Interferometer Design for the Holometer
Lee McCuller
2012 Midwest Relativity Meeting
Lee McCuller
2012 Midwest Relativity Meeting
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Collaboration:
Fermilab: A. Chou (co-PI, Project Manager), C. Hogan, C. Stoughton, R. Tomlin, J. Volk, W. Wester
U. Chicago: S. Meyer (co-PI)
Students: Bobby Lanza, Lee McCuller, Jonathan Richardson
MIT (LIGO): M. Evans, S. Waldman, R. Weiss
U. Michigan (LIGO): D. Gustafson
Northwestern: J. Steffen
Diffraction Limit
Theories displaying an information bound on standard physics.
[1] | Craig Hogan, "Covariant Macroscopic Quantum Geometry." arXiv:1204.5948 [gr-qc] |
Inferferometer sensitivity is an autocorrelation \(\Xi(\tau) = \left<dL(t)dL(t-\tau)\right> = (2l_p/\pi)(2L-c\tau)\) for \(\tau > 0\)
\(L = 40\mathrm{m} \rightarrow \sqrt{\Xi(0)} = 2.8 \cdot 10^{-17}\mathrm{m}\)
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[2] | Craig Hogan, Phys. Rev. D 85, 064007 (2012) |
Schematic
"Coherent" beams have poisson statistics with \(\Delta N = \sqrt{N}\)
A 1W, A \(\lambda = 1064\mathrm{nm}\) beam gives phase sensitivity of
With 2kW power, shot noise length sensitivity becomes:
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Schematic
on a 2W input beam, gain is:
Advantages (intrinsic):
- High power at the beamsplitter
- Filtering of input laser
Schematic
on a 2W input beam, gain is:
Disadvantages (operational)
- High sensitivity to light output: \(T_\mathrm{asym} = 1 - \cos(\phi_\mathrm{op})\)
- High sensitivity to alignment: \(T_\mathrm{align}\)
- High quality optics: \(T_\mathrm{loss}\)
- Contrast Defect (thermal lensing and lens wavefront smoothness): \(T_\mathrm{contrast}\)
Lee McCuller
2012 Midwest Relativity Meeting