The standard model of cosmology provides a robust description of the evolution of the universe. Nevertheless, the small magnitude of the vacuum energy is troubling from a theoretical point of view 9 . An appealing resolution to this problem is to introduce additional scalar fields. However, these have so far escaped experimental detection, suggesting some kind of screening mechanism may be at play. Although extensive exclusion regions in parameter space have been established for one screening candidate -chameleon fields 10,17 -another natural screening mechanism based on spontaneous symmetry breaking has also been proposed, in the form of symmetrons 11 . Such fields would change the energy of quantum states of ultra-cold neutrons in the gravitational potential of the earth. Here we demonstrate a spectroscopic approach based on the Rabi resonance method that probes these quantum states with a resolution of Δ = 2 × 10 −15 eV. This allows us to exclude the symmetron as the origin of Dark Energy for a large volume of the three-dimensional parameter space.Resonance spectroscopy -originally introduced by I. Rabi 1 as a "molecular beam resonance method" -has evolved into an indispensable method for precision experiments with two-levelsystems. Here, the energy difference between two quantum states translates via the Planck-Einstein relation = ℎ into a frequency, which can be measured with unprecedented accuracy. Rabi's experiment has led to new insights into physics, chemistry and biology providing detailed information about the structure, dynamics, reaction state, and chemical environment of molecules. This work, realized by the qBounce collaboration, extends the quantum technique of Rabi spectroscopy to the gravitational sector. The experiment measures transition frequencies of bound quantum states of neutrons in the gravitational field of the earth. These discrete quantum states occur when very slow ultra-cold neutrons (UCN) totally reflect on perfectly polished horizontal surfaces. The typical spatial extent of the corresponding wave functions is of order of ten microns. The eigenenergies are in the pico-eV range and depend on the local acceleration g, the neutron mass m, and the reduced Planck constant ℏ. Furthermore, any two states can be treated as an effective two-level system. This offers the possibility of applying resonance spectroscopy techniques to test gravity at short distances.

Gravity experiments with very slow, so-called ultracold neutrons connect quantum mechanics with tests of Newton's inverse square law at short distances. These experiments face a low count rate and hence need highly optimized detector concepts. In the frame of this paper, we present low-background ultracold neutron counters and track detectors with micron resolution based on a 10B converter. We discuss the optimization of 10B converter layers, detector design and concepts for read-out electronics focusing on high-efficiency and low-background. We describe modifications of the counters that allow one to detect ultracold neutrons selectively on their spin-orientation. This is required for searches of hypothetical forces with spin–mass couplings.The mentioned experiments utilize a beam-monitoring concept which accounts for variations in the neutron flux that are typical for nuclear research facilities. The converter can also be used for detectors, which feature high efficiencies paired with high spatial resolution of 1normal–20.25emnormalμnormalm. They allow one to resolve the quantum mechanical wave function of an ultracold neutron bound in the gravity potential above a neutron mirror.

We report a measurement of the local acceleration with ultracold neutrons based on quantum states in the gravity potential of the Earth. The new method uses resonant transitions between the states |1 ↔ |3 and for the first time between |1 ↔ |4 . The measurements demonstrate that Newton's Inverse Square Law of Gravity is understood at micron distances at an energy level of 10 −14 eV with ∆g g = 4 × 10 −3 . The results provide constraints on any possible gravitylike interaction at a micrometer interaction range. In particular, a dark energy candidate, the chameleon field is restricted to β < 6.9 × 10 6 for n = 2 (95% C.L.).

Neutrons are the ideal probes to test gravity at short distances -electrically neutral and only hardly polarizable. Furthermore, very slow, so-called ultracold neutrons form bound quantum states in the gravity potential of the Earth. This allows combining gravity experiments at short distances with powerful resonance spectroscopy techniques, as well as tests of the interplay between gravity and quantum mechanics. In the last decade, the qBOUNCE collaboration has been performing several measurement campaigns at the ultracold and very cold neutron facility PF2 at the Institut Laue-Langevin. A new spectroscopy technique, Gravity Resonance Spectroscopy, was developed. The results were applied to test various Dark Energy and Dark Matter scenarios in the lab, like Axions, Chameleons and Symmetrons. This article reviews Gravity Resonance Spectroscopy, explains its key technology and summarizes the results obtained during the past decade.