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Detuned signal-recycling interferometer

worse sensitivity. enhanced sensitivity. unstable resonance. Detuned signal-recycling interferometer. 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).

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Detuned signal-recycling interferometer

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  1. worse sensitivity enhanced sensitivity unstable resonance Detuned signal-recycling interferometer 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) Deteriorated sensitivity belowoptomechanical resonance Deteriorated sensitivity belowoptomechanical resonance Unstable optomechanical resonance Unstable optomechanical resonance    

  2. ETM ITM BS PRM ITM ETM SRM Signal transfer function Signal transfer function 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. Signal transfer function Non-optical spring scenario

  4. Signal transfer function Optical spring scenario

  5. Local readout scheme 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 [H. Rehbein et al., 2007]

  6. Multi-carrier interferometer Classical noise Vacuum input GW signal Interferometer transfer function Optimal filter Optimally combined noise spectral density

  7. 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. 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. 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. 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. Optical Spring: classical dynamics • 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) + Damping (¡>0) • Can we combine two optical springs such that the resulting system exhibits • Restoring (K>0) + Damping (¡>0) ? Reddetuned Bluedetuned Damping Anti-damping -0.5 -1 -0.2 Statically unstable Stable Restoring -0.1 -2 10 5 -5 -10 2 Anti-restoring Dynamically unstable 0.1 Anti-stable 0.2 1 0.5

  12. Mechanical analogue Statically unstable Stable restoring +damping anti-restoring +damping restoring +anti-damping anti-restoring+anti-damping Anti-stable Dynamically unstable

  13. Stable double optical spring • When two optical springs are combined, their complex spring constants add up: • Precise stability condition: all roots of the characteristic equationmust have negative imaginary parts ! vector addition! Staticallyunstable Stable Anti-stable Dynamicallyunstable

  14. Double optical spring interferometer Double optical spring scheme • 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 ETMB ITMB BS carrier sub-carrier PRM ITMA ETMA SRM

  15. total spring spring Bsubcarrier spring Acarrier Example 1: weak stabilization scenario • 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. total spring spring Bsubcarrier spring Acarrier Example 1: weak stabilization scenario • 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. 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 systemShot noise limited sensitivity remains unchanged Improved sensitivity in low frequency regime due to cancelled optical spring spring Bsubcarrier spring Acarrier Example 2: annihilation scenario

  18. Spectral densities with classical noise • Comparison of single optical spring Advanced LIGO narrowband configuration with optimized DOS schemes • Advanced LIGO classical noise budget pre-estimated by simulation tool Bench • Same reflectivity of the SR mirror assumed for both carriers • Optimal configuration for detection of NS-NS binaries: annihilation scenario

  19. Spectral densities with classical noise • Comparison of single optical spring Advanced LIGO narrowband configuration with optimized DOS schemes • Advanced LIGO classical noise budget pre-estimated by simulation tool Bench • 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

  20. 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. Double optical spring experiment

  22. Summary Local readout scheme Double optical spring scheme • 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 • 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 ETMB ETMB • Significantly improved sensitivity • Possible upgrade of Advanced LIGO • Candidate design for thirdgeneration detectors ITMB ITMB BS carrier BS carrier subcarrier subcarrier PRM ITMA ETMA ITMA PRM SRM ETMA SRM

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