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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

Tracking moving masses in several degrees of freedom with high precision and large dynamic range is a central aspect in many current and future gravitational physics experiments. Laser interferometers have been established as one of the tools of choice for such measurement schemes. Using sinusoidal phase modulation homodyne interferometry allows a drastic reduction of the complexity of the optical setup, a key limitation of multi-channel interferometry. By shifting the complexity of the setup to the signal processing stage, these methods enable devices with a size and weight not feasible using conventional techniques. In this paper we present the design of a novel sensor topology based on deep frequency modulation interferometry: the self-referenced single-element dual-interferometer (SEDI) inertial sensor, which takes simplification one step further by accommodating two interferometers in one optic. Using a combination of computer models and analytical methods we show that an inertial sensor with sub-picometer precision for frequencies above 10 mHz, in a package of a few cubic inches, seems feasible with our approach. Moreover we show that by combining two of these devices it is possible to reach sub-picometer precision down to 2 mHz. In combination with the given compactness, this makes the SEDI sensor a promising approach for applications in high precision inertial sensing for both next-generation space-based gravity missions employing drag-free control, and ground-based experiments employing inertial isolation systems with optical readout., Comment: 18 pages, 9 figures