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

TL;DR

This paper explores how optical lattice clock networks can detect the stochastic gravitational-wave background, analyzing configuration effects and proposing an optimal orbital setup with sensitivity comparable to existing detectors.

Contribution

It introduces an equivalent configuration transformation for OLC networks, systematically compares different geometries, and designs a feasible orbital configuration for gravitational wave detection.

Findings

Equivalent transformation preserves the ORF modulus.

Compared ORFs of different trapezoidal configurations.

Proposed orbital setup achieves sensitivity comparable to LISA.

Abstract

This paper studies the use of optical lattice clock (OLC) detector networks for detecting the stochastic gravitational-wave background (SGWB). Starting from the cross-correlation formalism for two OLC detectors, we analyze how the detector geometry influences the overlap reduction function (ORF) and systematically search for configuration transformations that preserve the modulus of the ORF. We identify an equivalent transformation in which the emitting and receiving ends of both OLC links are exchanged, while the modulus of the ORF remains invariant. We then numerically compare the ORFs of isosceles trapezoidal configurations with different separations and included angles. Based on these results, we design a feasible four-spacecraft orbital configuration and evaluate its strain sensitivity and noise energy-density spectrum in comparison with LISA, Taiji, and TianQin.