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

We carry out a theoretical investigation on the collective dynamics of an ensemble of correlatedatoms, subject to both vacuum fluctuations of spacetime and stochastic gravitational waves. Ageneral approach is taken with the derivation of a quantum master equation capable of describingarbitrary confined nonrelativistic matter systems in an open quantum gravitational environment. Itenables us to relate the spectral function for gravitational waves and the distribution function forquantum gravitational fluctuations and to indeed introduce a new spectral function for the zeropointfluctuations of spacetime. The formulation is applied to 2-level identical bosonic atoms in anoff-resonant high-Q cavity that effectively inhibits undesirable electromagnetic delays, leading to agravitational transition mechanism through certain quadrupole moment operators. The overall relaxationrate before reaching equilibrium is found to generally scale collectively with the number Nof atoms. However, we are also able to identify certain states whose decay and excitation rates withstochastic gravitational waves and vacuum spacetime fluctuations amplify more significantly witha factor of N2. Using such favourable states as a means of measuring both conventional stochasticgravitational waves and novel zero-point spacetime fluctuations, we determine the theoretical lowerbounds for the respective spectral functions. Finally, we discuss the implications of our findingson 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 anopportunity to generate initial evidence and further guidance of quantum gravity