1. Overview of quantum noise suppression techniques
Helge Müller-Ebhardt, Henning Rehbein, Kentaro Somiya, Roman Schnabel, Karsten Danzmann and Yanbei Chen
Max-Planck-Institut für Gravitationsphysik (AEI)
Institut für Gravitationsphysik, Leibniz Universität Hannover
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2. Quantum measurement noise
measurement noise = photon shot noise + radiation pressure noise
free mass dynamics
quantum measurement process
no correlation in shot and back-action noise
measurement frequency

3. Quantum measurement noise
measurement noise = photon shot noise + radiation pressure noise
free mass dynamics
quantum measurement process
use correlation in shot and back-action noise
measurement frequency

4. balanced homodyne detection
QND techniques
scheme
benefit
frequency band
balanced homodyne detection
pushes quantum noise down to shot noise level
in radiation pressure dominated regime
variational output
overall frequencies
squeezed input
reduces quantum noise by the squeezing factor
signal recycling
increases sensitivity
around resonances
speed meter
quantum noise parallel to standard quantum limit
transducer
at low frequencies
double carrier
at low frequencies and around resonances 4

5. QND techniques
balanced homodyne detection at frequency-independent quadrature angle
variational output with frequency-dependent quadrature angle
[Kimble et al, 2001]

6. balanced homodyne detection
QND techniques
scheme
benefit
frequency band
balanced homodyne detection
pushes quantum noise down to shot noise level
in radiation pressure dominated regime
variational output
overall frequencies
squeezed input
reduces quantum noise by the squeezing factor
signal recycling
increases sensitivity
around resonances
speed meter
quantum noise parallel to standard quantum limit
transducer
at low frequencies
double carrier
at low frequencies and around resonances 6

7. QND techniques
10 dB squeezed input at frequency-independent quadrature angle
10 dB squeezed input with frequency-dependent quadrature angle
[Kimble et al, 2001]

8. balanced homodyne detection
QND techniques
scheme
benefit
frequency band
balanced homodyne detection
pushes quantum noise down to shot noise level
in radiation pressure dominated regime
variational output
overall frequencies
squeezed input
reduces quantum noise by the squeezing factor
signal recycling
increases sensitivity
around resonances
speed meter
quantum noise parallel to standard quantum limit
transducer
at low frequencies
double carrier
at low frequencies and around resonances

9. Signal-recycled Michelson interferometer
signal-recycling mirror at the dark output port → signal becomes amplified due to an increasing interaction time
[Meers, 1988]
detuned signal-recycling cavity → optical spring produces additional resonance
[Buonanno & Chen, 2001 – 2003]

10. Optical spring effect
a cavity which is detuned from the carrier's frequency makes the power inside the cavity dependent on the motion of the mirror

11. Optical spring effect
a cavity which is detuned from the carrier's frequency makes the power inside the cavity dependent on the motion of the mirror
damping
anti-damping
optical power lags behind the cavity motion → complex spring constant → system becomes unstable
possible solution: stable double optical spring

12. Speed meter idea
measure position difference after time delay → measure speed
[Braginsky & Khalili, 1990]
conserved momentum usually proportional to speed → real QND?
no: because the coupling to speed changes conserved momentum
[Khalili, 2002]

13. Speed meter realization
two different optical realizations
Michelson interferometer Sagnac interferometer
[Purdue, 2002]
[Chen, 2003]

14. Optical inertia effect
a speed meter which is detuned from the carrier's frequency makes the fluctuating radiation-pressure force dependent on the acceleration of the mirror
dynamical mass is modified

15. Signal-recycled Sagnac interferometer
signal-recycling mirror at the dark output port
- two optical resonances
degenerated resonance case → speed meter
bandwidth important factor

16. Signal-recycled Sagnac interferometer
optimize quantum noise in vicinity of standard classical noise budget
AdvLIGO-scale
parameters fixed
40 kg mirrors
4 km arms
800 kW power
optimization
parameters
sr detuning
sr bandwidth
arm cavity bandwidth (250 Hz)
→ finesse (150)
improves AdvLIGO by 45 % in the event rate

17. Signal-recycled Sagnac interferometer
optimize quantum noise in vicinity of future classical noise budget
AdvLIGO-scale
parameters fixed
40 kg mirrors
4 km arms
800 kW power
optimization
parameters
sr detuning
sr bandwidth
arm cavity bandwidth (125 Hz)
→ finesse (300)
improves Michelson by 230 % in the event rate

18. Transducer idea
radiation pressure force can transduce motion between front and end mirror of a detuned cavity
SQL of a local meter
optical bar detector
[Braginsky, Gorodetsky & Khalili, 1997]

19. Position meter transducer
infinite optical inertia
rigid optical spring
zero optical inertia
every position meter transducer becomes an optical bar at low frequencies
SQL beating
narrowband SQL beating

20. Speed meter transducer
infinite optical inertia
zero optical inertia
speed meter transducer is more flexible at low frequencies

21. Local readout scheme second carrier senses motion of input mirrors
both outputs are optimally filtered