1. Stefan Hild, Andreas Freise, Simon Chelkowski University of Birmingham GWADW, ELBA, May 2008 Virtual Interferometry for future GW detectors

2. Stefan Hild ELBA GWADW, May 2008 Slide 2 Virtual interferometry (the Idea)  Inspiration from time-delay interferometry  3rd generation detectors are likely to consist of several individual instruments (Triangle …)  Optical and/or electronical combination of the several outputs of the individual instruments might allow to do nice things:  Null streams ?  Displacement noise free interferometry ?  Frequency noise rejection ?  … many more … (hopefully ?)  This is a huge multi-dimensional playground.

3. Stefan Hild ELBA GWADW, May 2008 Slide 3 Virtual interferometry (the Idea)  Inspiration from time-delay interferometry  3rd generation detectors are like to consists of several individual instruments (Triangle…)  Optical and/or electronical combination of the several outputs of the individual instruments might allow to do nice things:  Null streams ?  Displacement noise free interferometry ?  Frequency noise rejection ?  … many more … (hopefully ?)  This is a huge multi-dimensional playground.

4. Stefan Hild ELBA GWADW, May 2008 Slide 4 The 3rd Generation Holy Grail: Displacement noise free interferometry (DNFI)  If you get DNFI to work: you can reduce many limiting noise sources. Example: 2nd Generation noise limits

5. Stefan Hild ELBA GWADW, May 2008 Slide 5 Starting point: DNFI a la Tarabrin: LIGO-P070109-00Z arXiv:0804.3955v1  Seems to be an interesting concept since it uses a standard Fabry-Perot cavity.  Modified version of the paper on the arXiv (end of April 2008)

6. Stefan Hild ELBA GWADW, May 2008 Slide 6 DNFI ala Tarabrin:  Using a double pumped (2 Laser of different polarisation) detuned Fabry Perot cavity  Read out at both ends of the cavity by 8 photo diodes (4 homodyne detectors)  Assumption: All auxiliary optics sit on isolated platforms (no relativ movement of the components on the platforms) Setup shown in the paper: arXiv:0804.3955v1

7. Stefan Hild ELBA GWADW, May 2008 Slide 7 DNFI ala Tarabrin: Experimental approch of the setup: Setup shown in the paper: arXiv:0804.3955v1

8. Stefan Hild ELBA GWADW, May 2008 Slide 8 Intuitive understanding of DNFI ala Tarabrin (1)  Using simple Finesse simulations  GW and mirror displacement can be distinguished in the signals Disp. M_aDisp. M_bGW  S1 - scaled(S2) gives a GW channel ‘free’ of M_a displacement In phase Out of phase

9. Stefan Hild ELBA GWADW, May 2008 Slide 9 What can we learn? Simple picture of a detuned cavity:  From the input side GW and end mirror displacement look identical  However, displacement of the input mirror looks different than GW (due to direct reflection)

10. Stefan Hild ELBA GWADW, May 2008 Slide 10 Intuitive understanding of DNFI ala Tarabrin (2) Disp. M_aDisp. M_b GW  S3 - scaled(S4) gives a GW channel ‘free’ of M_b displacement In phase Out of phase  Now using the signals from LASER-B.

11. Stefan Hild ELBA GWADW, May 2008 Slide 11 Creation DNFI channel for Tarabrin setup  Building a linear combination it is possible to create DNFI channel.  We can suppress mirror displacement for frequencies below the detuning of the cavity. DNFI-channel = k1*S1 + k2*S2 + k3*S3 + k4*S4

12. Stefan Hild ELBA GWADW, May 2008 Slide 12 Problems of the Tarabrin Concept  Detuning reduces power buildup inside the cavity  Frequency noise (no common mode rejection)  Displacement noise of optics on the Platforms (Homodyne detectors) arXiv:0804.3955v1

13. Stefan Hild ELBA GWADW, May 2008 Slide 13 Going forward with the Tarabrin Concept ??  Detuning reduces power buildup inside the cavity  Frequency noise (no common mode rejection)  Displacement noise of optics on the Platforms (Homodyne detectors) Perhaps one can use more powerful lasers or larger power recycling factors ? Combine 2 cavities to form a Michelson interferometer Replace the homodyne detectors by the conventional beam splitter of the Michelson interferometer

14. Stefan Hild ELBA GWADW, May 2008 Slide 14 Our Playground …  Single Michelson IFO with douple pumped arm cavities.  3 Laser: all slightly different frequency (few GHz).  4 Photo detectors.  PD1 only sees Laser1  PD2 only sees Laser2  PD3 only sees Laser3  PD123 sees an optical mix of all lasers  2 Output mode cleaners.  Arm length of 3km.  Cavity detuning of a few kHz.

15. Stefan Hild ELBA GWADW, May 2008 Slide 15 Signal Transfer functions  Using a linear combination of PD1, PD2 and PD3 we can remove displacement of IX and IY. (as expected)  But we have no chance to remove EY and EX. (as expected)  To remove EX and EY we probably need sensing at the end of the arms (in reflection of EY and EX).

16. Stefan Hild ELBA GWADW, May 2008 Slide 16 Extending our Playground …  A triangle of 3 Michelson IFOs with arm cavities.  Each test mass is part of two Michelson IFOs.  3 Laser: all slightly different frequency (few GHz).  12 Photo detectors.  6 Output mode cleaners.  Arm length of 3km.  Cavity detuning of a few kHz

17. Stefan Hild ELBA GWADW, May 2008 Slide 17 Signal TFs of single Michelson  Now we can subtract IX, IY, EX and EY.  One Michelson (made of X and Y arm) ‘displacement noise free’ !!

18. Stefan Hild ELBA GWADW, May 2008 Slide 18 Displacement noise free Michelson interferometer  One Michelson (made of X and Y arm) ‘displacement noise free’ !! DNFI-channel = k1*PD1 + k2*PD2 + k3*PD3 + k4*PDb2 + k5*PDc3  BUT this result is cheating… (for two reasons) Displacement noise suppression inside the detection (audio) band

19. Stefan Hild ELBA GWADW, May 2008 Slide 19 How we were cheating…  If any displacement or GW signal is present in the Z- arm this will couple into PDb2 and PDc3.  PD2 and PD3 will be contaminated by laser frequency noise (no common mode rejection) DNFI-channel = k1*PD1 + k2*PD2 + k3*PD3 + k4*PDb2 + k5*PDc3

20. Stefan Hild ELBA GWADW, May 2008 Slide 20 ET design study is a good frame to do this …

21. Stefan Hild ELBA GWADW, May 2008 Slide 21 Summary  Virtual interferometry might be highly beneficial for 3rd Generation GW detectors  Holy Grail = Realize Displacement noise free interferometry that combines:  Noise suppression at (sub)audio band frequencies  Keep the common mode rejection of frequency noise  Using feasible geometries  The Tarabrin-Concept might be useful.  We presented some first and very preliminary analyses, but this needs to be continued.

22. Stefan Hild ELBA GWADW, May 2008 Slide 22 E N D