Gravitons probing from stochastic gravitational waves background

Abstract: Quantum gravity is a challenge in physics, and the existence of graviton is the prime question at present. We study the detectability of the quantum noise induced by gravitons in this letter. The correlation of the quantum noise in the squeezed state is calculated, but we are surprised to find that the result is the same as those from Grishchuk et.al. and Parikh et.al. This implies that they are essentially about one thing: the quantum noise from the gravitons. The further discussion shows the quantum noise should be completed from the leading order of the interaction between gravitation and the detector. The squeezed factor is estimated, and with it, the spectrum of the quantum noise is found to be of the form $\Omega_0 \sim \nu^{4+a_0 \beta+b_0}$. After comparing it to the sensitivities of several gravitational wave detectors, we conclude that the quantum noise is detectable in the future.