AN EXPERIMENT TO MEASURE OPTOMECHANICAL SQUEEZING AT THE 40M PROTOTYPE INTERFEROMETER
4.2 Optical loss
of [60].
It is worth emphasizing that the goal of this particular experiment isnotto maximize the signal-to-noise ratio of the DARM signal (which is the primary objective at terrestrial observatories, since better SNR would presumably lead to more precise astrophysical measurements and probes of deviations from General Relativity). The quadrature which should be selected for that purpose is different from what is selected for the optomechanical squeezing experiment. We seek the quadrature at which the ratio of noise variance inbζ to unsqueezed vacuum is minimized. Other ways of validating the quantum-mechanical nature of the interferometer, encoded in the matrixC, include injecting well-characterizedsqueezedvacuum into the AS port, measure the output field, and inferring theoptomechanicalsqueezing operation by mapping the relationship between the two - this was the approach adopted in [47].
photodiodess), due to scattering, mode-mismatch between the OMC’s and the IFO’s cavity eigenmodes, and imperfect quantum efficiency of the detection photodiodes.
These sources of loss can be accounted for in the same way as theCmatrix accounts for unsqueezed vacuum entering the AS port. I have listed the sources of loss in this way to indicate that there are different mechanisms at play, but from an analysis point of view, (ii),(iii), and (iv) are grouped together as "SRC losses". So Eq. (4.1) would have additional terms, which are 2×2 matrices - lettersP,Q, andNare used in [54] to refer to "SRC losses", photodetection chain losses, and arm cavity losses respectively. This more complete version of Eq. (4.1), with the effects of optical loss on the quadrature noise included, was what was explored numerically to identify the interferometer configuration that would allow us to measure an optomechanically squeezed field in the presence of classical noise sources. For this analysis, losses due to mode-mismatch between optical cavities is treated in a simplified way that does not account for cavity enhancement effects in the SRC.
4.2.2 Limited optical power buildup
We are relying on the optomechanical interaction between the high circulating power in the arm cavities and the suspended mirrors to generate a squeezed state.
The stronger this interaction, the greater the squeezing, and hence, we will have better immunity to degradation of the generated squeezed state due to imperfections elsewhere in the interferometer and the photodetection chain. The radiation pressure force exerted by a beam with powerPis 2P/c, and so it is desirable to have as high a power resonate in the arm cavity as is practically feasible. We rely on the resonant enhancement in the PRC and arm cavities to realize this high power buildup, with O(10 kW)power in the 40m resonant arm cavities whose mirrors weigh 250 g, for O(10 W)amount of power input to the IFO4. Furthermore, there are at least two high- finesse cavities, the PMC and the IMC, in addition to the Input Faraday Isolator (IFI), between the amplifier output housed in an enclosure outside the vacuum envelope, and the PRM, which is inside the vacuum envelope. The transmissivity of these cavities is strongly dependent on the intracavity losses. The relationship between the power in the arm cavities, Parm and the laser amplifier output, Pamp may be written as
4At the time of writing, compact fiber-pumped amplifier units are available that can generate O(10 W) of light with sufficient frequency and intensity stability, with O(100 mW) input from a stable source such as an NPRO [66].
Parm= Pamp·TPMC·TIMC·TIFI·α·GPRC ·TBS·Garm, (4.2) whereGidenotes the power gain of the cavityi,Tjdenotes the power transmissivity of the element j, andαdenotes an effective mode-matching between the input beam and the arm cavity’s spatial eigenmodes. Using multiple different measurement techniques, we have verified that it is possible to get theround-triploss in the 40m arm cavities to be as low as 20-30 ppm, so we expectGarm ≈ 270. As discussed in Section3.4.9,GPRCis currently limited to≈20 due to the internal losses in the PRC - once we replace the folding mirrors, we expect that we can realizeGPRC ≈40. TBS is 50%, whileTPMC ≈85%. From the arm cavity scans discussed in Section2.6, the mode-matching efficiency between the input beam and the arm cavity’s eigenmode is
≈93%, but this number does not account for possible mismatches between the PRC and arm cavity eigenmode. Finally, the productTIMC·TIFIis estimated to be≈ 50 %.
Putting all these numbers together, I estimate Parm ≈ 2200Pamp. We expect to be able to improve this toParm ≈ 4000Pamp, if we can increase the productTIMC·TIFI to 0.9, which we expect to be able to do with a vent of the vacuum system to clean the IMC optics and tune the polarization optics in the IFI. The numbers related to optical loss used for the modeling results presented in this thesis are summarized in Table4.1.
Parameter Value
Arm cavity lossesLarm 20 ppm
PRC losses,LPRC 1000ppm
SRC losses,LSRC 1000ppm
PMC transmission,TPMC 85%
IMC transmission,TIMC 95%
IFI transmission,TIFI 95%
Effective mode-matching,α 93%
Power recycling gain,GPRC 40
Arm cavity gain,Garm 280
Photodetection chain losses,LPD 5%
Table 4.1: Optical losses at various points in the 40m interferometer. Numbers inboldare optimistic projections of what will be achievable, while other numbers have been measured in the current 40m interferometer.
101 102 103 104
Frequency [Hz]
10−20 10−19 10−18 10−17
Displacement noise [ m / √ Hz ]
φ=−0.01◦ ζ = 88.00◦
Larm= 30ppm
LPRC= 1000ppm
LSRC= 1000ppm
Pin= 1.0 W Pin= 2.0 W Pin= 5.0 W Pin= 10.0 W Pin= 30.0 W SQL Displacement noises
Figure 4.1: Quantum noise as a function of input power for the 40m. The parameters in Table4.1can be used together with Eq. (4.2) to mapPinin the legend to circulating power in the arm cavities. See text for what the solid and dashed lines indicate.