25-09-2014, Pisa Gyroscopes IN GEneral Relativity Jacopo Belf Istituto Nazionale di Fisica Nucleare, Pisa Congresso Nazionale SIF 2014, Pisa.
The collaboration J. Belfi, F. Bosi, G. Cella, R. Santagata, A. Di Virgilio INFN Sez. di Pisa, Pisa, Italy A.Ortolan Laboratori Nazionali di Legnaro, INFN Legnaro (Padova), Italy A. Porzio and S. Solimeno University of Naples and CNR-SPIN, Naples, Italy A. Beghi, D. Cuccato, A. Donazzan, G. Naletto, M. Pellizzo University of Padova, Italy G. Saccorotti INGV sez. di Pisa, Italy N. Beverini, B. Bouhadef, M. Calamai, G. Carelli, E. Maccioni University of Pisa and CNISM, Pisa, Italy M. L. Ruggiero and A. Tartaglia Polit. of Torino and INFN, Torino, Italy K. U. Schreiber and A. Gebauer Technische Universitaet Muenchen, Forschungseinrichtung Satellitengeodaesie Fundamentalstation Wettzell, 93444 Bad Koetzting, Germany J-P. R. Wells, R Hurst Department of Physics and Astronomy, University of Canterbury, New Zealand Congresso Nazionale SIF 2014, Pisa
Outline GINGER experiment Ideas, motivations and requirements Ring Laser Gyroscopes Sagnac effect State of the art Experimental Activity Earth's rotation measurements Sensor model and noise fltering Interferometric control of the cavity geometry Outlook and conclusion Congresso Nazionale SIF 2014, Pisa
Rotations in GR The axis of a gyroscope will precess following the curvature of the local space-time due to: Earth's Mass (Geodetic precession) and Earth's Rotation (Lense-Thirring or Frame Dragging) Space-Test LAGEOS+GRACE (2004-2007): Dragging 10% GRAVITY PROBE B (2004-2007): Geodetic 0.28% Dragging 19% LARES (2012-) expected 1-2% on Frame Dragging On ground δ Ω GM G ^ Ω sin θ e + J Ω E [ j^e 3( j^e u^r ) e^r ] θ E 2 2 3 E c R c R 6.98 10 10 Ω E Congresso Nazionale SIF 2014, Pisa 2.31 10 10 Ω E
GINGER (Gyroscopes In General Relativity) Testing GR with a very accurate measurement of Earth's rotation rate F. Bosi et al., Phys. Rev. D 84, 122002 (2011) Quasars 1: from IERS (International Earth Rotation and Reference System Service) system (inertial reference frame) 2: from an ultra sensitive Gyroscopes array based underground (dragged reference frame) Inertial-frame Ω E rotation measurement 3-axial Ring-Laser rotation Ω E ' Local measurement
GINGER (Gyroscopes In General Relativity) Motivations In space the observer is in geodetic motion (free fall) In a ground laboratory the observer is in a non inertial motion Quasars Metric is tested on different length scales (planetary meter-scale) Absolutely different interpretation, no need of gravitational feld not necessary Multidisciplinarity (Geodesy, Geophysics) 3-axial Ring-Laser
Sagnac Interferometers Sagnac effect ω Ω ΔL 4A Δ t Sagnac= 2 Ω n c Advantages No moving masses No signal for a linearly accelerating reference-frame L > 1 m Earth rotation is the bias! Resonant cavity Ω 4A Δ f Sagnac = Ω n Pλ Quantum limit c P h νt δω shot = 4 AQ 2P out t ( Low cavity losses High power Large size Congresso Nazionale SIF 2014, Pisa 1 /2 )
State of the art: the G ring laser Wettzell observatory (GE) GEODESY Days Diurnal (Oppolzer) K.U.Schreiber, et al., J. Geophys. Res.. 109, B06405 (2004) Annual (circular)+chandler (elliptical) Wobble T=432 s.d. K.U.Schreiber, et al., PRL. 107, 173904 (2011)
GINGER key-points How to do better than G-Wettzel? Use a tri-axial gyro, no absolute orientation is required. Measure the vector modulus. Δf i= 4 Ai P i λi n^ i +syst. Ω δ Ω Ω E 10 10 Geometry of the ring must be controlled actively (optical frequency references) Local ground rotational noise must be low (underground lab.) Minimize laser dynamics non-reciprocal effects (L>6m)+modeling Calibration procedure w.r.t. local space-time (external metrology) Congresso Nazionale SIF 2014, Pisa
G-Pisa Ring Laser Δ f s =K R (1+K A )Ω+Δ f 0 +Δ f bs [Hz] A. Velikoseltsev, PhD thesis (2005) J. Belf et al., Applied Physics B, 106(2):271-281. (2012) [Hours]
Ring laser hacking Sagnac A. Beghi et al. Applied Optics 51, 31 (2012) I1 b c rb I2 rc ra P( E1,2 ) rd d a Active medium He+20Ne+22Ne 2 2i μ (3) (2) ab P ( E 1,2 )= γ χ (v )ρ (v, E 1,2) dv 1,2 ab Opposite beams dynamics I 1=α1 I 1 β I 21 θ2 I 2 I 1 +r 2 I 1 I 2 cos( ψ ϵ2 ), I 2=α 2 I 2 β I 22 θ1 I 2 I 1 +r 1 I 1 I 2 cos(ψ+ϵ2 ), ψ =ω s + τ 1 I 1 τ 2 I 2 r 2 I2 I1 sin (ψ ϵ2 ) r 1 sin( ψ+ ϵ1 ) I1 I2
