An optical readout configuration for advanced massive GW detectors

Transcription

1 An optical readout configuration for advanced massive GW detectors Francesco Marin, Livia Conti, Maurizio De Rosa Dipartimento di Fisica, Università di Firenze,LENS and INFN, Sezione di Firenze Via Sansone, 1, I Sesto Fiorentino (FI), Italy

2 Optical readout of displacement Standard detection technique in interferometers Proposed in the 80 s for bar detectors 1 Recently applied to a room temperature detector 2 [1] J.-P. Richard, J. Appl. Phys. 64, 2202 (1988) [2] L. Conti et al., J. Appl. Phys. 93, 3589 (2003)

3 Room temperature Weber bar with optical readout

4 Room temperature Weber bar with optical readout beam-splitter optical fiber transducer cavity Nd:YAG laser Phase mod. Power stab. Frequency locking FM sidebands technique FM sidebands technique S hh (1/ Hz) reference cavity pzt actuator Low frequency locking Data acquisition temperature control Frequency (Hz)

5 Room temperature Weber bar with optical readout Work in progress: Cleaner vacuum system New mechanical suspension Higher Finesse transducer cavity Cooling (at least 77K)

6 Brownian noise and radiation pressure (back-action) are the usual sensitivity limiting sources in a few-modes model, together with the displacement detection sensitivity (displacement noise) In a real, massive system: several modes, with their thermal noise and back-action. Small interrogation region means large fluctuations One must average over high order modes: needs large interrogation region

7 We must consider local effects: Thermal noise - photothermal - thermodynamic -Brownian Depends on material parameters At cryo-t: Radiation pressure - best material is sapphire - predominant Brownian

8 S 2 F S cav P in Brownian noise: Br (!) = 4 k BT S! Im [(!)] Radiation pressure effect: 2 0 B j(!)j = (!) rp S 1 C 2 A intracavity radiation noise spectral power: 0 B 1 C 2 = 2 h A

9 single Br (!) = 4 k BT S 1 ; 2 2 h P in Gaussian spot on a half-infinite mirror: Im [(!)] ' j(!)j χ single = 1 π 1/2 w Single-spot noise: 1 σ 2 Y 1 w Y 1=2! 1 C 2 0 2(1 ; 2 )F single rp = S B C A 3=2 cy w

10 Main figures Sapphire (1 K): Young modulus Y = Pa Poisson coefficient σ = 0.25 Loss angle φ = Cavity Finesse: F = 10 6 Displacement sensitivity with 1 W: with 10 W: m 2 /Hz m 2 /Hz

11 Target (Ex.: dual sphere *) Best stiffness: for laser power = 7 W Thermal noise negligible for Q/T > S xx = m 2 /Hz but With a waist of w = 1 mm: S Br = m 2 /Hz S rp = m 2 /Hz We need a waist of w >20cm!!!! * M. Cerdonio et al., Phys. Rev. Lett. 87, (2001)

12 Possible solutions? Concave Convex cavity : (-R 2 ) = R 1 + r Stable if d > r If (d r) << d << R 1, R 2 : w 2 λr π d d r Plano-concave Cavity: w 2 λ π Rd Ex. : R = 10 m r = 10 mm d r = 0.1 mm λ = µm W = 5.8 mm Delay line : Low equivalent Finesse

13 Folded Fabry-Perot (FFP) M4 M3 θ M1 M3 θ M1 M2 M2 (a) (b) F. Marin, L. Conti, M. De Rosa: A folded Fabry- Perot cavity for optical sensing in gravitational wave detectors, Phys. Lett. A 309, 15 (2003)

14 Folded Fabry-Perot (FFP) M4 M3 M1 D M2 Signal: N Brownian noise: N Radiation pressure: N F (constant) Displacement noise: 1/F N Linewidth ( bandwidth): 1/(N F) (constant)

15 For non-correlated spot fluctuations Brownian noise effect: single S Br 2L Br 2 S (2L) 2 = S 1 2 D 2 N Radiation pressure = effect: S ν ν 2 = S2L rp (2L) 2 = Ssingle rp 1 4D 2 N 2

16 FFP Br (!) = 4 k BT S FFP rp = 2 c! (4 N + 4 N single ) S cav 2 N +2 N 0 +2 single 2 Taking into account correlations NX X n;1 0 jr n ; r q j 2 0 jr n ; r q j 2 I A A C 1 1 N = single N +2 exp C B 2w 2 2w 2 q=1 n=2 N Nakagawa et al., Phys. Rev. D 65, (2002) Brownian noise effect: Radiation pressure effect: A

17 Correlation effect 100 N χ N / χ u }2-dim. array d/w } 1-dim. array

18 P in = 1 W S ν / ν 2 (Hz -1 ) a c d b e D = 6 mm R = - 10 m d = 4 w N a: radiation pressure effect (no correlations) b: radiation pressure effect (full) c: Brownian 1.3 khz (no correlations) d: Brownian 1.3 khz (full) e: Shot-noise limited displacement sensitivity

19 P in = 7 W S ν / ν 2 (Hz -1 ) c a d b e D = 6 mm R = - 10 m d = 4 w N a: radiation pressure effect (no correlations) b: radiation pressure effect (full) c: Brownian 1.3 khz (no correlations) d: Brownian 1.3 khz (full) e: Shot-noise limited displacement sensitivity Power density: 10 kw/mm 2

20 Conclusions The FFP allows to closely approach with the present technology the quantum-limited sensitivity and best stiffness calculated for the main modes of a high sensitivity, wide bandwidth dual detector