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
Helge Müller-Ebhardt
ET meeting, 2008, Cascina
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
Helge Müller-Ebhardt
ET meeting, 2008, Cascina
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
Helge Müller-Ebhardt
ET meeting, 2008, Cascina
QND techniques
scheme
benefit
balanced homodyne pushes quantum noise
detection
down to shot noise level
variational output
pushes quantum noise
down to shot noise level
frequency band
in radiation pressure
dominated regime
overall frequencies
squeezed input
reduces quantum noise by
overall frequencies
the squeezing factor
signal recycling
increases sensitivity
around resonances
quantum noise parallel to
standard quantum limit
in radiation pressure
dominated regime
transducer
increases sensitivity
at low frequencies
double carrier
increases sensitivity
at low frequencies and
around resonances
speed meter
Helge Müller-Ebhardt
ET meeting, 2008, Cascina
QND techniques
balanced homodyne detection
at frequency-independent
quadrature angle
variational output with frequencydependent quadrature angle
[Kimble et al, 2001]
Helge Müller-Ebhardt
ET meeting, 2008, Cascina
QND techniques
scheme
benefit
balanced homodyne pushes quantum noise
detection
down to shot noise level
variational output
pushes quantum noise
down to shot noise level
frequency band
in radiation pressure
dominated regime
overall frequencies
squeezed input
reduces quantum noise by
overall frequencies
the squeezing factor
signal recycling
increases sensitivity
around resonances
quantum noise parallel to
standard quantum limit
in radiation pressure
dominated regime
transducer
increases sensitivity
at low frequencies
double carrier
increases sensitivity
at low frequencies and
around resonances
speed meter
Helge Müller-Ebhardt
ET meeting, 2008, Cascina
QND techniques
10 dB squeezed input at
frequency-independent
quadrature angle
10 dB squeezed input with frequencydependent quadrature angle
[Kimble et al, 2001]
Helge Müller-Ebhardt
ET meeting, 2008, Cascina
QND techniques
scheme
benefit
balanced homodyne pushes quantum noise
detection
down to shot noise level
variational output
pushes quantum noise
down to shot noise level
frequency band
in radiation pressure
dominated regime
overall frequencies
squeezed input
reduces quantum noise by
overall frequencies
the squeezing factor
signal recycling
increases sensitivity
around resonances
quantum noise parallel to
standard quantum limit
in radiation pressure
dominated regime
transducer
increases sensitivity
at low frequencies
double carrier
increases sensitivity
at low frequencies and
around resonances
speed meter
Helge Müller-Ebhardt
ET meeting, 2008, Cascina
[Meers, 1988]
Signal-recycled Michelson interferometer
signal-recycling mirror
at the dark output port
→ signal becomes
amplified due to an
increasing interaction
time
detuned signal-recycling cavity
→ optical spring produces
additional resonance
[Buonanno & Chen, 2001 – 2003]
Helge Müller-Ebhardt
ET meeting, 2008, Cascina
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
Helge Müller-Ebhardt
ET meeting, 2008, Cascina
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
optical power lags behind the cavity motion → complex spring
constant → system becomes unstable
possible solution: stable double optical spring
Helge Müller-Ebhardt
ET meeting, 2008, Cascina
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]
Helge Müller-Ebhardt
ET meeting, 2008, Cascina
Speed meter realization
two different optical realizations
Michelson interferometer
[Purdue, 2002]
Helge Müller-Ebhardt
Sagnac interferometer
[Chen, 2003]
ET meeting, 2008, Cascina
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
Helge Müller-Ebhardt
ET meeting, 2008, Cascina
Signal-recycled Sagnac interferometer
signal-recycling mirror
at the dark output port
- two optical resonances
- degenerated resonance
case → speed meter
- bandwidth important factor
Helge Müller-Ebhardt
ET meeting, 2008, Cascina
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)
Helge Müller-Ebhardt
improves AdvLIGO by
45 % in the event rate
ET meeting, 2008, Cascina
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)
Helge Müller-Ebhardt
improves Michelson by
230 % in the event rate
ET meeting, 2008, Cascina
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]
Helge Müller-Ebhardt
ET meeting, 2008, Cascina
Position meter transducer
rigid optical
spring
infinite optical
inertia
zero optical
inertia
every position meter
transducer becomes
an optical bar at low
frequencies
SQL beating
narrowband
SQL beating
Helge Müller-Ebhardt
ET meeting, 2008, Cascina
Speed meter transducer
zero optical
inertia
infinite optical
inertia
speed meter
transducer is
more flexible at
low frequencies
Helge Müller-Ebhardt
ET meeting, 2008, Cascina
Local readout scheme
second carrier
senses motion of
input mirrors
both outputs are optimally
filtered
Helge Müller-Ebhardt
ET meeting, 2008, Cascina