Interferometer Design for the Holometer

Lee McCuller

2012 Midwest Relativity Meeting

Brief Introduction

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Contents

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

Basis for Holographic Noise

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The Hogan Noise Interpretation

Theories displaying an information bound on standard physics.

Noise Prediction

Inferferometer sensitivity is an autocorrelation \(\Xi(\tau) = \left<dL(t)dL(t-\tau)\right> = (2l_p/\pi)(2L-c\tau)\) for \(\tau > 0\)

\(L = 40\mathrm{m} \rightarrow \sqrt{\Xi(0)} = 2.8 \cdot 10^{-17}\mathrm{m}\)

_images/correlation_base.png _images/spectrum_base.png

Interferometer Design

\[(\Delta N) (\Delta\phi) \ge \frac{1}{2}\]

"Coherent" beams have poisson statistics with \(\Delta N = \sqrt{N}\)

A 1W, A \(\lambda = 1064\mathrm{nm}\) beam gives phase sensitivity of

\[4 \cdot 10^{-10}\frac{\mathrm{rad}}{\sqrt{\mathrm{Hz}}} \rightarrow 7.3 \cdot 10^{-17} \frac{\mathrm{m}}{\sqrt{\mathrm{Hz}}}\]

Signal Level

With 2kW power, shot noise length sensitivity becomes:

\[1.6 \cdot 10^{-18} \frac{\mathrm{m}}{\sqrt{\mathrm{Hz}}}\]
_images/spectral_noisy.png _images/correlation_noisy.png

Power Recycling

on a 2W input beam, gain is:

\[\frac{T_\mathrm{prm}}{(1 - \sqrt{T_{\mathrm{rt}}})^2} = 1000\]

Power Recycling

on a 2W input beam, gain is:

\[\frac{T_\mathrm{prm}}{(1 - \sqrt{T_{\mathrm{rt}}})^2} = 1000\]\[T_{\mathrm{rt}} = T_\mathrm{asym} + T_\mathrm{align} + T_\mathrm{loss} + T_\mathrm{contrast}\]

Interferometer Design for the Holometer

Lee McCuller

2012 Midwest Relativity Meeting