Transcript Document

Imagining the Future
What can we do about the Quantum Noise
Limit in Gravitational-wave Detectors?
Nergis Mavalvala
Penn State
October 2004
Quantum Noise in Optical Measurements
 Measurement process
 Interaction of light with test mass
 Counting signal photons with a photodetector
 Noise in measurement process
 Poissonian statistics of force on test mass due
to photons
 radiation pressure noise (RPN)
(amplitude fluctuations)
 Poissonian statistics of counting the photons
 shot noise (SN)
(phase fluctuations)
Limiting Noise Sources: Optical Noise
 Shot Noise
 Uncertainty in number of photons
1
h( f ) 
detected a
Pbs
 Higher circulating power P
bs
a low optical losses
 Frequency dependence a light (GW signal)
storage time in the interferometer
 Radiation Pressure Noise
 Photons impart momentum to cavity mirrors
Fluctuations in number of photons a
 Lower power, Pbs
h
(
f
 Frequency dependence
a response of mass to forces
)
 Optimal input power depends on frequency
Pbs
Mf 4
Free particle SQL
S RP
I0

M 2
uncorrelated
SShot
0.1 MW
1 MW
10 MW
1

I0
In the presence of correlations
 Output  Shot  Radiation Pressure  Signal
Stotal  S SN  S RPN  2 Scorr
 Heisenberg uncertainty principle in
spectral domain
Sshot S RP  S
2
corr
2
SSQL
8

where SSQL () 
4
M 2 L2
 Follows that
S shot S RP
2
SSQL

when Scorr  0
4
Initial LIGO
Signal-tuned Interferometers
The Next Generation
A Quantum Limited Interferometer
LIGO I
LIGO II
How will we get there?
 Seismic noise
 Active isolation system
 Mirrors suspended as fourth (!!) stage of
quadruple pendulums
 Thermal noise
 Suspension  fused quartz; ribbons
 Test mass  higher mechanical Q material,
e.g. sapphire; more massive (40 kg)
 Optical noise
 Input laser power  increase to ~200 W
 Optimize interferometer response
 signal recycling
Signal-recycled Interferometer
Cavity forms compound
output coupler with
complex reflectivity. Peak
response tuned by
changing position of SRM
800 kW
r (l )e j (l )
125 W
ℓ
signal
Signal
Recycling
Reflects GW
photons back into
interferometer to
accrue more phase
Advanced LIGO Sensitivity
Improved and Tunable
broadband
detuned
narrowband
thermal noise
  0.025
  0.120
  0.025
  0.120
  0.93
  0.93
  0.93
  0.99
Sub-Quantum Interferometers
Squeezed input vacuum state
in Michelson Interferometer
 GW signal in the phase
quadrature
 Not true for all
interferometer
configurations
 Detuned signal recycled
interferometer 
GW signal in both
quadratures

XX
++
XX

XX
+
X
+
X
 Orient squeezed state
to reduce noise in
phase quadrature
Back Action Produces Squeezing
Squeezing produced by backaction force of fluctuating
radiation
pressure
on mirrors
 Vacuum
state enters
ba
b  S  r,  port
a
anti-symmetric
 Amplitude fluctuations of
b1 input
a1 state drive mirror
position
b2 Mirror
a2 motion
a1 imposes
 h
those amplitude
1 phase
2 r onto
fluctuations
Sb1 (of) output
e field


