Refined clock-jitter reduction in the Sagnac-type time-delay interferometry combinations

TL;DR

This paper presents refined methods for reducing clock-jitter noise in Sagnac-type time-delay interferometry, significantly improving gravitational wave detection sensitivity in space-based laser interferometers.

Contribution

It introduces new cancellation combinations using geometric TDI, enhancing residual clock noise suppression for specific Sagnac configurations and providing a general-purpose scheme.

Findings

Residual clock noise is significantly reduced.

The new combinations improve sensitivity to gravitational waves.

The scheme is applicable to arbitrary TDI configurations.

Abstract

The ongoing development of the space-based laser interferometer missions is aiming at unprecedented gravitational wave detections in the millihertz frequency band. The spaceborne nature of the experimental setups leads to a degree of subtlety regarding the otherwise overwhelming laser frequency noise. The cancellation of the latter is accomplished through the time-delay interferometry technique. Moreover, to eventually achieve the desired noise level, the phase fluctuations of the onboard ultra-stable oscillator must also be suppressed. This can be fulfilled by introducing sideband signals which, in turn, give rise to an improved cancellation scheme accounting for the clock-jitter noise. Nonetheless, for certain Sagnac-type interferometry layouts, it can be shown that resultant residual clock noise found in the literature can be further improved. In this regard, we propose refined cancellation combinations for two specific clock noise patterns. This is achieved by employing the so-called geometric time-delay interferometry interpretation. It is shown that for specific Sagnac combinations, the residual noise diminishes significantly to attain the experimentally acceptable sensitivity level. Moreover, we argue that the derived combination, in addition to the existing ones in the literature, furnishes a general-purpose cancellation scheme that serves for arbitrary time-delay interferometry combinations. The subsequential residual noise will only involve factors proportional to the commutators between the delay operators. Our arguments reside in the form of the clock noise expressed in terms of the coefficients of the generating set of the first module of syzygies, the linear combination of which originally constitutes the very solution for laser noise reduction.