Fundamental Limits of Quantum Sensors for Gravitational Wave Detection

Abstract

Recent advances in quantum sensing---optical clocks, frequency-dependent squeezing below the standard quantum limit, and quantum magnetometers---raise a natural question: can these technologies detect gravitational waves directly, or enhance existing detectors? We show that the answer is set primarily by the \emph{coupling mechanism} between wave and sensor. From the tidal Hamiltonian in Fermi normal coordinates we identify three physically distinct mechanisms by which a gravitational wave couples directly to a quantum system, and derive their transducer gains within linearized general relativity and non-relativistic quantum mechanics. Internal atomic coupling yields a transducer gain $G_A=2.4\times 10^{-20}$, with vanishing first-order energy shifts for all $J=0$ clock states---a $\sim 10^{35}$ deficit relative to laser interferometry. Center-of-mass (Doppler) coupling reaches strain sensitivities of $\sim 10^{-18}$, still $10^4$ above LISA requirements. Only light-propagation coupling provides the enormous transducer gain that makes laser and atom interferometry viable. For detectors of this third kind we quantify the quantum enhancement accessible through the noise architecture: LISA's noise budget is predominantly classical, capping the combined enhancement at $\mathcal{E}\approx 1.04$, while ground-based detectors in the shot-noise-dominated regime achieve $\mathcal{E}=1.6$--$2.1$. Atom interferometers exploit the same mechanism to target the 0.01--10~Hz band.

This is an author-created, un-copyedited version of an article published in Classical and Quantum Gravity. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at \url{https://doi.org/10.1088/1361-6382/ae9449}