHz),5, 1,5 1,,5, -,5-1, -1,5 -, GHz Sweep in 8µs, lasers locked Master Repumper YIG Frequency change (MHz) Time (ms) -, Time (ms) 8 Phase error (mrad) ms to sweep by GHz 3 ms to reach the 1 mrad level Time (ms)

9 87 Rb Atomic interferometer ϕ 1 (t) = k 1 z(t) + ϕ 1 (t) 5P 3/ > GHz i > π/ φ( ) = φ(t) = ϕ (t) ϕ 1 (t) is printed on the atomic phase 78 nm π π/ 1 φ( T ) = keff gt φ( T ) = k gt eff Interferometer s phase shift Φ = φ ( ) φ ( T ) + φ(t ) 5S 1/ > f > 6.8 GHz f 1 > P 1+ cos( Φ) = Φ = k eff ϕ (t) = k z(t) + ϕ (t). g. T + φ () φ ( T ) + φ (T ) T=5ms => ~1 6 rad

10 Transfer function H(ω) for laser phase noise Sϕ(ω) σ Φ = H(ω) Sϕ(ω)dω Phase power spectral density Theory (T=5ms): H(f)² Experiment (gyroscope) 1 1,1,1 Theory Experiment 1 1E-3 1 1E Frequency (Hz) <H(f) >,1,1 /(πf/ω) 1 1 1E Frequency (Hz) H(f),1,1 1E-3 4iωΩ H ω) = ω Ω ( ω( T sin( + τ R ) ω( T )(cos( + τ R ) Ω ωt ) + sin( )) ω 1E Frequency (Hz)

11 Two possible sources: Raman laser phase noise Reference frequency phase stability: 1. mrad Estimated for state of the art quartz oscillator Residual noise of the Phaselock loop: σ Φ = 1E-8 Experimental result Weighted with H(ω): T=1ms and τ=1 µs σ Φ =1.3 mrad σ Φ Total contribution: = 1.75 mrad => 9 ng/shot Sφ(f) (rad.hz -1 ) 1E-9 1E-1 1E-11 1E E7 Frequency (Hz)

12 phase/position δφ <=> k eff δz Sensitivity to vibrations σ Φ = ω H ( ) keff Sa( ω) dω ω 4 acceleration noise (m s -4 /Hz) 1E-9 1E-1 1E-11 1E-1 1E-13 1E-14 1E-15 Noise level in the lab Weighted noise 1E-16, Frequency (Hz) Required vibration noise level (>.3 Hz) : 1 ng/hz 1/ Up to 8 Hz : Need for vibration isolation and compensation

13 Vibration rejection Act on the Raman phase difference to compensate for vibrations Seismometer Interferometer PLL ECL Method tested on auxiliary experiment H A A? J E * Raman laser N / # 4 A B & " = 8 +! - +, ),, )?? 6 B!!! With a seismometer

14 D-MOT Detection Photodiode Progress report 3D-MOT trapping lasers Cold atoms 5x1 8 3D-MOT D-MOT flux density (at.m -1 ) 4x1 8 3x1 8 x1 8 1x1 8 Atoms loaded,x1 9 1,5x1 9 1,x1 9 5,x speed (m.s -1 ) D-MOT total flux =1 1 atoms.s -1,,,5 1, Time (s) 3D-MOT loading rate = atoms.s -1

15 Conclusion Expected sensitivity : 1-9 g after a few seconds Expected accuracy : 1-9 g - Cold atom sources obtained - Raman lasers phase-locked -First atom interferometry signals: early 5 Limited by vibrations Preliminary vacuum chamber => test the system -Implement the vibration isolation platform and the vibration rejection

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