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Albert-Einstein-Institute Hannover ET filter cavities for third generation detectors ET filter cavities for third generation detectors Keiko Kokeyama Andre Thüring

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Albert-Einstein-Institute Hannover 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. Kokeyama and Andre Thüring 17 May 2010, GWADW

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Albert-Einstein-Institute Hannover 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. Kokeyama and Andre Thüring 17 May 2010, GWADW

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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 & 1550nm laser HG00 mode 1/20 S. Hild et al. CQG 27 (2010) K. Kokeyama and Andre Thüring 17 May 2010, GWADW

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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 10dB We dream of a broadband QN-reduction by 10dB A broadband quantum noise reduction requires the frequency dependent squeezing, therefore filter cavities are necessary A broadband quantum noise reduction requires the frequency dependent squeezing, therefore filter cavities are necessary 2/20 K. Kokeyama and Andre Thüring 17 May 2010, GWADW

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Albert-Einstein-Institute Hannover 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. Kokeyama and Andre Thüring 17 May 2010, GWADW

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Albert-Einstein-Institute Hannover 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. Kokeyama and Andre Thüring 17 May 2010, GWADW

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Albert-Einstein-Institute Hannover Quantum noise in a Michelson interferometer X1X1 X2X2 X1X1 X2X2 Quantum noise reduction with squeezed light X1X1 X2X2 Filter cavities can optimize the squessing angles 3/20 K. Kokeyama and Andre Thüring 17 May 2010, GWADW

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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 In this talk we consider the two input filter cavities 4/20 K. Kokeyama and Andre Thüring 17 May 2010, GWADW

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Albert-Einstein-Institute Hannover 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. Kokeyama and Andre Thüring 17 May 2010, GWADW

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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 Limitations Infrastructure, optical loss (e.g. scattering), phase noise,......And the optical layout (Part2) 5/20 K. Kokeyama and Andre Thüring 17 May 2010, GWADW

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Albert-Einstein-Institute Hannover Degrading of squeezing due to optical loss A cavity reflectance R<1 means loss. The degrading of squeezing is then frequency dependent At every open (lossy) port vacuum noise couples in coupling mirror 6/20 K. Kokeyama and Andre Thüring 17 May 2010, GWADW

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Albert-Einstein-Institute Hannover The impact of intra-cavity loss There exists a lower limit L min. For L < L min the filter cavity is under- coupled and the compensation of the phase-space rotation fails! The filter‘s coupling mirror reflectance R c needs to be chosen with respect to 1. the required bandwidth accounting for 2. the round-trip loss l RT 3. a given length L 7/20 K. Kokeyama and Andre Thüring 17 May 2010, GWADW

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Albert-Einstein-Institute Hannover The impact of shortening the cavity length Example for ET-C LF detuning = 7.1 Hz 100 ppm round-trip loss, bandwidth = 2.1 Hz If L < Lmin ~ 1136 m the filter is under-coupled and the filtering does not work For L 1 The filter cavity must be as long as possible for ET-LF 8/20 K. Kokeyama and Andre Thüring 17 May 2010, GWADW

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Albert-Einstein-Institute Hannover Narrow bandwidths filter are more challenging Assumptions: L = 10 km, 100 ppm round-trip loss, Detuning = 2x bandwidth Assumptions: L = 10 km, 100 ppm round-trip loss, Detuning = 2x bandwidth Filter cavities with a bandwidth greater than 10 Hz are comparatively easy to realize 9/20 K. Kokeyama and Andre Thüring 17 May 2010, GWADW

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Albert-Einstein-Institute Hannover Exemplary considerations for ET-C LF Filter I: = 2.1 Hz f res = 7.1 Hz Filter II: = 12.4 Hz f res = 25.1 Hz Filter I: L = 2 km F = Rc = % Filter I: L = 2 km F = Rc = % Filter I: L = 5 km F = 7138 Rc = % Filter I: L = 5 km F = 7138 Rc = % Filter I: L = 10 km F = 3569 Rc = % Filter I: L = 10 km F = 3569 Rc = % Filter II: L = 2 km F = 3022 Rc = % Filter II: L = 2 km F = 3022 Rc = % Filter II: L = 5 km F = 1209 Rc = % Filter II: L = 5 km F = 1209 Rc = % Filter II: L = 10 km F = 604 Rc = % Filter II: L = 10 km F = 604 Rc = % 15dB squeezing 100ppm RT - loss 7% propagation loss 10/20 K. Kokeyama and Andre Thüring 17 May 2010, GWADW

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Albert-Einstein-Institute Hannover 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. Kokeyama and Andre Thüring 17 May 2010, GWADW

