QND for advanced GW detectors

Transcription

1 QND techniques for advanced GW detectors 1 for the MQM group 1 Lomonosov Moscow State University, Faculty of Physics GWADW 2010, Kyoto, Japan, May 2010

2 Outline Quantum noise & optical losses 1 Quantum noise in conventional GW detector. Optical losses 2 3 4

3 Outline Quantum noise & optical losses 1 Quantum noise in conventional GW detector. Optical losses 2 3 4

4 Quantum noise anatomy GW signal GW tidal force is transformed by interferometer into the modulation of reflected light phase: φ out b 2 (Ω) p 2K(Ω) h GW (Ω) h SQL with FP optomechanical coupling strength K(Ω) = 2Ic γ 4 I SQL Ω 2 (Ω 2 + γ 2 ), free mass q SQL for GW strain h SQL = 8 MΩ 2 L 2, and I SQL = McLγ3 4ω p circulating power needed to reach the SQL at frequency Ω = γ hsql, Hz FP response 1 H.J. Kimble et al, Phys. Rev. D 65, (2001); Y. Chen et al, arxiv: (2009)

5 Quantum noise anatomy Ponderomotive squeezing due to radiation pressure squeezing, db sq. angle, rad Π 4 Π 6 Π

6 Quantum noise anatomy Conventional interferometers quantum noise Conventional detectors: Phase quadrature b 2 is measured; RPN and SN are not correlated; Dark port vacuum is not squeezed S conv h = h2 h SQL 1 2 K {z} SN i + K {z} RP N hconv, Hz I SQL Shot noise 10 I SQL L Conventional interferometer features: Best sensitivity is always at SQL, the point where RPN and SN become equal. The only handle to turn is optical power. Variation of circulating power only makes sensitivity curve to slide along the SQL line but not surpass it! H.J. Kimble et al, Phys. Rev. D 65, (2001); Y. Chen et al, arxiv: (2009)

7 Optical losses. Optical loss in advanced interferometers Main source of optical losses is quantum inefficiency of readout photodetectors η 0.9; Losses limit achievable squeeze factor and destroy quantum correlation in variational schemes;

8 Outline Quantum noise & optical losses 1 Quantum noise in conventional GW detector. Optical losses 2 3 4

9 Squeezed-input interferometers. Externally generated squeezed vacuum is injected into dark port of the interferometer. Squeezing angle λ(ω) and/or squeezing factor e 2r(Ω) properly depending on frequency compensates RPN at LF and SN at HF.

10 Variants of squeeze input interferometers 1 Fully optimal phase pre-filtering (H.J. Kimble et al, Phys. Rev. D 65, (2001)); 2 Amplitude pre-filtering (T. Corbitt, N. Mavalvala and S. Whitcomb, Phys. Rev. D 70, (2004)); 3 Single short filter cavity amplitude pre-filtering with double squeezors and double readout channels. (F.Ya. Khalili, H. Miao, and Y. Chen, Phys. Rev. D 80, (2009)); 4 Single short filter cavity amplitude-phase pre-filtering with double squeezors and double readout channels.(f.ya.khalili, (2010));

11 Variants of squeeze input interferometers 1 Fully optimal phase pre-filtering (H.J. Kimble et al, Phys. Rev. D 65, (2001)); 2 Amplitude pre-filtering (T. Corbitt, N. Mavalvala and S. Whitcomb, Phys. Rev. D 70, (2004)); 3 Single short filter cavity amplitude pre-filtering with double squeezors and double readout channels. (F.Ya. Khalili, H. Miao, and Y. Chen, Phys. Rev. D 80, (2009)); 4 Single short filter cavity amplitude-phase pre-filtering with double squeezors and double readout channels.(f.ya.khalili, (2010));

12 Variants of squeeze input interferometers 1 Fully optimal phase pre-filtering (H.J. Kimble et al, Phys. Rev. D 65, (2001)); 2 Amplitude pre-filtering (T. Corbitt, N. Mavalvala and S. Whitcomb, Phys. Rev. D 70, (2004)); 3 Single short filter cavity amplitude pre-filtering with double squeezors and double readout channels. (F.Ya. Khalili, H. Miao, and Y. Chen, Phys. Rev. D 80, (2009)); 4 Single short filter cavity amplitude-phase pre-filtering with double squeezors and double readout channels.(f.ya.khalili, (2010));

13 Variants of squeeze input interferometers 1 Fully optimal phase pre-filtering (H.J. Kimble et al, Phys. Rev. D 65, (2001)); 2 Amplitude pre-filtering (T. Corbitt, N. Mavalvala and S. Whitcomb, Phys. Rev. D 70, (2004)); 3 Single short filter cavity amplitude pre-filtering with double squeezors and double readout channels. (F.Ya. Khalili, H. Miao, and Y. Chen, Phys. Rev. D 80, (2009)); 4 Single short filter cavity amplitude-phase pre-filtering with double squeezors and double readout channels.(f.ya.khalili, (2010));

