Gravitational Decoherence

The recent exciting first detections of gravitational waves, which marked a new era in astrophysics and cosmology, have pushed the scientific community towards the construction of ever more sophisticated ground and space based detectors to observe waves in a variety of ranges, possibly down to the cosmic background gravitational radiation. Detecting the latter would open the possibility to gain crucial information about the universe at its very primordial stage, at about 10^(-22) s after the Big Bang, where we expect our description of gravity to fail, especially because of its unclear relation with quantum matter. Most gravitational waves (which can be thought of as small perturbations of the metric propagating through spacetime at the speed of light) that arrive on the Earth are produced by different unresolved mechanisms and sources, and thus result in a stochastic perturbation of the flat spacetime background. Within the framework of quantum theory, this altered background affects the dynamics of matter propagation and, when the quantum state is in a superposition, it leads to decoherence effects, as it's typical of any noisy environment. In this scenario, the extreme sensitivity of matter waves to gravity gradients makes matter-wave interferometers a perfect candidate for exploring the gravitational wave background and, at the same time, for possibly answering some fundamental questions regarding the nature of gravity, and its coupling to quantum matter. Besides the technological challenge of building sensitive (therefore large) enough matter-wave interferometers, which realistically would have to operate in outer space, even from the theoretical point of view it is not clear how they would respond to a gravitational background produced by random sources, as no comprehensive dynamical description of the gravity induced decoherence process has been so far proposed. The decoherence effect of a stochastic (or quantum) perturbation of the metric has in fact been studied by several authors, each of whom has produced a different model for the evolution of off-diagonal elements of the density matrix of a quantum state or, more generally, the loss of interference in the system. However, that of giving a universal and meaningful description of the phenomenon is still an open problem, as the different models so far proposed refer to particular regimes of approximation and thus seem to lead to different and apparently incompatible conclusions. The goal of our work is to formulate a more general description of gravity induced deocherence, in the form of a master equation, which is able to encompass the existing literature and explain the apparent discrepancies, as well as extend the so far know results. With a more general and unambiguous dynamics, we aim at assessing whether and to what extent matter-wave interferometers constitute a viable platform for probing of the cosmic gravitational background.