GINGER (Gyroscope IN General Relativity) G-GranSasso R&D...G-GranSasso (Angela Di Virgilio) The Sagnac e ect and the Ring-Laser G in Wettzell GINGER Pisa, LNL, NA, PD, TO in collaboration

GINGER (Gyroscope IN General Relativity)G-GranSasso R&D

Pisa, LNL, NA, PD, TOin collaboration with TUM and LMU and University of

Canterbury (NZ)

July 1, 2012

Pisa, LNL, NA, PD, TO in collaboration with TUM and LMU and University of Canterbury (NZ)GINGER (Gyroscope IN General Relativity) G-GranSasso R&D

G-GranSasso (Angela Di Virgilio)

The Sagnac effect and the Ring-Laser

G in Wettzell

GINGER


The Sagnac Effect

two beams conter-propagating inside a ring of radiusR complete the path at different time if the ring is rotating withangular velocity Ω

∆t =4πR2Ω

c2(1)


in a ring-laser the measured quantity is the beat note between thetwo laser modesfb = δν/2 = c2

λP δTwhere P is the length of the path (Perimeter) for a ring laserattached to the Earthδν = 4 A

λP × Ω× [1− 2 µR sin θuθ + GJ⊕

c2R3 (2 cos(θ)ur + sin(θ)uθ)]

pure Sagnac term (Earth Angular Velocity)

Geodetic (de Sitter)

Gravitomagnetic Term (LenseThirring)


The beat note has 3 terms: the Sagnac one, the de Sitter(Geodetic term) and the Gravitomagnetic one (LenseThirring)

The Earth angular velocity is measured with very highaccuracy by VLBI, which measures the Earth rotation withrespect to the fixed stars

the Relativistic terms can be obtained by subctracting

from the ringlaser data the Sagnac term measured by VLBI



Requirements

Required sensitivity 10−14rad/s/√Hz ,

Earth angular velocity measured with accuracy one part in 109

on the surface of the planet

the geometry of the apparatus controlled with accuracy fewparts in 1010

So far, sensitivity and accuracy so high can be obtained byring-lasers only. Very promising instruments based on cold atomsat the moment are not so powerful, and it is commonly assumedthat they will not be able to reach such level in the next decade;by now experiments to measure the de Sitter term only have beenrecently proposed [kasevich et al.].


Gravity-Probe B, LAGEOS/LARES

Gravity probe B (GPB) has obtained a 19% accuracy for theLense-Thirring effect, and a 0.28% the Geodetic precession(de Sitter). These results have been obtained considering thecumulative effect of many orbits and depend on the averagegravitational field along one orbit. Knowledge of thegravito-electric field of the earth is needed (based on themeasurements of the GOCE experiment).

10% has been obtained by measuring the precession of theplane of the orbits of the LAGEOS and LAGEOS II satellitesusing laser ranging. The same technique as above is beingexploited by the LARES dedicated mission, started onFebruary 13th 2012. The expected accuracy for theLense-Thirring effect is in the order of 1− 2%. Both theLAGEOS and LARES results depend on the knowledge of thegravito-electric field all along the orbits of the satellites(GRACE and GOCE experiments).


We stress that, being the whole proposed experiment fixed on thesurface of the Earth, it has a constant gravito-electric (Newtonian)field so it does not need any modelling of the interior of the Earthor of the shape of the planet. Furthermore, all measurements aremade in one and the same reference frame and there is no need oftransporting time and space measurements from elsewhere. Theexperiment is fully local (a part for the comparison with VLBIdata, as explained below); the tested gravito-magnetic field as wellas the coupling between the angular velocity of the Earth and thegravito-electric field are the ones of the laboratory. There is notime and space averaging over scales bigger than the one of thelaboratory.


Question: what is it possible to learn comparing the twokinds of experiments (Space/Earth)?

The experiments in space are based on the precession of physicalgyroscopes induced by the gravitational field in its generalrelativistic form. Indeed the coupling of the angular momentum ofa gyroscope with the gravitational field induces a torque dependingon the configuration and on the features of the field. In the case ofGP-B the angular momentum is the one of four spinning spheres;in the case of LAGEOS and LARES the angular momentum is theone associated with the orbital motion of the satellites. Ourexperiment instead exploits the anisotropic propagation of light inthe screw symmetric space-time associated with rotating bodies.Our technique is thus complementary to the one used in space;furthermore it allows for a terrestrial location, provided the sizeand sensitivity of the ring-lasers is high enough.


High Sensitivity RingLaser and G-Wettzell

G in Wettzel is amonolithic device, made with a huge zerodur block, with mirrorsoptically contacted. A very expensive object, it is not possible tobuilt a new one, and as well it would be impossible to make it 3dimensional, in order to reconstruct the vector of the angularvelocity


Signals and Accuracy

The Shot Noise δωsn = cP4AQ

√hνlWT rad/s


The Environment

An apparatus directly linked to the EarthFundamental Physics, Geodesy and Geophysics

GINGER, un array of ring-lasers underground located


Experimental Work 2012

G-Pisa

New Stabilised Laser

The Perimeter control signal

The Data Acquisition

The Lasr dynamics and the first use of KALMAN filter

Analysis of the Data of G in Wettzell

The model of the Fabry-Perot and the control problem


The Laboratory

G-Pisa has been running more than one year inside the Virgocentral room, and has been moved inside the former CMS cleanroom in S. Piero a Grado. A lot of care has been necessary in orderto restart the functionality of the room itself

unfortunately the table has astrong resonance around 5− 6Hz . It will be necessary to moveG-Pisa on top of a more rigidmonument.