14 Comparison and optimization by F.Ya.Khalili, 1 Relatively short single filter cavities ( m) can provide significant increase in SNR ( 2 5 compared to frequency independent squeezing schemes); 2 Phase pre-filtering scheme of Kimble appeared optimal allowing to reduce the total quantum noise by e r : h i S sq.opt. h = h2 SQL 1 2 K + K e 2r

15 Comparison and optimization by F.Ya.Khalili, 1 Relatively short single filter cavities ( m) can provide significant increase in SNR ( 2 5 compared to frequency independent squeezing schemes); 2 Phase pre-filtering scheme of Kimble appeared optimal allowing to reduce the total quantum noise by e r : h i S sq.opt. h = h2 SQL 1 2 K + K e 2r

16 Outline Quantum noise & optical losses 1 Quantum noise in conventional GW detector. Optical losses 2 3 4

17 Variational interferometers Idea of variational measurement Instead of phase quadrature one should measure output quadrature that has minimal uncertainty: y ζ = b 1 sin ζ + b 2 cos ζ. Optimal ζ allows to eliminate radiation pressure contribution to the output noise at given frequency Ω. [S.P. Vyatchanin and A.B. Matsko, JETP 77, p. 218 (1993); S.P. Vyatchanin and E.A. Zubova, Phys. Lett. A 203, p. 269 (1995)]

18 Variational interferometers VM sensitivity with fixed homodyne angle ζ: S v.fix. h = h2 SQL 2 e 2r + [cot ζ K] 2 e 2r K Arbitrary quadrature measurement performed by homodyne detector;, As at different frequencies optimal ζ is different with fixed homodyne angle ζ only narrow-band SQL beating is possible;

19 Variational interferometers VM sensitivity with optimal ζ(ω): S v.opt. h = h2 SQL 2K e 2r, ζ opt(ω) = arccotk. Optimal frequency dependence for ζ requires additional km-scale post-filter cavities [H.J. Kimble et al, PRD 65, (2001)] Any phase shift of the form arctanˆ P n k=0 A kω 2k / P n k=0 B kω 2k can be provided by a train of n filter cavities [P.Purdue and Y. Chen, PRD 66, (2002)]

20 Optical losses in variational interferometers Sesitivity of variational interferometer with losses " # Sh loss = h2 SQL e 2r + ξloss 4 K + 2 K e 2r + ξ 4 loss and optimal frequency dependent homodyne angle is K(Ω) ζ(ω) = arccot 1 + ξloss 4. e 2r with ξ loss = 4 s 1 η η In lossy variational position meter radiation pressure noise can not be fully compensated even with optimal auxiliary km-scale filter cavities; There is a limit for sensitivity of position meters imposed by optical losses: s h noise e 2r + ξ 4 loss 4 h SQL ξ 4 loss + = h noise ξ e 2r loss 2 h, if e 2r ξloss 4. SQL

21 Optical losses in variational interferometers Method not relying on optimal correlation between SN and RPN is needed!

22 Outline Quantum noise & optical losses 1 Quantum noise in conventional GW detector. Optical losses 2 3 4

23 Velocity measurement as quasi-qnd technique One step towards canonical QND measurement. Speed meter QND measurement implies sensing of the conserved quantity of the test body, e.g. free mass momentum p = no back-action on p = no SQL; Problem: nobody knows how to measure momentum; Way out: measure test mass velocity v that is proportional to the free mass momentum; Velocity is not a true QND observable though, but allows to subdue radiation pressure significantly! Idea of optical speed measurement Let the light be coherently reflected from the test object twice with delay τ, then the output light phase will depend on the difference of the object position at times separated by τ, that is object s mean velocity. V.B. Braginsky and F.Ya. Khalili, Phys. Lett. A 147, p.251 (1990)

24 Practical speedmeter schemes. Sloshing speedmeter: Two coupled FP cavities; 1-st cavity is resonantly pumped (main FP-Michelson interferometer according to scaling law ); 2-nd is kept unexcited and serves as sloshing cavity (auxiliary FP cavity); Coupling between cavities makes signal to slosh between the cavities changing sign at every cycle; After each cycle signal in main resonator is proportional to difference of mirror positions at times separated by sloshing period = mean velocity. V.B. Braginsky and F.Ya. Khalili, Phys. Lett. A 147, p.251 (1990); V.B. Braginsky et al, Phys. Rev. D 61, p.4002 (2000); P. Purdue and Y. Chen, Phys. Rev. D 66, (2002)

