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
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
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 5.1-8 Kg over 3 years goal of 1-8 of relative precision Balance a mechanical power with an electrical power BIPM standard Kg
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
General Principle Raman laser Beams 87 Rb atoms cooled In a D-MOT 1 9 to 1 1 atoms.s -1 1 8 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
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
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
Transition to φ-lock Error Signal (MHz) 3 5 15 1 GHz Sweep in 8µs, lasers unlocked Master Repumper YIG 15 1 5-5 -1 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 15 1 5-5 -1 Frequency change (MHz) 5-15 5 1 15 5 3 35 4 45 5 Time (ms) -,5-15 1 3 4 5 6 7 8 9 1 Time (ms) 8 Phase error (mrad) 6 4 -.8 ms to sweep by GHz 3 ms to reach the 1 mrad level -4-4 6 8 Time (ms)
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
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-4 1 3 4 5 6 Frequency (Hz) <H(f) >,1,1 /(πf/ω) 1 1 1E-3 1 1 1 1 3 1 4 1 5 1 6 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-4 131 1315 13 135 133 Frequency (Hz)
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-1 1 1 1 1 1 1 1 1E7 Frequency (Hz)
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-16,1 1 1 1 Frequency (Hz) Required vibration noise level (>.3 Hz) : 1 ng/hz 1/ Up to 8 Hz : Need for vibration isolation and compensation
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
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,x1 8 4 6 8 speed (m.s -1 ) D-MOT total flux =1 1 atoms.s -1,,,5 1, Time (s) 3D-MOT loading rate = 3.1 9 atoms.s -1
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