AN EXPERIMENT TO MEASURE OPTOMECHANICAL SQUEEZING AT THE 40M PROTOTYPE INTERFEROMETER
4.4 Prospects for measuring optomechanical squeezing in aLIGO
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Frequency [Hz]
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Displacement noise [ m / √ Hz ]
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10−20 10−19
φ= 80◦ φ= 85◦
φ= 90◦(nominal RSE) φ= 95◦
φ= 100◦
Measured DARM (@φ= 90◦) Classical noise estimate (@φ= 90◦)
Figure 4.2: Modelled quantum noise in aLIGO as a function of SRC detuning. The
"classical noise estimate" trace is reproduced from [47] - unlike Fig.4.1which plots only the displacement noises, this trace includesallnoise sources other than quan- tum noise. The "masured DARM" curve is included to show that below≈ 30 Hz, classical noises dominate the total measured noise. As in Fig.4.1, solid lines indicate unsqueezed vacuum injected from the dark port transformed by optomechanical in- teraction with the interferometer, while dashed lines are signal-referred unsqueezed vacuum levels (plotted in the same color for a givenφ).
4.4.1 Prospects with DC readout
First, let us consider the case where the field is read out using a special type of homodyne readout, called "DC readout". This is the system currently implemented at H1 and L1 to measure the gravitational wave signal. It differs from a traditional homodyne detection setup in that the LO field used to measure the IFO’s output field is sourced by introducing a deliberatesmallasymmetry in DARM, allowing a small amount of carrier light to leak out at the AS port. While this scheme offers many advantages, we are constrained to reading out fields at a fixed quadrature, namely ζ = φSRC. As shown in Fig.4.2, there aren’t any clear frequency bands where the solid lines dip below the dashed - indeed, the classical noises can only be considered negligible relative to quantum noise above≈ 200 Hz. This is not a surprising con- clusion - as explained in Sec 3.2 of [60], in the RSE configuration withφSRC ≈90◦,
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Frequency [Hz]
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Displacement noise [ m / √ Hz ]
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10−20 10−19
φ= 85◦,ζ= 164◦ φ= 90◦,ζ= 155◦
Classical noise estimate (@φ= 90◦) GWINC displacement noises
Figure 4.3: Modelled quantum noise in aLIGO as a function of SRC detuning, with BHD. Since the BHD system is a planned future upgrade, I have also assumed slightly different interferometer parameters in calculating these curves relative to Fig.4.2. The input power to the interferometer is increased from≈35 W to≈ 50 W, and that the losses in the arm cavity are improved toLrt = 50 ppm. The net effect of these is to increase the circulating power in the arm cavities to≈ 350 kW compared to ≈ 200 kW in Fig. 4.2. A "GWINC displacement noises" curve is included to indicate what the expected level of displacement noises should be, based on our best models and measurements of seismic and thermal noises.
readout quadraturesζ ≈90◦will exhibit varying amounts ofanti-squeezing. For an interferometer configured close to the RSE state, our best chance of measuring an optomechanically squeezed state is in fact close to ζ = 0◦ orζ = 180◦. With stan- dard DC readout, we cannot access arbitrary quadratures. Therefore, we conclude that in its current configuration, measuring an optomechanically squeezed state is not possible at H1 or L1.
4.4.2 Prospects with BHD readout
Fortunately, H1 and L1 are undergoing an upgrade in the near future that will see both interferometers fitted with Balanced Homodyne Readout (see Chapter 5 for more details). There is still some uncertainty about the exact control scheme that
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Frequency [Hz]
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Optomechanical coupling K
H1/L1 (Parm≈375 kW,mTM≈40 kg,Larm≈4 km) C1 (Parm≈30 kW,mTM≈0.25 kg,Larm≈40 m)
Figure 4.4: Optomechanical coupling coefficient for the C1 and H1/L1 interferom- eters. This parameter is only a function of the measurement frequency, arm cavity bandwidth, power in the arm cavity, and mirror mass.
will be used to keep the homodyne phaseζfixed (i.e. the relative phase between the LO and IFO fields must be kept fixed), and what levels of RMS stability inζ can be realistically achieved. Nevertheless, the BHD technique offers, at least in-principle, the ability to read out arbitrary quadratures of the IFO’s output field. So, we repeat the analysis of Section4.4.1, but explore homodyne angles nearζ =0◦orζ = 180◦ instead. Fig. 4.3 shows the result of such a modeling effort. Two representative traces are shown here, with the φ = 90◦ trace showing that it may be possible to measure an optomechanically squeezed state even at the nominal SRC operating point, once we have access to arbitrary quadratures of the output field. The classical noise trace from [47] is included again, to show that above≈50 Hz, quantum noise will be the largest contributor to the readout, and indeed, the solid lines are lower than their dashed counterparts over some range of frequencies.
While the technical noise levels at 100 Hz are≈ 100×lower in the H1/L1 interfer- ometers compared to C1, the factor by which the unsqueezed input vacuum field is optomechanically squeezed by H1/L1 is also smaller as shown in Fig.4.4. The H1/L1 interferometers have ≈ 10× smaller Parm/mTM ratio than the planned C1 configuration, and the arm cavity bandwidth is also≈100×smaller. The net effect is that the optomechanical coupling strength at H1/L1, which is physically respon- sible for generating optomechanical squeezing, is ≈ 10× smaller below the arm
cavity pole frequency of≈ 40 Hz, and drops off even more at higher frequencies.
This is also the reason why the dips in the quantum noise curves in Fig.4.1 are at higher frequencies than in Figs. 4.2 and4.3 - since C1 has largerK out to higher frequencies than H1/L1, we can then try and find φSRC, ζ which allow measuring a squeezed state at those frequencies, where technical noise contributions are typi- cally smaller than at lower frequencies. Therefore, it is difficult to make a definitive case that measuring even modest squeeze factors of ≈ 2 dB below vacuum will be significantly easier at H1/L1 than at C1.