This monument is inpreparation, and we expect toinstall it before august. In thisway we will be less sensitive tolocal tilts, this is the optimalorientation to measure the earthrotation.


Problem of the present set-up in S. Piero

G-Pisa must be moved on top of a stable platformPisa, LNL, NA, PD, TO in collaboration with TUM and LMU and University of Canterbury (NZ)GINGER (Gyroscope IN General Relativity) G-GranSasso R&D

The new reference system

The Iodine stabilized laser (stability of the order of 1 part 1012)hasarrived at the end of 2011 Because the low power of our ring-laser(1 nW ) a lot of care has been necessary in order to have a goodcontrol signal. After a lot of work we have been able to optimizethe signal-to-noise-ratio from less than 4.5 dB up to 27 dB.


The Data Acquisition and contol system

During our stay inside Virgo we have used the Virgo’s acquisitionsystem and for the control a pc/LabView based system. It hasbeen necessary to build up a complete acquisition system based ona PXI, which takes care as well of the controls (two feedbacks:discharge power and perimeter). We need a continuousacquisition, with a bunch of signals at few Hz and 4 channelsat a rate of 5 kHz. We need as well to have a fast access toextract data related to earthquakes. This system, still undertest, has been recently completed. It is as well important tosay that the PXI system is transportable


The Laser Dynamic and the first exercise with Kalman

paper in preparation

I1 =c

L

[α1I1 − β1I 21 − θ12I1I2 + 2r2

√I1I2 cos(ψ + ε)

]I2 =

c

L

[α2I2 − β2I 22 − θ21I1I2 + 2r1

√I1I2 cos(ψ − ε)

](2)

ψ =ωs + σ2 − σ1 + τ21I1 − τ12I2−

− c

L

[r1

√I1I2

sin(ψ − ε) + r2

√I2I1

sin(ψ + ε)

],

The non-constant Lamb parameters are evaluated from themono-beam signals and using the Kalman the apparatus responsecan be improved


Kalman&Control

Work still in progress. Argument in close relation with: Control ofthe Gain Factor and relative alignment of the different rings


Preliminary Results

0 1 2 3 4 5 6107.1

107.15

107.2

107.25

107.3

107.35

107.4

107.45

107.5

107.55

Time [h]

Est

imat

ed S

agna

c F

requ

ency

[hz]

Comparison EKF vs AR2 13/05/2012

EKFAR2


The model of the Fabry-Perot and the control problem

Work still in progress. Argument in close relation with: Control ofthe Gain Factor and relative alignment of the different rings


Interest from Taiwan


3 Years Plan

2012‐1 2012‐2 2012‐3 2012‐4 2013‐1 2013‐2 2013‐3 2013‐4 2014‐1 2014‐2 2014‐3 2014‐4Eliminate/avoid BackscatteringSplit Mode OperationTheory of backscatteringkalman filters application on dataMonolithic by control'definition of observable for controldiagonals study Theorydiagonal study Experimentalperfect square deviceDigital InterferometryStandard InterferometryReconstruction of the angular velocity vectoroctahedron study, property and modelsExperimental, 1microrad resolution3 components installation in Munich5m triangular ring1 or 2 G‐Pisa like installation1 more componentLNGS InstallationObservation of relevance for GEODESYGG‐PISAGermany 3axis componentLNGS Observation of relevance for GEOPHYSICSGG‐PISAGermany 3axis componentLNGSGINGERSite SelectionMechanical DesignOctahedrom, 1 nrad resolution


2013 experimental plan

Experiment in S. Piero with a new ringlaser with improveddesign: 4 piezos, the four diagonals available to makeFabry-Perot cavities,

Installation of G-Pisa inside LNGS (characterization of thelaboratory)

Installation of G-Pisa inside the geophysical observatory ofBaviera (reconstruction of the angular velocity vector)


People

Allegrini 40 Bosi 20

Belfi 100 Maccioni 30

Beverini 50 Terreni 20

Carelli 50 Stefani 30

Cella 20

Di Virgilio 80

Sorrentino 20


People

MI 18

ME 25

Consumi 33

Trasporti 5

Manutenzioni 3

Inventario 45

Costruzione Apparato (up-graded ring)

77

Totale 206kE


Richieste Servizi

3 MU Alte Tecnologie

2 MU Elettronica

2 MU officina


Several Remaks

EU foundings?

make more effective the collaboration with Schreiber and Igel(TUM and LMU) , we will have a meeting in Rome July 6


The Letter of Intent


Documents

GINGER (Gyroscope IN General Relativity) G-GranSasso R&D...G-GranSasso (Angela Di Virgilio) The Sagnac e ect and the Ring-Laser G in Wettzell GINGER Pisa, LNL, NA, PD, TO in collaboration