1. ET-ILIAS_GWA joint meeting, 24-26. Nov. 2008 Henning Rehbein Detuned signal-recycling interferometer unstableresonance worsesensitivity enhancedsensitivity Local readout scheme H. Rehbein et al.: Phys. Rev. D, 76, 062002 (2007) Double optical spring H. Rehbein et al.: Phys. Rev. D, 78, 062003 (2008) Unstable optomechanical resonance Deteriorated sensitivity below optomechanical resonance   Unstable optomechanical resonance Deteriorated sensitivity below optomechanical resonance 

2. ET-ILIAS_GWA joint meeting, 24-26. Nov. 2008 Henning Rehbein Signal transfer function ETM SRM ETM ITM PRM BS Optical spring rigidly connects input test mass mirrors (ITMs) and end test mass mirrors (ETMs) at frequencies below the optomechanical resonance → cf. optical bar scheme Optical spring rigidity

3. ET-ILIAS_GWA joint meeting, 24-26. Nov. 2008 Henning Rehbein Signal transfer function Non-optical spring scenario

4. ET-ILIAS_GWA joint meeting, 24-26. Nov. 2008 Henning Rehbein Signal transfer function Optical spring scenario

5. ET-ILIAS_GWA joint meeting, 24-26. Nov. 2008 Henning Rehbein Local meter Local meter senses ITMs’ differential motion Local meter offers complementary sensitivity for frequencies below optical spring resonance Secondary laser beam (subcarrier) does not enter arm cavities Carrier and subcarrier must differ in frequency and/or polarization Effective mass sensed by local meter is twice that of ITM or ETM (assuming equal masses) Additional degrees of freedom usable for fine tuning of noise spectral density Extension to stand-alone optical bar or SR schemes Local readout scheme [H. Rehbein et al., 2007]

6. ET-ILIAS_GWA joint meeting, 24-26. Nov. 2008 Henning Rehbein Multi-carrier interferometer Vacuum input Classical noise GW signal Interferometer transfer function Interferometer Optimal filter Optimally combined noise spectral density Optimally combined noise spectral density

7. ET-ILIAS_GWA joint meeting, 24-26. Nov. 2008 Henning Rehbein Quantum noise spectral densities Improvement of sensitivity above optomechanical resonance Local meter’s performance only depends on ratio P (2) / ² (2) Requirement: SR cavity parameters independently adjustable for carrier and subcarrier

8. ET-ILIAS_GWA joint meeting, 24-26. Nov. 2008 Henning Rehbein Quantum noise spectral densities Improvement of sensitivity above optomechanical resonance Local meter’s performance only depends on ratio P (2) / ² (2) Requirement: SR cavity parameters independently adjustable for carrier and subcarrier

9. ET-ILIAS_GWA joint meeting, 24-26. Nov. 2008 Henning Rehbein Spectral densities with classical noise Advanced LIGO classical noise budget pre- estimated by simulation tool Bench Improvement in event rate normalized to Advanced LIGO narrowband performance Optimization for detection of neutron star binary systems with total mass of M=2.8M ¯ (narrowband optimization) Broadband optimization: sensitivity shifted by well-defined amount from low frequencies to high frequency regime

10. ET-ILIAS_GWA joint meeting, 24-26. Nov. 2008 Henning Rehbein Combination with QND techniques Variational squeezed light input or variational homodyne readout applied to local meter Local meter is tuned and exhibits large bandwidth ) input and/or output optics can be modified easily Squeezed light: noise spectral density reduced by constant factor Variational homodyne readout: cancellation of radiation pressure noise

11. ET-ILIAS_GWA joint meeting, 24-26. Nov. 2008 Henning Rehbein Optical Spring: classical dynamics Damping Anti-damping Restoring Anti-restoring Blue detuned Red detuned Frequency dependent spring constant: (anti-) restoring K, (anti-) damping ¡ Depending on sign of detuning ¸ we obtain either Restoring (K>0) + Anti-damping ( ¡ <0) or Anti-restoring (K 0) Can we combine two optical springs such that the resulting system exhibits Restoring ( K >0) + Damping ( ¡ >0) ? Stable Anti-stable Statically unstable Dynamically unstable 10 5 2 1 0.5 0.2 0.1 -10-5 -2 -0.5 -0.2 -0.1

12. ET-ILIAS_GWA joint meeting, 24-26. Nov. 2008 Henning Rehbein Mechanical analogue Stable Anti-stable Statically unstable Dynamically unstable restoring + damping anti-restoring + damping anti-restoring + anti-damping restoring + anti-damping

13. ET-ILIAS_GWA joint meeting, 24-26. Nov. 2008 Henning Rehbein Stable double optical spring When two optical springs are combined, their complex spring constants add up: Precise stability condition: all roots of the characteristic equation must have negative imaginary parts Stable Anti-stable Statically unstable Dynamically unstable ! vector addition!

