Figure 1 (Left) Neutron mirror apparatus. An ultracold neutron (UCN) enters a space between two mirrors that act as potential wells, giving rise to a discrete energy spectrum. A detector measures neutrons exiting the cavity formed by the mirrors. The bottom mirror sits upon a nanopositioning table that induces a vertical oscillation that produces dips in the neutron transmission at the resonances. (Right) Energy-level diagram for the neutrons in a gravitational field caught between the walls, which oscillate owing to the mirror motion (horizontal direction here is vertical in the apparatus). This, in turn, causes the neutrons to move up and down energy levels. A measurement of the energy-level spacing yields constraints on parameters of scenarios describing dark energy and dark matter, which would slightly shift the levels as indicated by the dashed lines.
Wolfgang P. Schleich, Ernst Rasel – http://physics.aps.org/articles/v7/39
The quantum behavior of a neutron bouncing in the gravitational field of the Earth can improve what we know about dark energy and dark matter.
Spectroscopy has always set the pace of physics. Indeed, the observation of the Balmer series of the hydrogen atom led to the Bohr-Sommerfeld model about 100 years ago. A little later the discreteness of the spectrum moved Werner Heisenberg to develop matrix mechanics and Erwin Schrödinger to formulate wave mechanics. In 1947, the observation of a level shift in hydrogen by Willis E. Lamb ushered in quantum electrodynamics.
Now, a group led by Hartmut Abele of the Technical University of Vienna, Austria, reports, in Physical Review Letters  [http://arxiv-web3.library.cornell.edu/abs/1404.4099], experiments that once more take advantage of the unique features of spectroscopy to put constraints on dark energy and dark matter scenarios. However, this time it is not a “real atom” (consisting of an electron bound to a proton) that provides the insight. Instead, the research team observes an “artificial atom”—a neutron bouncing up and down in the attractive gravitational field of the Earth (Fig. 1). This motion is quantized, and the measurement of the separation of the corresponding energy levels allows these authors to make conclusions about Newton’s inverse square law of gravity at short distances.
Setup and results for the employed gravity resonance spectroscopy: Left: The lowest eigenstates and eigenenergies with conning mirrors at bottom and top separated by 30.1 µm. The observed transitions are marked by arrows. Center: The transmission curve determined from the neutron count rate behind the mirrors as a function of oscillation frequency shows dips corresponding to the transitions shown on the left. Right: Upon resonance at 280 Hz the transmission decreases with the oscillation amplitude in contrast to the detuned 160 Hz. Because of the damping no revival occurs. [arxiv]
The energy wave function of a quantum particle in a linear potential , corresponding, for example, to the gravitational field close to the surface of the Earth, has a continuous energy spectrum . However, when a quantum particle such as a neutron is also restricted in its motion by two potential walls, the resulting spectrum is discrete.
Read also: “With neutrons, scientists can now look for dark energy in the lab“
This elementary problem of nonrelativistic quantum mechanics is a slight generalization of the familiar “particle in a box” where the bottom of the box, which usually corresponds to a constant potential, is replaced by a linear one representing the gravitational field. Continue reading Neutrons Knock at the Cosmic Door