AlbertEinsteinInstitute Hannover ET filter cavities for third generation
Albert-Einstein-Institute Hannover ET filter cavities for third generation detectors Keiko Kokeyama Andre Thüring
Albert-Einstein-Institute Hannover Contents • Introduction of Filter cavities for ET Part 1. Filter-cavity-length requirement - Frequency dependant squeezing - Filter cavity length and the resulting squeezing level Part 2. Layout requirement from the scattering light analysis • Summary K. Kokeyama and Andre Thüring 17 May 2010, GWADW
Albert-Einstein-Institute Hannover Contents • Introduction of Filter cavities for ET Part 1. Filter-cavity-length requirement - Frequency dependant squeezing - Filter cavity length and the resulting squeezing level Part 2. Layout requirement from the scattering light analysis • Summary K. Kokeyama and Andre Thüring 17 May 2010, GWADW
Albert-Einstein-Institute Hannover Design sensitivity for ET-C Lets focus 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 & 1550 nm laser • HG 00 mode S. Hild et al. CQG 27 (2010) 015003 K. Kokeyama and Andre Thüring 17 May 2010, GWADW 1/20
Albert-Einstein-Institute Hannover To reach the targeted sensitivity, we have to utilize squeezed states of light We dream of a broadband QN-reduction by 10 d. B A broadband quantum noise reduction requires the frequency dependent squeezing, therefore filter cavities are necessary K. Kokeyama and Andre Thüring 17 May 2010, GWADW 2/20
Albert-Einstein-Institute Hannover Contents • Introduction of Filter cavities for ET Part 1. Filter-cavity-length requirement - Frequency dependant squeezing - Filter cavity length and the resulting squeezing level Part 2. Layout requirement from the scattering light analysis • Summary K. Kokeyama and Andre Thüring 17 May 2010, GWADW
Albert-Einstein-Institute Hannover Contents • Introduction of Filter cavities for ET Part 1. Filter-cavity-length requirement - Frequency dependant squeezing - Filter cavity length and the resulting squeezing level Part 2. Layout requirement from the scattering light analysis • Summary K. Kokeyama and Andre Thüring 17 May 2010, GWADW
Albert-Einstein-Institute Hannover Quantum noise in a Michelson interferometer X 2 X 1 Quantum noise reduction with squeezed light X 2 X 1 Filter cavities can optimize the squessing angles K. Kokeyama and Andre Thüring 17 May 2010, GWADW 3/20
Albert-Einstein-Institute Hannover ET-C LF bases on detuned signal-recycling Optical spring resonance Optical resonance Two filter cavities are required for an optimum generation of frequency dependent squeezing In this talk we consider the two input filter cavities K. Kokeyama and Andre Thüring 17 May 2010, GWADW 4/20
Albert-Einstein-Institute Hannover Contents • Introduction of Filter cavities for ET Part 1. Filter-cavity-length requirement - Frequency dependant squeezing - Filter cavity length and the resulting squeezing level Part 2. Layout requirement from the scattering light analysis • Summary K. Kokeyama and Andre Thüring 17 May 2010, GWADW
Albert-Einstein-Institute Hannover Requirements defined by the interferometer set-up: The bandwidths and detunings of the filter cavities What we can choose The lengths of the filter cavities . . . And the optical layout (Part 2) Limitations Infrastructure, optical loss (e. g. scattering) , phase noise, . . . K. Kokeyama and Andre Thüring 17 May 2010, GWADW 5/20
Albert-Einstein-Institute Hannover Degrading of squeezing due to optical loss At every open (lossy) port vacuum noise couples in coupling mirror A cavity reflectance R<1 means loss. The degrading of squeezing is then frequency dependent K. Kokeyama and Andre Thüring 17 May 2010, GWADW 6/20
Albert-Einstein-Institute Hannover The impact of intra-cavity loss The filter‘s coupling mirror reflectance Rc needs to be chosen with respect to 1. the required bandwidth g accounting for 2. the round-trip loss l. RT 3. a given length L There exists a lower limit Lmin. For L < Lmin the filter cavity is undercoupled and the compensation of the phase-space rotation fails! K. Kokeyama and Andre Thüring 17 May 2010, GWADW 7/20
Albert-Einstein-Institute Hannover The impact of shortening the cavity length If L < Lmin ~ 1136 m the filter is under-coupled and the filtering does not work Example for ET-C LF detuning = 7. 1 Hz 100 ppm round-trip loss, bandwidth = 2. 1 Hz For L < 568 m Rc needs to be >1 The filter cavity must be as long as possible for ET-LF K. Kokeyama and Andre Thüring 17 May 2010, GWADW 8/20
Albert-Einstein-Institute Hannover Narrow bandwidths filter are more challenging Assumptions: L = 10 km, 100 ppm round-trip loss, Detuning = 2 x bandwidth Filter cavities with a bandwidth greater than 10 Hz are comparatively easy to realize K. Kokeyama and Andre Thüring 17 May 2010, GWADW 9/20
