1. Ho Jung Paik University of Maryland GW Astronomy, Korea August, 2016
Terrestrial Tensor GW Detector
Based on Superconducting Instrumentation
Ho Jung Paik University of Maryland GW Astronomy, Korea August, 2016

2. GW detector bandwidths
Missing frequency band
Merger of IMBHs and inspiraling stellar mass BHs are expected to produce signals at 0.1 to 10 Hz bandwidth.
Even if LISA flies, the middle frequency band will be missed.
DECIGO, space interferometer, has been proposed to fill this band.
Could a terrestrial antenna be built to fill this missing band?
Paik

3. Long-baseline resonant-mass detector
In the Newtonian limit,
Gravity gradiometer is a GW detector.
Paik

4. Analyzed three detector options: 1. Atom-laser interferometer
2. TOBA with laser interferometer
3. Michelson interferometer
Low-frequency detector would be astrophysically interesting,
if one can reach Sh½(f ) = 1020 Hz1/2 in Hz band.
Paik

5. Newtonian gravity noise
Seismic and atmospheric density modulations cause Newtonian gravity gravity gradient noise (NN).
At 0.1 Hz, s ~ 35 km >> L.
Gravity gradient noise  L.
Newtonian noise (NN)
Rayleigh wave NN residual
Infrasound NN subtraction
Need to develop more sensitive seismometers and microphones.
NN from infrasound can be mitigated only at certain incident angles.
Detecting and removing NN appears to be extremely challenging.
Paik

6. SGG (Superconducting Gravity Gradiometer)
Sensitive SGGs have been under development for over 30 years at UM.
3 x Hz-1/2
Moody et al., RSI 73, (2002)
Test masses are mechanically suspended (fDM ~ 10 Hz).
CM platform vibration noise is rejected to 3 parts in 108.
By early 1990’s, SGG achieved amplitude sensitivity 102 times better than TOBA and 103 times better than atom interferometers to date.
Paik

7. Tensor SGG with levitated test masses
More sensitive SGG is under development with NASA support.
Test masses are magnetically
suspend (fDM ~ 0.01 Hz).
times higher sensitivity
Test masses are levitated by a current induced along a tube.
Six test masses mounted a cube form a tensor gradiometer.
Paik

8. Improved CM rejection
Sensitive axes are aligned to  10-6 rad in situ using Cryo Linear Actuator PiezoKnobs (Janssen Precision Eng).
CMRR = 106
Residual CM errors are compensated to 10-4.
CMRR = 1010
Intrinsic noise of the SGG for Earth science mission
Paik

9. SOGRO (Superconducting Omni-directional Gravitational Radiation Observatory)
Each test mass has 3 DOF.
Combining six test masses, tensor GW detector is formed.
Source direction (, ) and wave polarization (h+, h) can be determined by a single antenna.
“Spherical” Antenna
x polarization
+ polarization
Paik

10. Antenna pattern  polarization LIGO + polarization
Sky location of GW150914
rms sensitivity
SOGRO
Diagonal
Off-diagonal
Total
Sky location by SOGRO
Paik

11. Design philosophy of SOGRO
Extremely low detector noise is required.
Low T, high Q, nearly quantum-limited amplifier.
Test mass suspension frequency should be lowered to below the signal bandwidth.
Almost free test masses by magnetic levitation.
Seismic noise is very difficult to isolate at low frequencies.
High CM rejection in a superconducting differential accelerometer.
Newtonian noise increases sharply below 10 Hz and cannot be shielded.
Tensor detector can help mitigate the NN.
H. J. Paik, C. E. Griggs, M. V. Moody, K. Venkateswara, H. M. Lee, A. B. Nielsen, E. Majorana and J. Harms, Class. Quantum Grav. 33, (2016)
Paik

12. Suspension of SOGRO platform
Go underground (~ 1 km) to reduce the seismic and Newtonian noise, as well as to be far away from moving objects.
Pendulum suspension
from center
Platform needs to be rigid with all DM modes > 10 Hz with Q > 106.
Careful engineering design is required.
Nodal support prevents odd harmonics from being excited.
25-m pendulum gives fp = 0.1 Hz for two horizontal modes and f < 103 Hz for torsional angular mode, and completely decouples ground tilt.
Provides passive isolation.
Additional passive or active isolation may be needed for vertical direction.
Alternative suspension: Optical rigid body
Simpler cryogenics, larger baseline ( 1 km?)
Paik

13. Magnetic levitation
To provide large area for levitation, test mass is made in the shape of square Nb shell with flanges.
Magnetic field required
to levitate test mass:
Horizontal DM frequencies can all be tuned to 0.01 Hz.
However, due to nonlinearities, strong levitation fields will cause vertical DM frequencies > 0.1 Hz.
Vertical accelerometers will be noisier.
Since the platform is isolated from tilt of the ground, hxz and hyz can also be obtained from horizontal motions of test masses only.
Paik