Study of systematics Max signal orientation: fs=155.5 Hz Observables 2 S (t)= a1 E1 (t )+a2 E 2 (t) 2 V 1 (t )= b1 E1 (t)+c 21 E 2 (t ) V 2 (t)= b2 E 2 (t )+c 12 E 1 (t)2 Calibration parameters INF S. P N lab i iero n ag rad o, P isa Congresso Nazionale SIF 2014, Pisa ξ1,2 : Optical detunings p : Gas pressure T Ne : Atomic temperature k 20,22 : Isotopic ratio μ 1,2 : cavity total losses G : single pass gain
Kalman filter on real data G-Pi s a sh ot n o ise Allan DEV of AR2 (upper curve) and EKF (lower curve) rotational frequency estimates. The straight line represents the shot noise level of G-PISA D. Cuccato et al. Metrologia 51, 97, (2014) Congresso Nazionale SIF 2014, Pisa Histograms of the estimates of AR2 (pale gray) and EKF (dark gray) during 2 days of G-PISA data. Red line: is the expected Sagnac frequency due to Earth rotation, Dotted lines represent its residual uncertainty bounds due to geometric and orientation tolerances.
GINGER geometry problem Tri-axial measurement of the Earth rotation down to LT implies: f Si = 4 Ai P i λi n^ i +syst. Ω S δ f i 10 <10 f i Systematics are strongly diluted if L>4 m Sensor stability limited by Geometrical stability Octahedral shape Rigidity can be obtained by locking internal degrees of freedom: 3 diagonals + 4 cavity perimeters Congresso Nazionale SIF 2014, Pisa
Single ring geometry controllability Scope: Adjust the beam path to the regular square shape 12 degrees of freedom -6 d.of. (Rigid body) = 6 d.of. (Cavity deformation) The only linear contribution to the perimeter length comes from E1 Strategy Block the diagonal cavity lengths to the same value (FP intrf.) [(E1,E5), E2] Optimize the residual 4 quadratic d.o.f. [E3(-), E4(-), E5(+), E6(+)] at the saddle point for the perimeter E1 E2 E3 E4 E1 E3 E5 E5 E2 E4 E6
Diagonal cavities length control: GP2 RLG Basic Idea Inject the 2 Fabry Pérot cavities with an external laser Measure the 2 absolute lengths Set them equal by controlling mirrors positions GP2 (r1,t1) (r2,t2) L Einc Etrans Eref R1 R2 Use a single laser for both the two cavities f n= c [n+ Ψ R +Φn ] 2L L 1 Ψ R =2 cos (1 ) r Φn =dielectric phase shift π 1) Lock the cavities to the laser (Pound-Drever-Hall) (set optical resonance frequency) 2) Measure the FSR (tuning FM side-bands to a multiple m of FSR) δ FSR Congresso Nazionale SIF 2014, Pisa 1 m
Diagonals interrogation scheme {[ Ei (t )=E 0 exp i ω 0 t +α sin ( ω A t ) +β sin ( ω B t +Δ sin ( ω C t ) ) ]} ω0 474 THz (optical frequency) ω A 10 MHz (carrier lock modulation) ω B m FSR 1 GHz (sidebands res.) ωc 10 khz (lock-in detection mod.) EOM fsb Laser He-Ne-Iodine Reference Laser: Stability 10-11 (t=100 s) P.D. α sin ( ω A t ) F.P. B.S. ωa + S carrier ωc β sin ( ω B t + γ sin ( ω C t ) ) S side
Optical-bench test Cavity lock error signal Sideband lock error signal
Closed loop performances Residual displacement noise Cavity 1 Cavity 2 Correction signals Blue line: cavity 1, red line: cavity 2. Thick trace: temperature of the lab.
Absolute length unbalance The two contributions from Gouy's phase and dielectric shift cancel out for equal mirrors and nd should be an integer number Frequency countings for the FSR estimation (70 min each) The estimated mean value of the mode number difference is nd = 7427.4 ± 1.6 Accuracy on the length difference δd = (λ/2) δnd 500nm. (Accepted for publication in CQG) Expected improvements Higher fnesse, Controlled environment, Lower noise in the electronics
Conclusion GINGER aims at a fully complementary test of the Earth's Frame Dragging. Key points 6m in side-length Tri-axial Active stabilization Experimental results Control of laser dynamics Study of the non-linearities (numerical model) EKF approach 10-fold increase in accuracy and stability of G-Pisa data Control geometrical scale factor (Test bench for diagonals locking) Development of the laser source, Stable lock to the carrier (10-11), Accuracy on the length difference of 500 nm Next Installation of GINGER-ino (L=3.6 m) in G-Sasso Underground Lab, Application of the geometry control to GP2 (L=1.6 m) in Pisa