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