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To reach sub-picometer sensitivity in the millihertz range, displacementsensors based on laser interferometry require suppression of laser-frequencynoise by several orders of magnitude. Many optical frequency stabilizationmethods exist with varying levels of complexity, size, and performance. In thispaper, we describe the performance of a compact Mach-Zehnder interferometerbased on a monolithic optic. The setup consists of a commercial fiber injector,a custom-designed pentaprism used to split and recombine the laser beam, andtwo photoreceivers placed at the complementary output ports of theinterferometer. The structural stability of the prism is transferred to thelaser frequency via amplification, integration, and feedback of thebalanced-detection signal, achieving a fractional frequency instability betterthan 6 parts in $10^{13}$, corresponding to an interferometer pathlengthstability better than $10^{-12}$ m$/\sqrt{\mathrm{Hz}}$.

Single-Element Dual-Interferometer for Precision Inertial Sensing:  Sub-picometer Structural Stability and Performance as a Reference for Laser  Frequency Stabilization