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To reach sub-picometer sensitivity in the millihertz range, displacement sensors based on laser interferometry require suppression of laser-frequency noise by several orders of magnitude. Many optical frequency stabilization methods exist with varying levels of complexity, size, and performance. In this paper, we describe the performance of a compact Mach-Zehnder interferometer based on a monolithic optic. The setup consists of a commercial fiber injector, a custom-designed pentaprism used to split and recombine the laser beam, and two photoreceivers placed at the complementary output ports of the interferometer. The structural stability of the prism is transferred to the laser frequency via amplification, integration, and feedback of the balanced-detection signal, achieving a fractional frequency instability better than 6 parts in $10^{13}$, corresponding to an interferometer pathlength stability better than $10^{-12}$ m$/\sqrt{\mathrm{Hz}}$., Comment: 10 pages, 4 figures

To achieve sub-picometer sensitivities in the millihertz band, laser interferometric inertial sensors rely on some form of reduction of the laser frequency noise, typically by locking the laser to a stable frequency reference, such as the narrow-linewidth resonance of an ultra-stable optical cavity or an atomic or molecular transition. In this paper we report on a compact laser frequency stabilization technique based on an unequal-arm Mach-Zehnder interferometer that is sub-nanometer stable at $10\,\mu$Hz, sub-picometer at $0.5\,$mHz, and reaches a noise floor of $7\,\mathrm{fm}/\!\sqrt{\mathrm{Hz}}$ at 1 Hz. The interferometer is used in conjunction with a DC servo to stabilize the frequency of a laser down to a fractional instability below $4 \times 10^{-13}$ at averaging times from 0.1 to 100 seconds. The technique offers a wide operating range, does not rely on complex lock acquisition procedures, and can be readily integrated as part of the optical bench in future gravity missions., Comment: 9 pages, 7 figures