gyroscopes in general relativity · 25-09-2014, pisa gyroscopes in general relativity jacopo belf...

25-09-2014, Pisa

Gyroscopes IN GEneral Relativity

Jacopo Belf

Istituto Nazionale di Fisica Nucleare, Pisa

Congresso Nazionale SIF 2014, Pisa.

Congresso Nazionale SIF 2014, Pisa

J. Belfi, F. Bosi, G. Cella, R. Santagata, A. Di VirgilioINFN Sez. di Pisa, Pisa, ItalyA.OrtolanLaboratori Nazionali di Legnaro, INFN Legnaro (Padova), ItalyA. Porzio and S. SolimenoUniversity of Naples and CNR-SPIN, Naples, ItalyA. Beghi, D. Cuccato, A. Donazzan, G. Naletto, M. PellizzoUniversity of Padova, ItalyG. SaccorottiINGV sez. di Pisa, ItalyN. Beverini, B. Bouhadef, M. Calamai, G. Carelli, E. MaccioniUniversity of Pisa and CNISM, Pisa, ItalyM. L. Ruggiero and A. TartagliaPolit. of Torino and INFN, Torino, ItalyK. U. Schreiber and A. GebauerTechnische Universitaet Muenchen, Forschungseinrichtung Satellitengeodaesie Fundamentalstation Wettzell, 93444 Bad Koetzting, GermanyJ-P. R. Wells, R HurstDepartment of Physics and Astronomy, University of Canterbury, New Zealand

The collaboration

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



“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)“

LAGEOS+GRACE (2004-2007): Dragging 10%

GRAVITY PROBE B (2004-2007): Geodetic 0.28% Dragging 19%

LARES (2012-) expected 1-2% on Frame Dragging

δ Ω≃GMc2 R

ΩE sinθ eθ+G

c2 R3 J EΩE [ jE−3( jE⋅ur) er ]

Space-Test

On ground

6.9810−10ΩE

2.31⋅10−10ΩE

Rotations in GR

Testing GR with a very accurate measurement of Earth's rotation rate

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)

ΩE

Local rotationmeasurement

“Inertial-frame” rotation measurement

ΩE '

3-axialRing-Laser

GINGER (Gyroscopes In General Relativity)

QuasarsF. Bosi et al., Phys. Rev. D 84, 122002 (2011)

Motivations

In space the observer is in geodetic motion (free fall) In a ground laboratory the observer is in a non inertial motion

Metric is tested on different length scales (planetary meter-scale) →

Absolutely different interpretation, no need of gravitational feld not necessary

Multidisciplinarity (Geodesy, Geophysics)

GINGER (Gyroscopes In General Relativity)

3-axialRing-Laser

Quasars

Δ fSagnac=4 APλ

Ω∘ n

No moving masses

No signal for a linearly acceleratingreference-frame

L > 1 m Earth rotation is the bias→ !

δΩ shot =c P

4 AQ ( h νT2Pout t )

1 /2

Low cavity losses High power Large size

Sagnac effect

ω

ΔL

Δ tSagnac=4 Ac2 Ω∘ n

Quantum limitResonant cavity

Ω

Ω


Sagnac Interferometers

Advantages

State of the art: the “G” ring laser

DaysGEODESY

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)

Wettzell observatory (GE)

Use a tri-axial gyro, no absolute orientation is required. Measure the vector modulus.

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)

Δ f i=4 A i

P i λ i

Ω⋅n i+syst .|δΩ||ΩE|

⩽10−10

GINGER key-points


How to do better than G-Wettzel?

[Hz]

[Hours] J. Belf et al., Applied Physics B, 106(2):271-281. (2012)

G-Pisa Ring Laser

Δ f s=K R (1+K A)Ω+Δ f 0+Δ f bsA. Velikoseltsev, PhD thesis (2005)

P(3)(E1,2)=−2iμab

2

γab∫−∞∞

χ1,2(v )ρ(2)(v , E1,2)dv

P(E1,2)

I2

rb

rc

ra r

d

a

b c

d

I1

Sagnac

Ring laser “hacking”