Albert-Einstein-Institute Hannover Exemplary considerations for ET-C LF 15 d. B squeezing 100 ppm RT - loss 7% propagation loss Filter I: g = 2. 1 Hz fres = 7. 1 Hz Filter II: g = 12. 4 Hz fres = 25. 1 Hz 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% K. Kokeyama and Andre Thüring 17 May 2010, GWADW 10/20
Albert-Einstein-Institute Hannover Contents • Introduction of Filter cavities for ET Part 1. Filter-cavity-length requirement - Frequency dependant squeezing - Filter cavity length and the resulting squeezing level Part 2. Layout requirement from the scattering light analysis • Summary K. Kokeyama and Andre Thüring 17 May 2010, GWADW
Albert-Einstein-Institute Hannover Stray light analysis for four designs Linear Rectangular Triangular - Conventional Bow-tie Which design is suitable for ET cavities from the point of view of the loss due to stray lights? K. Kokeyama and Andre Thüring 17 May 2010, GWADW 11/20
Albert-Einstein-Institute Hannover Scattering Angle and Fields Linear Triangular Rectangular Bow-tie K. Kokeyama and Andre Thüring 17 May 2010, GWADW 12/20
Albert-Einstein-Institute Hannover Scattering Field Category Counterpropagating Normalpropagating # f 0 f Scat field Scat power 1 Small 0 Rigorous field Large 2 Large 0 Rigorous field Small 3 Small Gauss tail small? 4 Large Spherical wave approx. Small 5 Small Gauss tail small? 6 Large Spherical wave approx. Small K. Kokeyama and Andre Thüring 17 May 2010, GWADW 13/20
Albert-Einstein-Institute Hannover Scattering Field Category Counterpropagating Normalpropagating # f 0 f Scat field Scat power 1 Small 0 Rigorous field Large 2 Large 0 Rigorous field Small 3 Small Gauss tail small? 4 Large Spherical wave approx. Small 5 Small Gauss tail small? 6 Large Spherical wave approx. Small K. Kokeyama and Andre Thüring 17 May 2010, GWADW 13/20
Albert-Einstein-Institute Hannover #1 Counter-Propagating, Small f 0, f~0 Coupling factor C 1 =A<ETEM 00 • m(x, y) • E*TEM 00> K. Kokeyama and Andre Thüring 17 May 2010, GWADW 14/20
Albert-Einstein-Institute Hannover Scattering Field Category Counterpropagating Normalpropagating # f 0 f Scat field Scat power 1 Small 0 Rigorous field Large 2 Large 0 Rigorous field Small 3 Small Gauss tail small? 4 Large Spherical wave approx. Small 5 Small Gauss tail small? 6 Large Spherical wave approx. Small K. Kokeyama and Andre Thüring 17 May 2010, GWADW 15/20
Albert-Einstein-Institute Hannover #2 Counter-Propagating, Large f 0, f=0 Coupling factor C 2= A<ETEM 00 • m(x, y) • E*TEM 00> K. Kokeyama and Andre Thüring 17 May 2010, GWADW 15/20
Albert-Einstein-Institute Hannover Scattering Field Category Counterpropagating Normalpropagating # f 0 f Scat field Scat power 1 Small 0 Rigorous field Large 2 Large 0 Rigorous field Small 3 Small Gauss tail small? 4 Large Spherical wave approx. Small 5 Small Gauss tail small? 6 Large Spherical wave approx. Small K. Kokeyama and Andre Thüring 17 May 2010, GWADW 16/20
Albert-Einstein-Institute Hannover #3 Counter-Propagating, Large f (at 2 nd scat) C 3=<ETEM 00 tail • E*TEM 00> #4 Counter-Propagating, Small f (at 2 nd scat) C 4 =<ESphe • E*TEM 00> K. Kokeyama and Andre Thüring 17 May 2010, GWADW 16/20
Albert-Einstein-Institute Hannover Scattering Field Category Counterpropagating Normalpropagating # f 0 f Scat field Scat power 1 Small 0 Rigorous field Large 2 Large 0 Rigorous field Small 3 Small Gauss tail small? 4 Large Spherical wave approx. Small 5 Small Gauss tail small? 6 Large Spherical wave approx. Small K. Kokeyama and Andre Thüring 17 May 2010, GWADW 17/20
Albert-Einstein-Institute Hannover #5 Normal-Propagating, Large f (at 2 nd scat) C 5=<ETEM 00 tail • E*#TEM 00> #6 Normal-Propagating, Small f (at 2 nd scat) C 6 =<ESphe • E*# TEM 00> K. Kokeyama and Andre Thüring 17 May 2010, GWADW 17/20
Albert-Einstein-Institute Hannover Liner Cavity Triangular Cavity Rectangular Cavity Bow-tie Cavity #1 (big scat) 0 A • C 1 0 4 A • C 1 #2 (small scat) 0 2 A • C 2 4 A • C 2 0 #3 (Gauss tail. cp) 0 0 2 • C 3 Negligible 0 2 • C 4 Negligible #4 (sphe. cp) -----= 0 #5 (Gauss tail. np) 0 0 2 • C 5 Negligible #6 (sphe, np) 0 0 2 • C 6 Negligible Total K. Kokeyama and Andre Thüring 17 May 2010, GWADW 18/20
Albert-Einstein-Institute Hannover Preliminary Results Liner Cavity Triangular Cavity Rectangular Cavity Bow-tie Cavity #1 (big scat) 0 A • C 1 0 4 A • C 1 #2 (small scat) 0 2 A • C 2 4 A • C 2 0 #3 (Gauss tail. cp) 0 0 2 • C 3 Negligible #4 (sphe. cp) 0 0 2 • C 4 Negligible #5 (Gauss tail. np) 0 0 2 • C 5 Negligible #6 (sphe, np) 0 0 2 • C 6 Negligible Total K. Kokeyama and Andre Thüring 17 May 2010, GWADW 19/20
Albert-Einstein-Institute Hannover 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 K. Kokeyama and Andre Thüring 17 May 2010, GWADW 20/20
- Slides: 31