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ET filter cavities for third generation detectors

This document discusses the design and performance of filter cavities for the Einstein Telescope (ET). It covers the required filter-cavity lengths, the influence of frequency-dependent squeezing on gravitational wave detection, and the necessary layout to mitigate scattering light. The authors, Keiko Kokeyama and Andre Thüring, present insights into the impact of optical loss and intra-cavity coupling. They emphasize the importance of maximizing squeezing to achieve targeted sensitivity levels for optimal functionality in advanced gravitational wave observatories.

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ET filter cavities for third generation detectors

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  1. ET filter cavities for third generation detectors Keiko Kokeyama Andre Thüring

  2. Contents • Introduction of Filter cavities for ET • Part1. Filter-cavity-length requirement • - Frequency dependant squeezing • - Filter cavity length and the resulting squeezing level • Part2. Layout requirement from the scattering light analysis • Summary K. Kokeyamaand Andre Thüring 17 May 2010, GWADW

  3. Contents • Introduction of Filter cavities for ET • Part1. Filter-cavity-length requirement • - Frequency dependant squeezing • - Filter cavity length and the resulting squeezing level • Part2. Layout requirement from the scattering light analysis • Summary K. Kokeyamaand Andre Thüring 17 May 2010, GWADW

  4. Design sensitivity for ET-C Letsfocus on the ET-C LF part. • ET-C : Xylophone consists of • ET-LF and ET-HF • ET-C LF • Low frequency part of the xylophone • Detuned RSE • Cryogenic • Silicon test mass & 1550nm laser • HG00 mode S. Hild et al. CQG 27 (2010) 015003 1/20 K. Kokeyamaand Andre Thüring 17 May 2010, GWADW

  5. To reach the targeted sensitivity, we have to utilize squeezed states of light We dream of a broadband QN-reduction by 10dB A broadband quantum noise reduction requires the frequency dependent squeezing, therefore filter cavities are necessary 2/20 K. Kokeyamaand Andre Thüring 17 May 2010, GWADW

  6. Contents • Introduction of Filter cavities for ET • Part1. Filter-cavity-length requirement • - Frequency dependant squeezing • - Filter cavity length and the resulting squeezing level • Part2. Layout requirement from the scattering light analysis • Summary K. Kokeyamaand Andre Thüring 17 May 2010, GWADW

  7. Contents • Introduction of Filter cavities for ET • Part1. Filter-cavity-length requirement • - Frequency dependant squeezing • - Filter cavity length and the resulting squeezing level • Part2. Layout requirement from the scattering light analysis • Summary K. Kokeyamaand Andre Thüring 17 May 2010, GWADW

  8. X2 X2 X1 X1 Quantum noise in a Michelson interferometer X2 X1 Quantum noise reduction with squeezed light Filter cavities can optimize the squessing angles 3/20 K. Kokeyamaand Andre Thüring 17 May 2010, GWADW

  9. ET-C LF bases on detuned signal-recycling Two filter cavities are required for an optimum generation of frequency dependent squeezing Optical spring resonance Opticalresonance In this talk we consider the two input filter cavities 4/20 K. Kokeyamaand Andre Thüring 17 May 2010, GWADW

  10. Contents • Introduction of Filter cavities for ET • Part1. Filter-cavity-length requirement • - Frequency dependant squeezing • - Filter cavity length and the resulting squeezing level • Part2. Layout requirement from the scattering light analysis • Summary K. Kokeyamaand Andre Thüring 17 May 2010, GWADW

  11. Requirementsdefinedbytheinterferometerset-up: Thebandwidths and detunings of thefiltercavities Whatwecanchoose The lengths of the filter cavities ...And the optical layout (Part2) Limitations Infrastructure, opticalloss (e.g. scattering) , phasenoise, ... 5/20 K. Kokeyamaand Andre Thüring 17 May 2010, GWADW

  12. Degrading of squeezing due to optical loss At everyopen (lossy) portvacuumnoisecouples in coupling mirror A cavity reflectance R<1 means loss . The degrading of squeezing is then frequency dependent 6/20 K. Kokeyamaand Andre Thüring 17 May 2010, GWADW

  13. The impact of intra-cavity loss The filter‘s coupling mirror reflectance Rc needs to be chosen with respect to 1. therequiredbandwidthg accountingfor 2. theround-triplosslRT 3. a givenlengthL Thereexists a lowerlimitLmin. For L < Lminthefiltercavityisunder-coupled and thecompensation of thephase-space rotation fails! 7/20 K. Kokeyamaand Andre Thüring 17 May 2010, GWADW