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Albert-Einstein-Institute Hannover Stray light analysis for four designs Which design is suitable for ET cavities from the point of view of the loss due to stray lights? Triangular - ConventionalLinear RectangularBow-tie 11/20 K. Kokeyama and Andre Thüring 17 May 2010, GWADW

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Albert-Einstein-Institute Hannover Scattering Angle and Fields TriangularLinear RectangularBow-tie 12/20 K. Kokeyama and Andre Thüring 17 May 2010, GWADW

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Albert-Einstein-Institute Hannover # Scat fieldScat power Counter- propagating 1Small0Rigorous fieldLarge 2 0Rigorous fieldSmall 3 Gauss tailsmall? 4LargeSpherical wave approx. Small Normal- propagating 5SmallGauss tailsmall? 6LargeSpherical wave approx. Small Scattering Field Category 13/20 K. Kokeyama and Andre Thüring 17 May 2010, GWADW

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Albert-Einstein-Institute Hannover # Scat fieldScat power Counter- propagating 1Small0Rigorous fieldLarge 2 0Rigorous fieldSmall 3 Gauss tailsmall? 4LargeSpherical wave approx. Small Normal- propagating 5SmallGauss tailsmall? 6LargeSpherical wave approx. Small Scattering Field Category 13/20 K. Kokeyama and Andre Thüring 17 May 2010, GWADW

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Albert-Einstein-Institute Hannover #1 Counter-Propagating, Small 0, C1 = A Coupling factor 14/20 K. Kokeyama and Andre Thüring 17 May 2010, GWADW

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Albert-Einstein-Institute Hannover # Scat fieldScat power Counter- propagating 1Small0Rigorous fieldLarge 2 0Rigorous fieldSmall 3 Gauss tailsmall? 4LargeSpherical wave approx. Small Normal- propagating 5SmallGauss tailsmall? 6LargeSpherical wave approx. Small Scattering Field Category 15/20 K. Kokeyama and Andre Thüring 17 May 2010, GWADW

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Albert-Einstein-Institute Hannover #2 Counter-Propagating, Large 0, Coupling factor C2= A 15/20 K. Kokeyama and Andre Thüring 17 May 2010, GWADW

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Albert-Einstein-Institute Hannover # Scat fieldScat power Counter- propagating 1Small0Rigorous fieldLarge 2 0Rigorous fieldSmall 3 Gauss tailsmall? 4LargeSpherical wave approx. Small Normal- propagating 5SmallGauss tailsmall? 6LargeSpherical wave approx. Small Scattering Field Category 16/20 K. Kokeyama and Andre Thüring 17 May 2010, GWADW

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Albert-Einstein-Institute Hannover #3 Counter-Propagating, Large (at 2 nd scat) C3= C4 = #4 Counter-Propagating, Small (at 2 nd scat) 16/20 K. Kokeyama and Andre Thüring 17 May 2010, GWADW

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Albert-Einstein-Institute Hannover # Scat fieldScat power Counter- propagating 1Small0Rigorous fieldLarge 2 0Rigorous fieldSmall 3 Gauss tailsmall? 4LargeSpherical wave approx. Small Normal- propagating 5SmallGauss tailsmall? 6LargeSpherical wave approx. Small Scattering Field Category 17/20 K. Kokeyama and Andre Thüring 17 May 2010, GWADW

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Albert-Einstein-Institute Hannover #5 Normal-Propagating, Large (at 2 nd scat) #6 Normal-Propagating, Small (at 2 nd scat) C5= C6 = 17/20 K. Kokeyama and Andre Thüring 17 May 2010, GWADW

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Albert-Einstein-Institute Hannover K. Kokeyama and Andre Thüring 17 May 2010, GWADW Liner Cavity Triangular Cavity Rectangular Cavity Bow-tie Cavity #1 (big scat) 0A C104A C1 #2 (small scat) 02A C24A C20 #3 (Gauss tail. cp) 002 C3Negligible #4 (sphe. cp) 002 C4Negligible #5 (Gauss tail. np) 002 C5Negligible #6 (sphe, np) 002 C6Negligible Total -----= 18/20

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Albert-Einstein-Institute Hannover Liner Cavity Triangular Cavity Rectangular Cavity Bow-tie Cavity #1 (big scat) 0A C104A C1 #2 (small scat) 02A C24A C20 #3 (Gauss tail. cp) 002 C3Negligible #4 (sphe. cp) 002 C4Negligible #5 (Gauss tail. np) 002 C5Negligible #6 (sphe, np) 002 C6Negligible Total Preliminary Results 19/20 K. Kokeyama and Andre Thüring 17 May 2010, GWADW

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Albert-Einstein-Institute Hannover 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 Summary 20/20 K. Kokeyama and Andre Thüring 17 May 2010, GWADW

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