14. Tuned capacitor-bridge transducer
Near quantum-limited SQUIDs have 1/f noise below 10 kHz.
Signal needs to be upconverted to  10 kHz by using active transducer.
Capacitor bridge coupled to nearly quantum-limited SQUID thru S/C transformer. (Cinquegrana et al., PRD 48, 448 (1993))
Bridge is driven at LC resonance frequency p .
Oscillator noise is rejected by the bridge balance.
Maintain precise balance by feedback.
Paik

15. Achievable detector noise
Parameter
SOGRO
aSOGRO
Method employed (/aSOGRO)
Each test mass M
5 ton
10 ton
Nb square shell
Arm-length L
30 m
100 m
Over “rigid” platform
Antenna temp T
1.5 K
0.1 K
Liquid He / He3-He4 dilution refrigerator
Platform temp Tpl
Qpl = 5  106 / 107
DM frequency fD
0.01 Hz
Magnetic levitation (horizontal only)
DM quality factor QD
5  108
109
Surface polished pure Nb
Signal frequency f Hz
Pump frequency fp
50 kHz
Tuned capacitor bridge transducer
Amplifier noise no. n 20 2
Two-stage dc SQUID
Detector noise Sh1/2(f )
21020 Hz1/2
21021 Hz1/2
Computed at 1 Hz
SOGRO requires QD ~ 109 for test masses and Qpl ~ 107 for the platform.
By using two-stage dc SQUIDs, 120 and 10 have been demonstrated at 1.5 and 0.1 K, respectively. (Falferi et al., 2003; 2008)
SOGRO requires improvement by a factor of 5-6.
Paik

16. Potential sensitivities of SOGRO
SOGRO would fill frequency gap 0.1 to 10 Hz between the terrestrial and future space interferometers.
Paik

17. Platform thermal noise
Internal damping model:
Thermal displacement noise PSD becomes
where M is the effective mass of the platform and Q = 1/.
Desirable to locate test masses at nodes of the mode, M  .
Very challenging due to the presence of multiple modes
Platform design needs to be optimized to minimize its thermal noise.
Preliminary analysis with ANSYS
Paik

18. Astrophysics with SOGRO
SOGRO could detect IMBH binaries with M◉ at a few billion light years away, and WD binaries within the Local Group.
aSOGRO would be able to detect BH binaries like GW with SNR ~ 10.
Alert interferometers days before merger.
Paik

19. Seismic noise Error compensation Amplitude noise level (m Hz1/2)
At 1 Hz
Seismic background
Axis alignment and
scale factor match
Error compensation
SOGRO intrinsic noise
aSOGRO intrinsic noise
Passive/active isolation
109
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
Seismic noise of underground sites
Amplitude noise level (m Hz1/2)
dB isolation/rejection is required.
CMRR = dB isolation required.
Pendulum suspension provides sufficient
passive isolation for angular and horizontal accelerations.
0-20 dB passive/active isolation must be provided to vertical acceleration.
Paik

20. Newtonian gravity noise
Seismic and atmospheric density fluctuations produce NN.
GWs are transverse whereas near-field Newtonian gradient is not.
Could GW signal be separated out from NN?
Tensor measurement is insufficient to remove NN from multiple waves.
Still requires external seismometers and microphones.
Paik

21. Mitigation of NN
NN due to Rayleigh waves removed by using h’13, h’23, h’33, az (CM), plus 7 seismometers with SNR = 103 at the radius of 5 km.
NN due to infrasound removed by using h’13, h’23, h’33 and 15 mikes of SNR = 104, 1 at the detector, 7 each at radius 600 m and 1 km.
First remove Rayleigh NN by using seismometers only, then remove infrasound NN by using microphones and cleaned up SOGRO outputs.
Unlike TOBA and laser interferometer, SOGRO can remove NN from infrasound for all incident angles.
Harms and Paik, PRD 92, (2015)
Paik

22. Conclusion and summary
By using six levitated superconducting test masses, low-frequency tensor GW detector can be constructed.
A single SOGRO could locate source and determine polarization.
SOGRO is uniquely capable of CM rejection and full-tensor detection.
SOGRO could overcome the seismic and Newtonian noise.
With h  1020 Hz1/2 at Hz, SOGRO could detect IMBH binaries at a few billion light years away, as well as BH binaries like GW
SOGRO could alert laser interferometers days before merger.
Test masses of 5-10 tons each and 3D platform of arm-length m ( tons) need to be cooled to below 4 K.
Large-scale civil, mechanical, and cryogenic engineering is required.
Very high Q’s must be obtained for test masses and platform, and nearly quantum-limited transducer-SQUID system must be developed.
Materials science and detector technology must be advanced.
SOGRO is a multi-disciplinary project like LIGO, Virgo and KAGRA.
Paik