[Kawakami, Tanaka, Saito]

Following the same procedure as in klog:37250, the lengths of SRX, PRX, and PRY were measured. The differences from the design values were found to be 2.80(13) cm for SRX, 0.677(11) cm for PRX, and −0.107(46) cm for PRY. Compared with the results reported in klog:37209 and klog:37223, the largest discrepancy is observed for PRX, but it corresponds to only about 1.25σ, indicating that the results are statistically consistent.

Furthermore, using these results together with the method described in klog:37248, the SRC length, PRC length, and Schnupp asymmetry were determined. The results are 66.61409(70) m for the SRC, 66.59425(24) m for the PRC, and 3.33791(45) m for the Schnupp asymmetry. Their differences from the design values are 2.279(70) cm for the SRC, 0.285(24) cm for the PRC, and 0.811(45) cm for the Schnupp asymmetry. Compared with the results of klog:37248, the largest discrepancy is found for the PRC, but it is only about 1.48σ, indicating that the two measurements are consistent.
 

• Following the same procedure as in klog:37250, the sub-laser PZT was driven directly for SRX, PRX, and PRY, and the Max Hold function of the spectrum analyzer was used to obtain transmission-power data as a function of beat frequency around 1.6 GHz, 800 MHz, −800 MHz, and −1.6 GHz. Here, the negative frequencies correspond to the case where the sub-laser frequency is lower than the main laser frequency. The peaks in the measured data were fitted both with and without a linear background. The fitting results for the individual peaks will be posted separately. The peak frequencies obtained from the fits and their uncertainties were used to determine the maximum and minimum values within the uncertainty range. The overall uncertainty range was taken as the union of the results with and without a linear background. The following data were therefore used to determine the lengths of SRX, PRX, and PRY.

  SRX
  Minimum (MHz)    Maximum (MHz)
  1543.4471    1543.4932
  884.8872    884.9360
  −856.1353    −855.8030
  −1654.9558    −1654.8394
  PRX
  Minimum (MHz)    Maximum (MHz)
  1631.4880    1631.4954
  867.3066    867.3270
  −874.0048    −873.9845
  −1646.9334    −1646.9256
  PRY
  Minimum (MHz)    Maximum (MHz)
  1627.6201    1627.6266
  868.0174    868.0423
  −882.0137    −881.9492
  −1632.3336    −1632.2710

• For each cavity, the midpoint frequency between the minimum and maximum values was divided by the FSR calculated from the design cavity length (68.2562 m for SRX, 68.2563 m for PRX, and 64.9265 m for PRY). The resulting values were rounded to the nearest integers, and the measured frequencies were fitted with the function AN+B, where A and B are fitting parameters and N is an integer. The fitting results are as follows.

  SRX (Fig. 1)
  A: 2.195180(42) MHz
  B: 0.256(25) MHz
  PRX (Fig. 2)
  A: 2.1958613(35) MHz
  B: −0.0348(25) MHz
  PRY (Fig. 3)
  A: 2.308744(17) MHz
  B: −0.042(11) MHz
   

• Since A corresponds to the FSR, the cavity lengths were calculated as follows.

  SRX
  Fitted length: 68.2842(13) m
  Design value: 68.2562 m
  Difference (fit − design): 2.80(13) cm
  PRX
  Fitted length: 68.26307(11) m
  Design value: 68.2563 m
  Difference (fit − design): 0.677(11) cm
  PRY
  Fitted length: 64.92543(46) m
  Design value: 64.9265 m
  Difference (fit − design): −0.107(46) cm

  Comparing these results with those reported in klog:37209 and klog:37223, namely, differences from the design values of 2.56(45) cm for SRX, 1.25(46) cm for PRX, and 0.15(33) cm for PRY, the largest discrepancy is found for PRX, but it corresponds to only about 1.25σ. Therefore, the results are considered to be consistent.
   

• Using these results together with the SRY measurement reported in klog:37250, the SRC length, PRC length, and Schnupp asymmetry were calculated following the same procedure as in klog:37248.

  SRC
  Calculated value: 66.61409(70) m
  Design value: 66.5913 m
  Difference (calculated − design): 2.279(70) cm
  PRC
  Calculated value: 66.59425(24) m
  Design value: 66.5914 m
  Difference (calculated − design): 0.285(24) cm
  Schnupp asymmetry
  Calculated from the SRC: 3.34023(139) m
  Calculated from the PRC: 3.337640(473) m
  Weighted average: 3.33791(45) m
  Design value: 3.3298 m
  Difference (weighted average − design): 0.811(45) cm

  Comparing these values with those reported in klog:37248, namely 66.6120(47) m for the SRC, 66.5984(28) m for the PRC, and 3.3405(48) m for the Schnupp asymmetry, the largest discrepancy is found for the PRC, but it corresponds to only about 1.48σ. Therefore, the present results are considered to be consistent with the previous measurements.