Detecting gravitational wave background with equivalent configurations in the network of space based optical lattice clocks

TL;DR

The paper develops a geometric framework for two-space-based optical lattice clock GW detectors by analyzing the overlap reduction function (ORF) $ abla(f)$. It identifies a nontrivial ORF-preserving transformation that maps a compact, noise-correlated configuration to a widely separated one, enabling high cross-correlation while reducing local noise. By constructing explicit equivalent configurations (A -> B -> C) and applying the method to PTA-like geometries, it compares the resulting sensitivity to LISA, Taiji, and TianQin, showing competitive performance in key bands. The work offers a novel design principle for space-based SGWB searches using OLC networks and suggests avenues for future nontrivial transformations and link-decomposition approaches.

Abstract

The network of space based optical lattice clocks (OLCs) has been proposed to detect the stochastic gravitational wave background. We investigate the overlap reduction function (ORF) of the OLC detector network and analytically derive a transformation that leaves the ORF invariant. This transformation is applicable to configurations with two OLC detectors, each equipped with a one-way link. It can map a configuration with small separation and high noise correlation to another configuration with larger separation and reduced noise correlation. Using this transformation, we obtain a favourable OLC detector network configuration with high cross-correlation response, and compare its sensitivity to that of space-based laser interferometer gravitational wave detectors.

Figures (7)

• Figure 1: The cross-correlation configuration between OLC detector 1 (red) and OLC detector 2 (blue). Each OLC detector consists of a single laser link connecting two satellites.
• Figure 2: A non-trivial transformation that leaves the ORF invariant. The original configuration {A} (Detectors 1 & 2) transforms into the new configuration {B} (Detectors 3 & 4). Here, detector $i$ is $\{\vec{x}_{i},L_i\hat{u}_{i}\}$, solid arrows indicate laser links, and dashed arrows represent auxiliary lines.
• Figure 3: Three types of detector configurations: (a) denotes two links sharing a common endpoint with an included angle $\theta$; (b) denotes the configuration that is equivalent to (a), where the distance between the link endpoints is $d$ = 2$L\mathrm{sin}(\theta/2)$; (c) denotes the configuration with two parallel links separated by the same distance $d$.
• Figure 4: The ORFs of the two types of configurations (b) and (c) in Fig. \ref{['fig:3']} are plotted based on Eq. \ref{['eq4']}, with $\theta={20}^\circ$, $L=2.5$Gm and 0.17Gm, respectively.
• Figure 5: Schematic of the OLC detector configuration (b) with $\theta={21.78}^\circ$ in a circular formation, which is analogous to LISA's orbital configuration.