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Reducing noises and enhancing signal-to-noise ratios (SNRs) have becomecritical for designing third-generation gravitational-wave (GW) detectors witha GW strain of less than $10^{-23}$/$\rm \sqrt{Hz}$. In this paper, we proposea potential third-generation GW detector based on autocorrelative weak-valueamplification (AWVA) for GW detection with a strain of $h_g =$ $4 \times10^{-25}$/$\rm \sqrt{Hz}$. In our scheme, a GW event induces a phase difference$\Delta \phi$ by passing through an 11-bounce delay line, 10-km arm-length,zero-area Sagnac interferometer illuminated with a 1064-nm laser. Subsequently,$\Delta \phi$ is amplified as the parameter of post-selection by choosing theappropriate pre-selected state and coupling strength in AWVA. In particular, wetheoretically investigate the AWVA measurements for GW detection within thefrequency band of 200 Hz $\leq$ $f_g$ $\leq$ 800 Hz, considering Gaussiannoises with negative-decibel SNRs. The peak response of the AWVA sensitivity$\kappa(f_g)$ occurs at frequency $f_{g, max}$ = 500 Hz, which falls within thefrequency band of interest of the current third-generation GW detectors. Oursimulation results indicate that AWVA can demonstrate a measurable sensitivityof $\Theta(f_g)$ within the frequency band of interest. Moreover, therobustness of WVA shows promising potential in mitigating the effects ofGaussian noises.

A potential third-generation gravitational-wave detector based on autocorrelative weak-value amplification