Development of a Readout Scheme for High Frequency Gravitational Waves

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Development of a Readout Scheme for High
Frequency Gravitational Waves

• Jared Markowitz
• Mentors Rick Savage
• Paul Schwinberg

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Abstract

• The LIGO Interferometer is currently configured
  for optimal sensitivity at approximately 150 Hz.
• The sensitivity of the interferometer peaks at
  every FSR, leading one to consider searching for
  gravitational waves at higher frequencies (37.5
  kHz).
• A readout channel for gravitational waves at 37.5
  kHz will be set up, and output data will be
  down-converted to low frequency to match the
  existing data-acquisition system.
• The data will be examined for sources of noise in
  this frequency range, and also will be surveyed
  for gravitational waves.

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The Fabry-Perot Cavity
T L/c ?fsr ?/T E(t) taEin(t)
rarbe-2ikLdL(t)E(t-2T)
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Tale of Two Transfer Functions

• The normalized frequency to signal transfer
  function H?(s), pictured above, has zeros at
  multiples of the FSR.
• The normalized frequency to length transfer
  function HL(s), shown below, has its maxima at
  multiples of the FSR.
• This indicates that at multiples of the FSR, the
  sensitivity to length variations is at a maximum
  while the sensitivity to frequency is at a
  minimum.
• This suggests searching for gravitational waves
  at multiples of the FSR.
• However, GW response more complicated than HL(s).

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Frequency to Signal Transfer Function Response at
FSR
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Hurdles to Clear

• Sources of gravitational waves at 37.5 kHz must
  be identified and characterized.
• Sources of background noise in the high frequency
  range of 37.5 kHz must be determined and
  accounted for.
• At multiples of the FSR, there is no response in
  an optimally-oriented interferometer to
  gravitational waves. This stems from the fact
  that gravitational waves affect both the light
  and the mirrors in the interferometer, making H?
  the pertinent quantity in calculating the
  response. However,gravitational waves may be
  detected with increased sensitivity at these
  frequencies for other orientations.

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Whats Been Done

• Background research on Fabry-Perot Cavities, PDH
  locking systems.
• Interfaced SR830 Lock-In Amplifier with Unix
  terminal via RS232 interface. (Thank you Richard
  and Dave!)
• Wrote a C program to cycle lock-in reference
  frequencies through the serial port, allowing the
  generation of transfer functions remotely.
• Tested program on a 37.5 kHz bandpass filter,
  feeding output to Matlab for plotting. Obtained
  same results as were seen from the dynamic signal
  analyzer plot.

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Lock-In Amplifier

• Used to extract a signal at a given reference
  frequency from background noise.
• Employs a PSD (phase sensitive detector) to
  multiply the input signal with the reference
  signal (a sine wave), resulting in a DC output at
  ?ref ?lock.
• Vprod VsigVlocksin(?reft ?sig)sin(?lockt
  ?ref)
• ½VsigVlockcos(?ref - ?lockt ?sig - ?ref) -
  ½VsigVlockcos(?ref ?lockt ?sig ?ref)
• The output signal is fed through a low-pass
  filter, essentially eliminating all but the DC
  signal.
• The phase dependency of the DC signal is
  eliminated through sending the signal through a
  second PSD, this time multiplying by the
  reference oscillator signal phase shifted by 90.
  This allows the lock-in to measure both the
  amplitude and phase of the component of the input
  signal equal in frequency to the reference.

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Where to go next

• Set up a 2kHz fast channel for down-converted
  higher frequency signals.
• Configure lock-in to down-convert high frequency
  signals.
• Calculate the band-limited RMS in low frequency
  bins.

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For more detail, see www.ligo-wa.caltech.edu/ja
redm