In this paper, we calculate the probability for resonantly inducing transitions in quantum states due to time-dependent gravitational perturbations. Contrary to common wisdom, the probability of inducing transitions is not infinitesimally small. We consider a system of ultracold neutrons, which are organized according to the energy levels of the Schrödinger equation in the presence of the Earth’s gravitational field. Transitions between energy levels are induced by an oscillating driving force of frequency $\omega$. The driving force is created by oscillating a macroscopic mass in the neighborhood of the system of neutrons. The neutron lifetime is approximately 880 sec while the probability of transitions increases as $t^2$. Hence, the optimal strategy is to drive the system for two lifetimes. The transition amplitude then is of the order of $1.06\times {10}^{-5}$, and hence with a million ultracold neutrons, one should be able to observe transitions.

• Received 1 February 2016

DOI:https://doi.org/10.1103/PhysRevD.93.122006