Opposite beams dynamics

I 1=α1 I 1−β I 12−θ2 I 2 I 1+r2√ I 1 I 2 cos(ψ−ϵ2) ,

I 2=α2 I 2−β I 22−θ1 I 2 I 1+r1√ I 1 I 2cos(ψ+ϵ2) ,

ψ=ωs+τ1 I 1−τ2 I 2−r2√ I 2

I 1

sin (ψ−ϵ2)−r1√ I 1

I 2

sin(ψ+ϵ1)

Active medium He+20Ne+22Ne

A. Beghi et al. Applied Optics 51, 31 (2012)

Study of systematics


INFN lab in S. Piero a Grado, Pisa

Max signal orientation:fs=155.5 Hz

S (t)=|a1 E1(t )+a2E2(t)2|

V 1(t )=|b1E1(t)+c21E2(t )2|

V 2(t)=|b2 E2(t )+c12E1(t)2|

Observables

ξ1,2 :Optical detuningsp :Gas pressureT Ne : Atomic temperaturek20,22 : Isotopic ratioμ1,2: cavity total lossesG : single pass gain

Calibration parameters

Allan DEV of AR2 (upper curve) and EKF (lower curve) rotational frequency estimates. The straight line represents the shot noise level of G-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.

D. Cuccato et al. Metrologia 51, 97, (2014)

Kalman filter on real data

G-Pisa shot noise


Tri-axial measurement of the Earth rotation down to LT implies:

Octahedral shapeRigidity can be obtained by locking internal degrees of freedom: 3 diagonals + 4 cavity perimeters

f Si=4 A i

P i λ i

Ω⋅n i+syst . |δ f i||f i|

<10−10

S

Systematics are strongly diluted if L>4 m → Sensor stability limited by Geometrical stability

GINGER geometry problem


The only linear contribution to the perimeter length comes from E

1

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

Single ring geometry “controllability”Scope: Adjust the beam path to the regular square shape

Strategy

12 degrees of freedom

-6 d.of. (Rigid body)

= 6 d.of. (Cavity deformation) E1E2

E3 E4

E5

E1E2

E3 E4

E5E6

Basic IdeaInject the 2 Fabry Pérot cavities with an external laser

Measure the 2 absolute lengths

Set them equal by controlling mirrors positions

LEinc

ErefEref

Etrans

R1 R2

(r1,t1) (r2,t2)

ΨR=2cos−1(1−

Lr)

Φn=dielectric phase shift∼π

f n=c2L

[n+ΨR+Φn]

Use a single laser for both the two cavities

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∼1m


Diagonal cavities length control: GP2 RLG

GP2

Ei(t )=E0 exp {i [ω0 t+α sin (ω A t )+βsin (ωB t+Δ sin (ωC t )) ] }

ω0∼474THzωA∼10MHzωB∼m ˙FSR∼1GHzωC∼10 kHz

(carrier lock modulation)

(sidebands res.)

(lock-in detection mod.)

(optical frequency)

He-Ne-Iodine Reference Laser: Stability 10-11 (t=100 s)

B.S.

P.D.

F.P.

ωA

ωC

S carrier

S side

+α sin (ω A t )

βsin (ωB t+γ sin (ωC t ) )

EOMfsbLaser

Diagonals interrogation scheme

Optical-bench testCavity lock error signal

Sideband lock error signal

Blue line: cavity 1, red line: cavity 2. Thick trace: temperature of the lab.

Residual displacement noise

Closed loop performances

Correction signals

Cavity 1

Cavity 2

The two contributions from Gouy's phase and dielectric shift cancel out for equal mirrors and n

D should be an integer number

Frequency countings for the FSR estimation (70 min each)

The estimated mean valueof the mode number difference isn

D = 7427.4 ± 1.6

Accuracy on the length difference

δD = (λ/2) · δnD 500nm.∼

Expected improvementsHigher fnesse, Controlled environment, Lower noise in the electronics

Absolute length unbalance

(Accepted for publication in CQG)

6m in side-length

Tri-axial

Active stabilization

Experimental results

GINGER aims at a fully complementary test of the Earth's Frame Dragging.

Control of laser dynamicsStudy 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

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

Key points

Next

Conclusion

gyroscopes in general relativity · 25-09-2014, pisa gyroscopes in general relativity jacopo belf...

Documents