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 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 identical bosonic atoms in
an off-resonant high-$Q$ cavity that effectively inhibits undesirable
electromagnetic delays, leading to a gravitational transition mechanism through
certain quadrupole moment operators. The overall relaxation rate before
reaching equilibrium is found to generally scale collectively with the number
$N$ of atoms. However, we are also able to identify certain states of which the
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.