  14. The impact of shortening the cavity length If L < Lmin ~ 1136 m thefilterisunder-coupled and thefilteringdoesnotwork Examplefor ET-C LF detuning = 7.1 Hz 100 ppmround-triploss, bandwidth = 2.1 Hz For L < 568m Rc needs to be >1 The filter cavity must be as long as possible for ET-LF 8/20 K. Kokeyamaand Andre Thüring 17 May 2010, GWADW

  15. Narrow bandwidths filter are more challenging Assumptions: L = 10 km, 100 ppmround-triploss, Detuning = 2x bandwidth Filter cavities with a bandwidth greater than 10 Hz are comparatively easy to realize 9/20 K. Kokeyamaand Andre Thüring 17 May 2010, GWADW

  16. Exemplary considerations for ET-C LF Filter I: g = 2.1 Hz fres = 7.1 Hz Filter II: g = 12.4 Hz fres = 25.1 Hz 15dB squeezing 100ppm RT - loss 7% propagationloss Filter I: L = 2 km F = 17845 Rc = 99.9748% Filter II: L = 2 km F = 3022 Rc = 99.8023% Filter I: L = 5 km F = 7138 Rc = 99.9220% Filter II: L = 5 km F = 1209 Rc = 99.4915% Filter I: L = 10 km F = 3569 Rc = 99.8341% Filter II: L = 10 km F = 604 Rc = 98.9757% 10/20 K. Kokeyamaand Andre Thüring 17 May 2010, GWADW

  17. Contents • Introduction of Filter cavities for ET • Part1. Filter-cavity-length requirement • - Frequency dependant squeezing • - Filter cavity length and the resulting squeezing level • Part2. Layout requirement from the scattering light analysis • Summary K. Kokeyamaand Andre Thüring 17 May 2010, GWADW

  18. Stray light analysis for four designs Linear Triangular - Conventional Rectangular Bow-tie Which design is suitable for ET cavities from the point of view of the loss due to stray lights? 11/20 K. Kokeyamaand Andre Thüring 17 May 2010, GWADW

  19. Scattering Angle and Fields Linear Triangular Rectangular Bow-tie 12/20 K. Kokeyamaand Andre Thüring 17 May 2010, GWADW

  20. Scattering Field Category 13/20 K. Kokeyamaand Andre Thüring 17 May 2010, GWADW

  21. Scattering Field Category 13/20 K. Kokeyamaand Andre Thüring 17 May 2010, GWADW

  22. #1 Counter-Propagating, Small f0,f~0 Coupling factor • C1 =A<ETEM00•m(x,y) •E*TEM00> 14/20 K. Kokeyamaand Andre Thüring 17 May 2010, GWADW

  23. Scattering Field Category 15/20 K. Kokeyamaand Andre Thüring 17 May 2010, GWADW

  24. #2 Counter-Propagating, Large f0,f=0 Coupling factor • C2= A<ETEM00•m(x,y) •E*TEM00> 15/20 K. Kokeyamaand Andre Thüring 17 May 2010, GWADW

  25. Scattering Field Category 16/20 K. Kokeyamaand Andre Thüring 17 May 2010, GWADW

  26. #3 Counter-Propagating, Large f (at 2nd scat) #4 Counter-Propagating, Small f (at 2nd scat) • C3=<ETEM00tail •E*TEM00> • C4 =<ESphe •E*TEM00> 16/20 K. Kokeyamaand Andre Thüring 17 May 2010, GWADW

  27. Scattering Field Category 17/20 K. Kokeyamaand Andre Thüring 17 May 2010, GWADW

  28. #5 Normal-Propagating, Large f (at 2nd scat) #6 Normal-Propagating, Small f (at 2nd scat) • C5=<ETEM00tail •E*#TEM00> • C6 =<ESphe •E*# TEM00> 17/20 K. Kokeyamaand Andre Thüring 17 May 2010, GWADW

  29. -----= 18/20 K. Kokeyamaand Andre Thüring 17 May 2010, GWADW

  30. Preliminary Results 19/20 K. Kokeyamaand Andre Thüring 17 May 2010, GWADW

  31. Summary • We have shown that the requirement of the filter-cavity length which can accomplish the necessary level of squeezing • We have evaluated the amount of scattered light from the geometry alone to select the cavity geometries for arm and filter cavities for ET. • As a next step coupling factors between each fields and the main beam should be calculated quantitatively so that total loss and coupling can be estimated. • At the same time the cavity geometries will be compared with respect to astigmatism, length & alignment control method 20/20 K. Kokeyamaand Andre Thüring 17 May 2010, GWADW

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