Detection of space-time perturbations with quantum-enhanced metrology

We present a new model of atomic decoherence by space-time perturbations. We propose that decoherence will arise as a result of two possible effects that gravitational fluctuations will have on the atom. One is that the nucleus will be displaced relative to the valence electron, which will be perceived as a sudden change in the electric potential. This will result in the wave function of the atom being partially projected into lower energy levels. The other is that the strain in space will change the local electric field as felt by the electron. This interaction will either induce a change in the angular momentum of the atom or a small shift in the transition of the energy levels, presenting two different experimental approaches for the detection of the effect. We calculate how the decoherence is related to the internal degrees of freedom of the atoms, obtaining that the effect will be more prominent for atoms initially in a highly excited state (Rydberg atoms). By applying the nuclear displacement model for the scattering of neutral particles, we suggest that it could be potentially useful for the detection of weakly-interacting particles, like possible candidates of Dark Matter. The overall effect of gravitational waves for the strained-space model was calculated to be several orders of magnitude higher than for the nuclear displacement model, allowing for detection in different ranges of frequencies. We analyze how different quantum states are affected according to the proposed model, calculating that the information from the measurement of correlated atoms will be significantly higher. The optimal quantum state that minimizes the uncertainty of the measurement is described for an arbitrary number of atoms, giving a relation that follows closely the Heisenberg limit.