Laser-Frequency Stabilization via a Quasimonolithic Mach-Zehnder Interferometer with Arms of Unequal Length and Balanced dc Readout

Low-frequency high-precision laser interferometry is subject to excess laser-frequency-noise coupling via arm-length differences which is commonly mitigated by locking the frequency to a stable reference system. This approach is crucial to achieve picometer-level sensitivities in the 0.1-mHz to 1-Hz regime, where laser-frequency noise is usually high and couples into the measurement phase via arm-length mismatches in the interferometers. Here we describe the results achieved by frequency stabilizing an external cavity diode laser to a quasimonolithic unequal arm-length Mach-Zehnder interferometer readout at midfringe via balanced detection. We find this stabilization scheme to be an elegant solution combining a minimal number of optical components, no additional laser modulations, and relatively low-frequency-noise levels. The Mach-Zehnder interferometer is designed and constructed to minimize the influence of thermal couplings and to reduce undesired stray light using the optical simulation tool ifocad. We achieve frequency-noise levels below $100\mathrm{Hz}/\sqrt{\mathrm{Hz}}$ at 1 Hz and are able to demonstrate the LISA frequency prestabilization requirement of $300\mathrm{Hz}/\sqrt{\mathrm{Hz}}$ down to frequencies of 100 mHz by beating the stabilized laser with an iodine-locked reference.

Figure 1

Layout of the Mach-Zehnder interferometer with additional output splitting in the north output of the recombination beam splitter created using a 2D output of the ifocad c++ library.

Figure 2

Photograph of the construction of the Mach-Zehnder interferometer. Shown is the alignment stage of the recombination beam splitter using a pointing finger assembly while monitoring the interferometric contrast using a strong laser-frequency modulation.

Figure 3

Sketch of the frequency-stabilization experiment. The optical setup outside the vacuum chamber (VAC) consists of single-mode, polarization-maintaining fiber components. The beat frequency is first mixed down to a frequency between 1 MHz and 40 MHz and then tracked by a digital phase-locked loop (PLL) implemented in a LISA-like phase meter. The vacuum level during the experiment is on the order of $5\times {10}^{-6}\mathrm{mbar}$. The interferometer and the analogue electronics are placed inside a thermal shield (TS) mounted in the vacuum chamber via thermally isolating feet. An additional thermal shield is placed around the baseplate of the interferometer and extended to cover the fiber coupler with multilayer insulation foil. The heat generated by the electronics is understood to be the main driver of the observed long-term drifts, with a thermal equilibrium still not achieved after a week of pumping. The optical input power of the interferometer is on the order of 10 mW. A dedicated analogue controller (PID) is used to provide feedback to the ECDL.

Figure 4

Temperature spectral densities of the vacuum chamber (VC) and the MZI during the performance measurements. Shown are also the thermal stability (TS) goal for the LISA optical bench environment, a $1\mu \mathrm{K}/\sqrt{\mathrm{Hz}}$ white noise relaxed towards lower frequencies, as well as a 10-time increase level for comparisons.

Figure 5

Frequency spectral densities of the beat note between the iodine-stabilized NPRO laser and the ECDL, once free running and once stabilised to the MZI. Shown are also a frequency-noise level of $4.5\mathrm{kHz}/\sqrt{\mathrm{Hz}}$ and the LISA frequency prestabilization requirement of $300\mathrm{Hz}/\sqrt{\mathrm{Hz}}$. The graph also shows the frequency noise measured between two iodine-stabilized NPRO lasers, which is a measure for the lowest noise levels achievable with an iodine-stabilized frequency reference [23]. The frequency-readout-noise floor (not shown) is measured separately using only electronic signals and is on the order of $1\mathrm{Hz}/\sqrt{\mathrm{Hz}}$, slightly increasing towards lower frequencies.

Figure 6

Shown are the deviation of the measured beat frequency and the temperature measured at the thermal shield on top of the interferometer. Linear drifts of $673.13\mathrm{Hz}/\mathrm{s}$ and $0.96\mu \mathrm{K}/\mathrm{s}$, respectively, are subtracted, as well as a mean value of the temperature of 25.669 65°.