Demonstrating sub-picometer non-reciprocity levels in the Three-Backlink Experiment for LISA

TL;DR

The paper investigates sub-picometer non-reciprocity in the Three-Backlink Experiment (3BL), evaluating two fiber-based Backlinks (Direct DFBL and Frequency-Separated FSFBL) and one free-beam Backlink (FBBL) in a space-mimicking LISA setup. Through a comprehensive commissioning program, it identifies dominant noise sources in readout, detection, straylight, temperature coupling, and laser noise, and implements mitigation strategies including balanced detection and active laser stabilization. Results show that all three Backlink designs can achieve non-reciprocity levels well below the 1 pm/√Hz·u(f) goal across most of the LISA band, with residuals mostly due to testbed limitations and environmental temperature coupling; FSFBL demonstrates insensitivity to fiber backscatter, while DFBL remains a viable baseline when balanced detection is used. The study concludes that the DFBL can serve as an upper-limit proxy for LISA-PRDS performance, informs Backlink design choices, and validates the 3BL as a critical testbed for LISA-like missions, while outlining remaining work to address low-frequency temperature effects and rotating-bench operation.

Abstract

The current planned space-based gravitational-wave detectors require a bidirectional optical connection, referred to as Backlink, between two adjacent optical benches to provide a mutual phase reference for the local interferometric measurements. However, if the Backlink shows asymmetry between the two propagation directions, the effective optical pathlengths of the counter-propagating beams can introduce a differential phase noise, called non-reciprocity, into the main interferometric measurement that will limit the achievable accuracy in time-delay interferometry (TDI) post-processing. Hence, it is important to understand the properties of the Backlink to ensure that it will not compromise the interferometric detection. The Three-Backlink Experiment (3BL), which consists of an optical test facility with two rotatable benches, was designed under the Laser Interferometer Space Antenna (LISA) framework to study the performance of three Backlink configurations: two fiber-based and one free-beam scheme. In this paper, we report recent experimental results from the 3BL. We describe the commissioning and the subsequent noise mitigation. We achieve a setup noise floor below $1\text{ pm}\sqrt{\text{Hz}}$ across most of the LISA measurement band, and provide an understanding of the current technical limitations. With this low-noise baseline, we measured the performance of the three Backlink implementations under non-rotational conditions. We show that all three Backlinks reach sub-picometer non-reciprocity levels across most of the frequency band, with the remaining part dominated by the mentioned testbed noise. This enabled us to conduct a preliminary study of the Backlink inherent noise, where we emphasized on the backscatter noise intrinsic to a straightforward fiber-based Backlink, as this is the current baseline for LISA.

Figures (6)

• Figure 1: Schematic of the 3BL optical design. The three Backlink connections are illustrated as dashed lines, with the respective interferometers indicated within a dashed box (DFBL, FSFBL+REF, FBBL) on the left (L) or right (R) bench. The four lasers involved in the experiment are defined as L2 and L3 in the left bench, and L1 and L4 in the right bench. Above each interferometer, the interfering lasers are shown, resulting in the corresponding beatnotes, e.g. L12. All four lasers are frequency stabilized to a fifth laser in a separate setup, not shown here. The colored lines show the optical laser beam paths. Additionally, the in-loop photodetectors for the power stabilization (PS) are represented. The figure is an adaptation from IsleifPhD.
• Figure 2: Influence of laser power noise (a) and laser frequency noise (b) in the Three-Backlink Experiment.
• Figure 4: Phase noise performance between DFBL and FBBL. The frequency span is divided into low-, center-, and high-frequency ranges for visual clarity, indicated by vertical dashed-gray lines. The individual noise contributions are assumed to be uncorrelated and summed in quadrature, resulting in the predicted total noise budget (yellow shaded area). The figure shows the differential non-reciprocities with (solid orange) and without (dash-dotted orange) balanced detection (BD). The differential non-reciprocity with BD meets the 1 pm/$\sqrt{\text{Hz}} \cdot u_(f)$ requirement (solid black) across the entire measurement band, with a marginal exceedance between 2 mHz and 4 mHz due to the testbed noise limitations, and remains below 3 pm/$\sqrt{\text{Hz}} \cdot u_(f)$ (dash-dotted gray) over the entire span.
• Figure 5: Phase noise performance between FSFBL and DFBL. The frequency span is divided into low-, center-, and high-frequency ranges for visual clarity, indicated by vertical dashed-gray lines. The individual noise contributions are assumed to be uncorrelated and summed in quadrature, resulting in the predicted total noise budget (yellow shaded area). The figure shows the differential non-reciprocities with (solid orange) and without (dash-dotted orange) balanced detection (BD). The differential non-reciprocity with BD meets the 1 pm/$\sqrt{\text{Hz}} \cdot u_(f)$ requirement (solid black) across most of the measurement band, except from $0.4 \text{ mHz}$ to $6 \text{ mHz}$ due to the testbed noise limitations, and remains below 3 pm/$\sqrt{\text{Hz}} \cdot u_(f)$ (dash-dotted gray) over the entire span.
• Figure 6: Phase noise performance between FSFBL and FBBL. The frequency span is divided into low-, center-, and high-frequency ranges for visual clarity, indicated by vertical dashed-gray lines. The individual noise contributions are assumed to be uncorrelated and summed in quadrature, resulting in the predicted total noise budget (yellow shaded area). The figure shows the differential non-reciprocities with (solid orange) and without (dash-dotted orange) balanced detection (BD). The differential non-reciprocity with BD meets the 1 pm/$\sqrt{\text{Hz}} \cdot u_(f)$ requirement (solid black), except from 0.5 mHz to 20 mHz due to the testbed noise limitations, and remains below 3 pm/$\sqrt{\text{Hz}} \cdot u_(f)$ (dash-dotted gray) over the entire span.