Space-based cm/kg-scale Laser Interferometer for Quantum Gravity

Abstract

The experimental verification of the quantum nature of gravity represents a milestone in quantum gravity research. Recently, interest has grown for testing it via gravitationally induced entanglement (GIE). Here, we propose a space-based interferometer inspired by the LISA Pathfinder (LPF). Our design employs two kg-scale gold-platinum test masses which, unlike in the LPF, are surrounded by a shield below 1 K and positioned side-by-side with a centimeter-scale separation. This configuration enables the detection of GIE through simultaneous measurements of differential and common-mode motions. To estimate the integration time required for GIE detection, we simulate quantum measurements of these modes, considering noise sources such as gas damping, black-body radiation, and cosmic-ray collisions. Our results show that GIE can be demonstrated with a few modifications to the LPF setup.

Figures (7)

• Figure 1: Experimental setup. The differential and common-mode of test mass 1 (TM1) and test mass 2 (TM2) are measured by laser interferometry with a wavelength of $1064\ \mathrm{nm}$.
• Figure 2: Contour plot of $E_N$ in the $\alpha_+$-$\Gamma T/(2\pi)$ plane. The green dashed line indicates the threshold for generating the GIE in Eq. \ref{['CoAB']}, the red curve shows the boundary where the relaxation time due to the Kalman filter is equal to half the thermal decoherence time (see Appendix \ref{['app:A']}). The star symbol corresponds to the parameters used in the simulation. The GIE can be generated when $\Gamma T/(2\pi)<4.5\times10^{-19}$ Hz K.
• Figure 3: An example of the common-mode ASD $S_{q_{+}}^{1/2}$, normalized by the zero-point amplitude $q^+_{\rm zpf}$, measured over $3\times10^{6}$ seconds. For a 1 kg test mass, the value 1 on the vertical axis corresponds to $1.8\times10^{-16}\ {\rm m/\sqrt{Hz}}$. Blue shows the true values, light blue the estimate, black the measured data. Yellow is shot noise, green is radiation pressure noise, magenta is thermal noise, orange is feedback noise, and red circles show fit results. The inset shows the time-series data $q_+$ from 0 to $2\times10^4$ seconds, with colors matching the main figure. Due to shot noise, the measured signal has an amplitude of about 20, causing the inset’s background to appear black.
• Figure 4: Contour plot of $\log(\Gamma T/(2\pi))$ in the $\log m$-$T_{\rm env}$ plane at $\alpha_+=0.031\ \mathrm{Hz^{1/2}}$.
• Figure 5: The calculated form factor $\Lambda$ as a function of the dimensionless geometric parameters $L/h$ and $R/h$. The value of $\Lambda$ converges to 1 for large separations, corresponding to the point-mass approximation. The red cross mark corresponds to the parameters selected in this study.