Advancements in optical readout technologies: Test mass sensing and laser-frequency stabilization techniques for optical compact interferometry

Abstract

Precision measurement of freely floating test masses across multiple degrees of freedom is a critical requirement for gravitational space missions or gravitational table-top experiments. Traditional methods like capacitive sensing or laser interferometry have demonstrated certain limitations in terms of precision and sensing in several degrees of freedom, respectively. This thesis presents recent advancements aimed at addressing these limitations.

Optical levers, combined with a modulation/demodulation technique, have been developed to achieve an angular resolution of below 400 nrad $\mathrm{Hz}^{-1/2}$ at frequencies between 10 mHz and 1 Hz (which is better than a conventional autocollimator in 1.5 orders of magnitude) across five degrees of freedom, offering a potential alternative to the constraints of capacitive sensing. This method's capability to potentially sense all six degrees of freedom suggests it could be a viable alternative to more complex laser interferometric setups.

Simultaneously, the development of new interferometric topologies like the self-referenced single-element dual-interferometer (SEDI) has been explored. Utilizing sinusoidal phase modulation homodyne interferometry, this approach reduces the complexity of the optical setup while maintaining sub-picometer precision in a compact design using a custom-designed prism. Such a design is advantageous for applications with stringent size and weight requirements.

Laser frequency stabilization, essential for low-frequency noise in ultra-low frequencies, has been addressed through two distinct techniques. The first employs an unequal-arm Mach-Zehnder interferometer, achieving a fractional instability below $4 \times 10^{-13}$ at averaging times from 0.1 to 100 seconds. The second method uses the SEDI prism in a compact setup to stabilize the laser frequency, achieving a fractional frequency instability below $4 \times 10^{-12}$ at averaging times from 0.1 to 1000 seconds.

In summary, these advancements provide enhanced precision and reduced complexity for future gravity missions, also offering improved tools and methodologies for future research endeavors.