Gravitational Decoherence and the Possibility of Its Interferometric Detection

We present a general master equation describing the quantum dynamics of a scalar bosonic field interacting with an external weak and stochastic gravitational field. The dynamics predicts decoherence both in position and in energy momentum. We show how the master equation reproduces, thus generalizing, the previous results in the literature by taking appropriate limits. We estimate the effect of gravitational decoherence in atom interferometers, providing also a straightforward way to assess the magnitude of the effect.

Figure 1

A quantum system moving in a stochastic gravitational background decoheres. If the scalar component of the metric dominates, then decoherence occurs in position. If the tensorial components dominate then decoherence occurs in momentum and/or energy. Decoherence can be detected by matter-wave interferometers, for example, atom interferometers. A wave packet is split in two parts traveling along different paths, before they recombine by a detector measuring the interference. The relevant parameters are the time of flight $t$ and the transverse momentum $p_k$.

Figure 2

Color plot showing the sensitivity of atom interferometers to stochastic scalar gravitational fluctuations, as a function of the correlation length $L$ and strength $\alpha$ of the fluctuations. The different shaded area represents the region of parameters where the perturbations induce a reduction of more that 10% in the visibility, for different experimental setups (see legend in the figure).

Figure 3

Same as Fig. 2, now with reference to stochastic tensorial gravitational fluctuations.