Quantum-noise limited sensitivity (of Advanced LIGO)
(An optics simulation with Finesse)
The following shows how to compute the quantum-noise limited sensitivity of an interferometric gravitational wave detector with Finesse.
The input file
%------------------------------------------------------------------------ % Finesse input file to model a Michelson interferometer % with power and signal recycling. The setup is based on % the aLIGO reference design, DCC number M060056 % Daniel Brown 17.05.2014 %------------------------------------------------------------------------ l l1 $Pin 0 nin s s1 0 nin nprc1 # Power recycling mirror m1 prm $prmT 37.5u 90 nprc1 nprc2 s prc $lprc nprc2 nbsin # Central beamsplitter bs bs1 .5 .5 0 45 nbsin n0y n0x nbsout # X-arm s ichx $lmichx n0x n1x m1 itmx $itmT 37.5u 90 n1x n2x s armx $Larm n2x n3x m1 etmx 5u 37.5u 89.999875 n3x n4x attr itmx mass $Mtm zmech sus1 attr etmx mass $Mtm zmech sus1 # Y-arm s ichy $lmichy n0y n1y m1 itmy $itmT 37.5u $michy_phi n1y n2y s army $Larm n2y n3y m1 etmy 5u 37.5u 0.000125 n3y n4y attr itmy mass $Mtm zmech sus1 attr etmy mass $Mtm zmech sus1 # Signal recycling mirror s src $lsrc nbsout nsrc1 m1 srm $srmT 37.5u $srm_phi nsrc1 nsrc2 # Force-to-position transfer function for longitudinal # motions of test masses tf sus1 1 0 p $mech_fres $mech_Q const mech_fres 1 # 9 sus-thermal spike const mech_Q 1M # Guess for suspension Q factor # DC readout: 100mW = michy_phi 0.07 _or_ darm_phi .00025 const michy_phi 0 const darm_phi .00025 const Larm 3995 const itmT 0.014 const srmT 0.2 const prmT 0.03 const Pin 125 const Mtm 40 const srm_phi -90 const lmichx 4.5 const lmichy 4.45 const lprc 53 const lsrc 50.525 # A squeezed source could be injected into the dark port sq sq1 0 0 90 nsrc2 # Differentially modulate the arm lengths fsig darm armx 1 0 fsig darm2 army 1 180 # Output the full quantum noise limited sensitivity qnoisedS NSR_with_RP 1 $fs nsrc2 # Output just the shot noise limited sensitivity qshotS NSR_without_RP 1 $fs nsrc2 # We could also display the quantum noise and the signal # separately by uncommenting these two lines. # qnoised noise 1 $fs nsrc2 # pd1 signal $fs nsrc2 xaxis darm f log 5 5k 1000 yaxis log abs
The file will firstly setup all the various optical cavities (using a plane waves model). It then proceeds to suspend the arm cavity mirrors whilst setting the mechanical suspension transfer functions to a simple pendulum with a resonance at 1 Hz. Next, a gravitational wave signal is injected as a modulation to both arm `spaces', out of phase by 180 degrees. Lastly we use the qnoisedS and qshotS detectors to output the noise-to-signal ratio, or the sensitivity.
The optical layout
The optical layout is a very much simplified version of the Advanced LIGO interferometer, a Michelson interferometer with Fabry-Perot cavities in the arms, power recycling and signal recycling. Squeezed light is injected into the so-called dark port, which is also the main detection port, in which we measure the sensitivity.
Output graph
The model is loosely based on the Advanced LIGO design file and thus we expect to see the peak sensitivity around 100 Hz at a sensitivity of about 10^(-23)/sqrt(Hz). We can see the both the qnoised and qshot agree at high frequencies, because they both model shot noise correctly. At low frequencies we see that they differ only qnoised takes into account the radiation pressure effects.