Using tunable coherence for reaching micrometer coherence lengths and suppressing stray light in a power-recycled Michelson interferometer

TL;DR

The paper demonstrates tunable coherence as a viable method to suppress stray light in laser interferometers by phase-modulating the input light with pseudo-random sequences at frequencies up to $10$ GHz. This approach reduces the remaining coherence length from macroscopic scales to below $5\,\text{cm}$ in a Michelson interferometer and to the micrometer scale inside a cavity, enabling substantial stray-light suppression without detailed knowledge of scatter sources. The authors extend the technique to a power-recycled Michelson, achieving notable reductions in stray-light power and improved SNR, and investigate a stand-alone cavity to map how coherence suppression scales with the ratio $\alpha = l_{ ext{cav}} / d_{ ext{coh}}$, finding that resonance sharpens as $\alpha$ increases and can reach sub-10 μm widths. These results suggest practical pathways for deploying tunable coherence in table-top and, with further optimization, larger-scale gravitational-wave detectors, while highlighting the need for improved modulation bandwidth and depth to realize full potential. The work also opens questions about coherence effects in very high-finesse cavities and potential interactions with quantum-noise reduction techniques such as squeezing.

Abstract

By reentering into laser interferometers, scattered or stray light introduces non-linear noise. This is a major limitation of precision interferometers as preventing such parasitic light is nearly impossible. Thus, substantial effort is put into mitigating the reentering of these fields in various ways. Ground-based laser interferometric gravitational wave detectors employ such mitigation techniques to reduce otherwise restrictive stray light noise. However, they are now reaching sensitivities where conventional mitigation techniques reach limitations. Further improvements planed for future observatories are placing even more demanding constraints on tolerable stray light power. We previously presented tunable coherence as a possible technique to ease these constraints and suppress unwanted coherent interference. For these promising demonstrations, the remaining coherence length and achievable suppression in length-constrained layouts was limited, among other things, by the used pseudo-random-noise phase modulation frequency. In this work, we demonstrate stray light suppression and cavity performance at modulation frequencies up to 10 GHz. This reduces the remaining coherence to a few centimeter in an interferometer, and even to the scale of the laser wavelength in a cavity. We further present a first demonstration of tunable coherence in a power-recycled Michelson interferometer, successfully suppressing stray light in a more complex topology.

Figures (4)

• Figure 1: Sketch depicting the individual parts of the experimental setup. The laser preparation with two EOMs, one for modulating the PRN sequence onto the light, and one for rf-sidebands used for the PDH-technique. The Michelson interferometer setup is depicted in the orange box with the possible addition of power-recycling. Without recycling, the interferometer was operated and read out at mid-fringe. Power-recycling case was realized by operating the interferometer at dark-fringe using a dither-lock and adding a PRM before the interferometer. The resulting power-recycling cavity was operated by locking the laser frequency to its resonance using the PDH-technique. The stand-alone cavity depicted in the blue box was operated separately. Its microscopic length was adjusted to keep it on resonance with the laser frequency using a PZT mirror and the PDH-technique.
• Figure 2: Measured stray light suppression in a Michelson interferometer using tunable coherence. Figure a) shows the dependence on the delay of the scattered light, measured for a PRN sequence length of 7.0 and 127.0 chips at $f_{\text{PRN}}\!=\!10GHz$. Both sequences reached either their expected suppression or the experimental limit at the longest delay of 10cm. For shorter delays they both showed some fluctuations and slower reduction of coherence for the longer sequence. Figure b) shows the dependence of measured suppression on sequence length for PRN frequencies of 5.0 and 10GHz. The shorter sequences showed some limitations, the longer sequences, starting with 127.0 chips in length, reach the experimental limits but residual stray light often remains.
• Figure 3: Power-spectral density recorded at the output of the power-recycled Michelson interferometer. On the left side the measured scattered light signal power and on the right side the measured dither signal power are shown. Recordings with the scattered light blocked are plotted in black and gray, the recording without PRN modulation is plotted in blue and the recording with the modulation active in orange. The stray light signal power is reduced by about 8.3dB, and the SNR between stray light and dither signal improved by about 5dB when using the PRN modulation.
• Figure 4: Measured macroscopic resonance of the cavity depending on the length matching between roundtrip length and PRN sequence length, shown for measurements using $f_{\text{PRN}}\!=\!5GHz$ in figure a and $f_{\text{PRN}}\!=\!10GHz$ in b. All combinations of integer multiples, given by $\alpha$, of sequence repetitions fitting into the cavity regain full resonance. With increasing $\alpha$, the resonance narrows. All measured FWHMs of the resonance are shown in figure c depending on $\alpha$ and PRN frequency.