25 Practical speedmeter schemes. Zero area Sagnac speedmeter: Laser light gets splited by the beamsplitter and then propagates in CW and CCW directions, passing both arm cavities sequentially; Light beam acquires phase shifts proportional to a sum of end mirrors displacements of both cavities, taken with delay cavity ctorage time τ arm γ 1 : φ R x N (t) + x E (t + τ arm), φ L x E (t) + x N (t + τ arm) After recombination at beamsplitter the outgoing light phase is proportional: φ R φ L ẋ E ẋ N + O(τ arm) F.Ya. Khalili, arxiv:gr-qc/ ,(2002); Y. Chen, Phys. Rev. D 67, (2003);, Phys. Rev. D 69, (2004)

26 Practical speedmeter schemes. Speed meter response to GW signal is: φ out b 2 (Ω) p 2KSM (Ω) h GW (Ω) h SQL where optomechanical coupling is different from the one for position meter: K SM = 4Ic γ 4 I SQL (γ 2 + Ω 2 ) 2 Main differences from PM: Response drops at low frequencies (Ω γ) as Ω; At high frequencies (Ω γ) it 2 times better than for PM and drops as Ω 1 ; RPN at low frequencies is supressed!

27 Sensitivity of speed meters Sensitivity of speed meter: In lossless limit speed meter sensitivity has the same shape as the one for PM: SM, lossless Sh = h SQL e 2r + [cot ζ K SM ] 2 e 2r 2 K SM Optomechanical coupling of speedmeter K SM is constant at low frequencies: K SM (Ω 0) = 4I c/i SQL Thus effective suppression of low-frequency part of quantum noise can be achieved with fixed homodyne phase ζ: ζ LF = arccotk SM (0) = arccot 4Ic I SQL

28 Sensitivity of speed meters Sensitivity of variational speed meter: Low frequency optimisation gives: SM, LF Sh = h SQL e 2r + [K SM (0) K SM ] 2 e 2r 2 K SM and full variational optimization with two km-scale filter cavities gives: S SMVM h = h SQL 2K SM e 2r with ζ(ω) = arccotk SM(Ω). What s the point in using speed meters if LF performance of variational position meters is much better? But this is true ONLY IN LOSSLESS CASE!

29 Optical losses in speed meters Sensitivity of lossy variational speed meter: BOTH photodetector losses and arm cavity optical losses contribute to total quantum noise SMVM, loss Sh = h " SQL e 2r + ξpd 4 / # sin2 ζ + [cot ζ K SM ] 2 e 2r + ξcav 4 2 K K PM SM where ξ PD 4 p (1 η)/η and ξ cav = 4p (1 η cav)/η cav Losses in arms are small (defined by photon loss per bounce in arms ɛ 10 5 and cavity finesse F): 1 η cav ɛf 2π 10 3 compared with PD inefficiency 1 η PD 0.1 But at low frequencies these losses behave like RPN of position meter, though suppressed by factor of ξ 2 cav 10 3 ;

30 Optical losses in speed meters Sensitivity of lossy variational speed meter: Optimal homodyne angle for lossy variational speed meter is that yields: SMVM, loss Sh = h SQL 2 K SM (Ω) ζ(ω) = arccot 1 + ξpd 4 e 2r " e 2r + ξ 4 PD K SM (Ω) # + K SM(Ω) ξ 4 PD + + ξ4 cavk PM. e 2r

31 Optical losses in speed meters

32 Optical losses in speed meters

33 Sloshing-Sagnac Speed Meter Coating thermal noise is one of the main obstacles on the way towards SQL; The possible way out = Khalili cavities; Can one couple speed meter with Khalili cavities? Sloshing-Sagnac Speed Meter (SSSM) Use FP-cavities with identical mirrors (T ITM = T ETM); Arrange 4 FP cavities in a zero area Sagnac topology; Let ETMs of each arm form Khalili cavities; Tune all FPs in resonance; Counter propagating pumping fields interfere destructively in the secondary FPs turning them into sloshing cavities

34 Sloshing-Sagnac Speed Meter Optomechanical coupling for SSSM: K SSSM = Ic γ 4 I SQL (γγ s Ω 2 ) 2 + γ 2 Ω 2 where γ s = ct s/4l is sloshing FP s half-bandwidth.

35 Sloshing-Sagnac Speed Meter

36 Summary 1 Squeezed vacuum source will become an inherent part of any SQL beating endeavor (but not sufficient!); 2 FD variational measurement with relatevely short single filter cavity looks a minimal requirement to form together with squeezer, an effective combined arms task force for successful attack on the SQL; 3 To cope with optical losses, speed meter seems the cheapest solution (in terms of required changes to conventional setups) among the QND schemes; 4 At the first glance, new sloshing Sagnac speed meter might also help to reduce the number of coating layers significantly and thus depress the coating thermal noise (more studies are necessary...)

37 THANK YOU FOR YOUR ATTENTION!!!