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Entry  Fri Feb 21 12:45:57 2014, ericq, Update, LSC, Equivalent Displacement Noise from QPD Dark Noise in SQRTINV SQRTINVspectra.pdfSQRTINV_DarkNoise.pdf
    Reply  Wed Mar 5 18:04:36 2014, ericq, Update, LSC, Equivalent Displacement Noise from QPD Dark Noise in SQRTINV calc1.jpgcalc2.jpgSQRTINVspectra.dat.zipdarkTransmonSpec.py
Message ID: 9693     Entry time: Wed Mar 5 18:04:36 2014     In reply to: 9660
Author: ericq 
Type: Update 
Category: LSC 
Subject: Equivalent Displacement Noise from QPD Dark Noise in SQRTINV 

At today's meeting, it was suspected that these noise levels were far too low. (ELOG 9660)

I've attached the math I did to get the conversions, as well as the dark noise SQRTINV spectra at various imitated transmission values and the python script that does the converting. 

I've gone over my calculations, and think they're self-consistent. However, a potential source of misestimation is the treatment of the Lorentzian profile simply existing with the coupled arm line width (38pm). The conversion to m/rtHz is directly proportional to the line width of the transmission peak, so if it is much broader in practice (because of imperfect PRC buildup or something), the noise will be that much worse.

I'm open to any other feedback about what I may have done wrong!


Attachment 1: calc1.jpg  1.099 MB  | Show | Hide all | Show all
Attachment 2: calc2.jpg  1016 kB  | Hide | Hide all | Show all
Attachment 3: SQRTINVspectra.dat.zip  346 kB
Attachment 4: darkTransmonSpec.py  688 Bytes  | Hide | Hide all | Show all
#! /usr/bin/env python
import numpy as np
import matplotlib.pyplot as plt

data = np.loadtxt('./SQRTINVspectra.dat')

# Coupled arm linewidth
w = 38e-12
# Lorentzian value at full resonance
I0 = 700
... 21 more lines ...
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