Max-Planck-Institut für Gravitationsphysik
(Albert-Einstein-Institut)
HOMODYNE AND HETERODYNE READOUT OF A SIGNAL-RECYCLED GRAVITATIONAL WAVE DETECTOR
S. Hild, H. Grote, J. Degallaix, A. Freise, M. Hewitson, H. Lück, K.A. Strain, J.R. Smith and B. Willke
Motivation for DC-readout
LIGO-G070443-00-Z
Reduced shot noise (no contributing terms from 2 times the heterodyne frequency)
Reduction of oscillator phase noise and oscillator amplitude noise
Stronger low pass filtering of local oscillator (due to PR cavity pole)
Simplify the GW detector Simpler calibration (GW-signal in a single data-stream, even for detuned SR) Simpler circuits for photodiodes and readout electronics Possibility to use photodiodes with larger area => reduced coupling of pointing Reduced number of beating light fields at the output photodiode => simpler
couplings of technical noise
Requires less effort for injecting squeezed light (=> useful precursor for GEO-HF)
LO and GW pass the same optical system (identical delay, filtering, spatial profile) => This advantage is especially important for detectors with arm cavities.
Increased coupling of laser power noise.
Usually an output mode cleaner (OMC) is required.
Very sensitive to imbalances of the interferometer arms.
DefinitionsTuning/detuning of the Signal-Recycling cavity (microscopic length)
• tuned: carrier is resonant in SR-cavity
• detuned: carrier is off resonance in SR-cavity (550 Hz or 1 kHz)
Readout system
• heterodyne: LO from RF sidebands (Schnupp modulation)
• DC-readout / homodyne: Carrier from dark fringe offset serves as LO
Optical gain
Transfer function from differential dis-placement to signal at the detection point.
Simulated shot noise
Rotation of optical response (for detuned SR)
Tuned Signal-Recycling
Detuned Signal-Recycling (550Hz)
Summary
102
103
10-10
10-9
10-8
10-7
Frequency (Hz)
Opt
ical
Pow
er @
dar
kpor
t (
Wat
t / H
z1/
2)
nfft/fs = 2.00 : navs = 60 : enbw = 0.75 : nsecs = 120
reference S5
10% MI midx
10% MI midx + TEM00 carrier
Frequency [Hz]
Da
rkp
ort
po
we
r [W
/sq
rt(H
z)}
Heterodyne 550 Hz
Red. MI modulation
Red. MI modulation+ carrier from dfo
Turning down the radio frequency modulation (stable operation is possible with 10 lower sidebands)
Dark port is dominated by carrier light (TEM00) from a 50 pm dark fringe offset
We demonstrated a DC-readout scheme without output mode cleaner in GEO600.
DC-readout and heterodyne detection has been compared for several Signal-Recycling tunings.
Using DC-readout a displacement sen-sitivity of 2·10-19m/sqrt(Hz) is achieved.
Simulations were performed with FINESSE.
DC-readout gives a better peak sensitivity than hetero-dyne readout, independent of the SR tuning.
For detuned SR: A “rotation” of the detector response is observed, when going from heterodyne to DC-readout
102
103
105
Frequency [Hz]
Op
tical G
ain
[a.u
.]
102
103
-200
-100
0
100
200
Ph
ase [
deg
]
Frequency [Hz]
DC-readoutHeterodyne
C GW+ GW- MI+ MI-
f<< 550 Hz 0 0 0 0 180
f>>550 Hz 0 0 180 0 180
The predicted rotation of the detector response is confirmed by the measurements.
This phenomenon can be explained by the opposite phase of the two heterodyne sidebands.
102
103
10-22
10-21
10-20
10-19
Frequency [Hz]
Stra
in [1
/sqr
t(Hz)
]
Simulated shotnoise, DC-readout 550HzSimulated shotnoise, heterodyne 550Hzh(f), heterodyne 550 Hzh(f), DC-readout 550 Hz
102
103
10-7
10-6
10-5
10-4
10-3
10-2
Frequency [Hz]
AS
D [V
/sqr
t(H
z)]
Noise projection for DC-readout with detuned SR
Mid visMID AA FB RotMID AA FB TiltSignal recycling longitudinal noiseLaser amplitude noise (BS ar)PR errorDark noiseModelled shot noiseSum of the noise
Shot noiseIncreased in DC-readout
Roughly same as with heterodyne (2e-19m/sqrt(Hz))
Increasedtechnical noise
Laser power noise limits the sensitivity at some frequencies below 300 Hz.
Above 300 Hz laser power noise seems not to be a problem.
102
103
105
Op
tical G
ain
[a.u
.]
102
103
-100
0
100
200
Ph
ase [
deg
]
Frequency [Hz]
+ offset (large)+ offset (small)- offset (small)- offset (large)
102
103
100
101
Mag
[a
.u.]
Frequency [Hz]
measured data, 550 HzSimulation, 550 HzSimulation, tuned SRSimulation, tuned SR, adjusted mod freqSimulation, tuned SR, adjusted mod freq, lower mod index
102
103
100
101
Mag
[a
.u.]
Frequency [Hz]
measured data, 550 HzSimulation, 550 HzSimulation, tuned SRSimulation, tuned SR, adjusted mod freqSimulation, tuned SR, adjusted mod freq, lower mod index
102
103
10-21
10-20
10-19
Frequency [Hz]
ST
RA
IN [
1/s
qrt
(Hz)
]
+ offset (large)+ offset (small)- offset (small)- offset (large)
Optical gain increases with the size of the dark fringe offset. Optical gain for + and – dark fringe offset have 180 degree different phase. Sensitivity seems to independent of sign and size of the dark fringe offset.
Tuned SR is realized by using a fast jumping technique.
Two different operation modes: resonant and non resonant RF modulation frequency.
Simulation of Laser power noise
DC-readout in GEO without OMCHow to achieve DC-readout?
102
103
10-22
10-21
Frequency [Hz]
Str
ain
[1/
sqrt
(Hz)
]
Homodyne, 550HzHeterodyne, 550HzHomodyne, 1kHzHeterodyne, 1kHzHomodyne, tuned SR Heterodyne, tuned SR