1. Dual Sphere Detectors by Krishna Venkateswara

2. Contents  Introduction  Review of noise sources in bar detectors  Spherical detectors  Dual sphere configuration  Sensitivity in SQL  Advantages/Drawbacks  Dual cylinders and sensitivity  Summary

3. Introduction Proposed by M. Cerdonio, L. Conti et. al. in 2001 Two nested spheres Fabry-Perot cavity as motion sensor Main advantages Wide bandwidth Spherical detector

4. Bar detectors with resonant transducers Noise energy=Thermal + Amplifier + Back-action β = energy coupling factor τ = i ntegration time  A large β is needed to reduce thermal noise.

5. Spherical Detectors  A sphere has a spherical symmetry and 5 degenerate quadrupole modes.  Uniform cross-section to GWs.  Can determine both source direction (, ) and wave polarization (h+, h).  Mount 6 radial transducers on truncated icosahedral configuration. “Spherically symmetric” detection of the sphere (Johnson & Merkowitz, 1993)

6. Dual sphere configuration Noise sources: Thermal noise Back-action noise Photon counting noise Inner sphere has quadrupole mode at f Outer sphere at 2-3 times f At frequencies in between, the two spheres are driven out of phase by GW

7. Noise spectral density for each sensor Response of the surface of a sphere to GW

8. Total strain noise density

9. Sensitivity at Standard Quantum Limit (SQL) Features  R = 0.95 m, and a = 0.57 m  Cross section proportional to ρv s 5  Molybdenum ρ = 10000 kg/m 3 and v s = 6.2 km/s Q ~ 20 million at T ≤ 4 K Input light power of 7 W, Q/T ≥ 2·10 8 K -1

10.  Beryllium ρ = 1900 kg/m 3 and vs= 13 km/s, Q ? Input light power of 12 W, Q/T ≥ 2·10 8 K -1  Sapphire ρ = 4000 kg/m 3 and vs= 10 km/s Q > 10 8 at T < 10 K

11. Advantages/Drawbacks  Wideband  Spherical detector  High sensitivity (at SQL)  Different frequency band  Complicated design  Sensor sensitivity difficult to realize

12. Dual Cylinders  Simpler design  Each mode contributes to noise while signal is mainly from Quadrupole mode selective readout  Low thermal noise from high frequency modes X d = x 1 – x 2 + x 3 – x 4

13. Readout and sensitivity  Required displacement sensitivity ~ 3 * 10 -23 m/√Hz  Demonstrated sensitivity ~ 5 * 10 -20 m/√Hz using a) Optomechanical sensor. b) Capacitive sensor using SQUID amplifiers.

14. Summary  Offers advantage of spherical detection and wide bandwidth in an uncovered frequency band  Requires advanced suspension and complicated construction  Dual cylinder design gives up isotropic sensitivity but naturally supports ‘selective readout’ and simpler design  Both require advances in optical transducers.

15. thank you!