Quantum principle of sensing gravitational waves: From the zero-point fluctuations to the cosmological stochastic background of spacetime

Abstract

We carry out a theoretical investigation on the collective dynamics of an ensemble of correlated atoms, subject to both vacuum fluctuations of spacetime and stochastic gravitational waves. A general approach is taken with the derivation of a quantum master equation capable of describing arbitrary confined nonrelativistic matter systems in an open quantum gravitational environment. It enables us to relate the spectral function for gravitational waves and the distribution function for quantum gravitational fluctuations and to indeed introduce a new spectral function for the zero-point fluctuations of spacetime. The formulation is applied to two-level Rydberg-like identical bosonic atoms in a cavity, leading to a gravitational transition mechanism through certain quadrupole moment operators. For a large number \(N\) of such atoms, we find their equilibrium state to satisfy the Boltzmann distribution. The overall relaxation rate before reaching equilibrium is found to scale collectively with \(N\). However, we are able to identify certain states whose decay and excitation rates with stochastic gravitational waves and vacuum spacetime fluctuations amplify more significantly with a factor of \(N^2\). Using such favourable states as a means of measuring both conventional stochastic gravitational waves and novel zero-point spacetime fluctuations, we determine the theoretical lower bounds for the respective spectral functions. Finally, we discuss the implications of our findings on future observations of gravitational waves of a wider spectral window than currently accessible. Especially, the possible sensing of the zero-point fluctuations of spacetime could provide an opportunity to generate initial evidence and further guidance of quantum gravity.