ba22

ba11
Sb2 ( )  e

2 r



Conventional Interferometer
with Arm Cavities
 Coupling coefficient 
converts a1 to b2
  and squeeze angle 
depends on I0, fcav,
losses, f
a b
Amplitude  b1 = a1
Phase
 b 2 = - a1 + a 2 + h
Radiation Pressure
Shot Noise
Optimal Squeeze Angle
 If we squeeze a2
 Shot noise is reduced at high frequencies
BUT
 Radiation pressure noise at low frequencies is
increased
 If we could squeeze - a1+a2 instead
 Could reduce the noise at all frequencies
 “Squeeze angle” describes the quadrature
being squeezed
Frequency-dependent Squeeze Angle
Realizing a frequency-dependent
squeeze angle
filter cavities
 Filter cavities
 Difficulties
 Low losses
 Highly detuned
 Multiple cavities
• Conventional interferometers 
• Kimble, Levin, Matsko, Thorne, and Vyatchanin, Phys. Rev. D 65, 022002 (2001).
• Signal tuned interferometers 
• Harms, Chen, Chelkowski, Franzen, Vahlbruch, Danzmann, and Schnabel,
gr-qc/0303066 (2003).
Squeezing – the ubiquitous fix?
 All interferometer configurations can benefit
from squeezing
 Radiation pressure noise can be removed from
readout in certain cases
 Shot noise limit only improved by more power
(yikes!) or squeezing (eek!)
 Reduction in shot noise by squeezing can allow
for reduction in circulating power (for the same
sensitivity) – important for power-handling
Sub-quantum-limited interferometer
X
Quantum correlations
(Buonanno and Chen)
Input squeezing
X+
 Requirements
Squeezed vacuum
 Squeezing at low frequencies (within GW band)
 Frequency-dependent squeeze angle
 Increased levels of squeezing
 Generation methods
 Non-linear optical media (c(2) and c(3) non-linearites) 
crystal-based squeezing (recent progress at ANU and MIT)
 Radiation pressure effects in interferometers 
ponderomotive squeezing (in design & construction phase)
 Challenges
 Frequency-dependence  filter cavities
 Amplitude filters
 Squeeze angle rotation filters
 Low-loss optical systems
Squeezing using
nonlinear optical media
Vacuum seeded OPO
ANU group  quant-ph/0405137
Squeezing using
back-action effects
The principle
 A “tabletop” interferometer to generate
squeezed light as an alternative nonlinear
optical media
 Use radiation pressure as the squeezing
mechanism
 Relies on intrinsic quantum physics of optical
fieldmechanical oscillator correlations
 Squeezing produced even when the sensitivity
is far worse than the SQL
 Due to noise suppression a la optical springs
Noise budget
Key ingredients
 High circulating laser power
 10 kW
 High-finesse cavities
 25000
 Light, low-noise mechanical oscillator
mirror
 1 gm with 1 Hz resonant frequency
 Optical spring
 Detuned arm cavities
Optical Springs
 Modify test mass dynamics
 Suppress displacement noise (compared to
free mass case)
 Why not use a
mechanical spring?
 Thermal noise
 Connect low-frequency
mechanical oscillator to
(nearly) noiseless optical
spring
Speed Meters
Speed meters
 Principle  weakly coupled oscillators
 Energy sloshes between the oscillators
 p phase shift after one slosh cycle
 Driving one oscillator excites the other
Implementation of a speed meter
sloshing cavity
homodyne detection




Position signal from arm cavity enters “sloshing” cavity
Exits “sloshing” cavity with p phase shift
Re-enters arm cavity and cancels position signal
Remaining signal  relative velocity of test masses
Purdue and Chen, Phys. Rev. D 66, 122004 (2002)
Intra-cavity readouts
Intra-cavity readouts
 Non-classical states of light exist inside
cavities (ponderomotive squeezing)
 Probe those intra-cavity squeezed fields
E  E  E  E
Braginsky et al., Phys. Lett. A 255, (1999)
Optical Bars and Optical Levers
 Couple a second “probe” mass to the test mass
 Probe mass does not interact with the strong light field in
the cavity
 Analogous to mechanical lever with advantage in the
ratio of unequal lever arms
Braginsky et al., Phys. Lett. A 232, (1997)
Interferometer Configurations
White Light Interferometers
 Broadband antenna response
 Make cavity longer for longer wavelengths
L0
b
a
L0
Guido Muller
All-reflective Interferometers
 Higher power-handling capability
 Grating beamsplitters
Peter Byersdorf
The Ultimate Wishlist
Technologies needed
 Low-noise high-power lasers
 What wavelength?
 Low absorption and scatter loss optics
 Low loss diffraction gratings
 High non-linearity optical materials
 High quantum efficiency photodetection
 Low mechanical loss oscillators
 With optical spring effect, oooh
In conclusion...
 Next generation – quantum noise limited
 Squeezing being pursued on two fronts
 Nonlinear optical media
 Back-action induced correlations
 Other Quantum Non-Demolition techniques
 Evade measurement back-action by measuring of an
observable that does not effect a later measurement
 Speed meters (Caltech, Moscow, ANU)
 Optical bars and levers (Moscow)
 Correlating SN and RPN quadratures
 Variational readout
 Power handling
 All-reflective
 Quadrature squeezing
Imagining the Future
What can we do about the Quantum Noise
Limit in Gravitational-wave Detectors?
Plenty!