14. ET-ILIAS_GWA joint meeting, 24-26. Nov. 2008 Henning Rehbein Double optical spring interferometer Carrier and subcarrier resonate inside arm cavities Carrier fields must differ in frequency and/or polarization Test masses trapped by stable ponderomotive potential well generated by two carrier fields with opposite detunings ) all optical stabilization Independent homodyne readout of each output field Optical detuning phase and SRM reflectivity can be varied independently for each carrier light Different SR cavities sensed by carrier and subcarrier are each equivalent to single detuned cavity Double optical spring scheme ETM B SRM ETM A ITM A ITM B PRM BS carrier sub- carrier

15. ET-ILIAS_GWA joint meeting, 24-26. Nov. 2008 Henning Rehbein Example 1: weak stabilization scenario spring B subcarrier spring A carrier total spring Weak second carrier is used to stabilize typical Advanced LIGO narrowband configuration Stable regions versus effective half bandwidth ² (2) and effective detuning ¸ (2) associated with second carrier in the case of three different circulating powers, i.e. P (2) = 8 kW, 40 kW and 80 kW

16. ET-ILIAS_GWA joint meeting, 24-26. Nov. 2008 Henning Rehbein Example 1: weak stabilization scenario spring B subcarrier spring A carrier total spring Weak second carrier is used to stabilize typical Advanced LIGO narrowband configuration Stable regions versus effective half bandwidth ² (2) and effective detuning ¸ (2) associated with second carrier in the case of three different circulating powers, i.e. P (2) = 8 kW, 40 kW and 80 kW

17. ET-ILIAS_GWA joint meeting, 24-26. Nov. 2008 Henning Rehbein Example 2: annihilation scenario spring B subcarrier spring A carrier Total circulating power equally distributed to the two carrier lights, i.e. P (1) =P (2) =400 kW Corresponding detunings are chosen oppositely Optical springs cancel each other  stable system Shot noise limited sensitivity remains unchanged Improved sensitivity in low frequency regime due to cancelled optical spring

18. ET-ILIAS_GWA joint meeting, 24-26. Nov. 2008 Henning Rehbein Spectral densities with classical noise Same reflectivity of the SR mirror assumed for both carriers Optimal configuration for detection of NS-NS binaries: annihilation scenario Comparison of single optical spring Advanced LIGO narrowband configuration with optimized DOS schemes Advanced LIGO classical noise budget pre-estimated by simulation tool Bench

19. ET-ILIAS_GWA joint meeting, 24-26. Nov. 2008 Henning Rehbein Spectral densities with classical noise Different SR mirror relativities for first and second carrier allowed ) additional degrees of freedom Noise spectral density almost follows borderline set by classical noise budget Comparison of single optical spring Advanced LIGO narrowband configuration with optimized DOS schemes Advanced LIGO classical noise budget pre-estimated by simulation tool Bench

20. ET-ILIAS_GWA joint meeting, 24-26. Nov. 2008 Henning Rehbein Sustainability of DOS configuration DOS scheme largely limited by classical noise Classical noise budget might be reduced in the near future We assume: –suspension thermal noise and gravity gradient noise lowered by factor of 10 in amplitude –coating thermal noise lowered by factor of 3 in amplitude Classical noise budget leaves further room for improvement! Options: –QND techniques (squeezing…) –Combining LR and DOS scheme

21. ET-ILIAS_GWA joint meeting, 24-26. Nov. 2008 Henning Rehbein Double optical spring experiment

22. ET-ILIAS_GWA joint meeting, 24-26. Nov. 2008 Henning Rehbein Summary Additional carrier field senses central Michelson degree of freedom of a detuned signal-recycled interferometer ) direct improvement of sensitivity below optomechanical resonance Local readout scheme unifies signal- recycling and optical bar technique ETM B SRM ETM A ITM A ITM B PRM BS carrier subcarrier ETM B SRM ETM A ITM A ITM B PRM BS carrier subcarrier Local readout schemeDouble optical spring scheme All-optical stabilization by combination of two optical springs provided by two carrier fields ) test masses trapped by stable ponderomotive potential Additional degrees of freedom ) flexibility in reshaping noise spectral density  Significantly improved sensitivity  Possible upgrade of Advanced LIGO  Candidate design for third generation detectors