Test of Gravitation with Quantum Objects

We propose to test the law of gravitation at small distances by quantum interference deep into the theoretically interesting regime of 1000 times gravity. The idea is to explore a unique system consisting of a particle, the neutron, and a macroscopic object, the mirror, and its precise measurement of quantum de Broglie phases. This will be done for the first time by an application of Ramsey`s method of separated oscillating fields to the spectroscopy of the quantum states in the gravity potential above a horizontal mirror. Such measurements with ultra-cold neutrons will offer a sensitivity to Newton`s law or hypothetical short-ranged interactions, which is about 21 orders of magnitude below the energy scale of electromagnetism. Our approach explores therefore a region of parameter space that is complementary to the supermicron reach of upcoming microcantilever and torsion balance experiments.

Quantum technologies provide highest precision through quantum interference. They are utilised in a variety of fields; from natural science to medicine. In particular resonance spectroscopy methods have opened up the field of low energy particle physics for the study of fundamental interactions. However, up to now, gravity is mostly out of scope for resonance spectroscopy. One reason is that there is so far no known quantum theory of gravitation. The other is that gravity experiments are usually based on astronomical observations or pendulum experiments. Often, the studied objects are taken as point-like test masses, which are certainly not considered as typical quantum tools. We present a novel resonant spectroscopy technique devoted to the study of gravitation and the related cosmological problems of Dark Matter and Dark Energy. The object is a quantum mechanical wavepacket of an ultra-cold neutron, and the new method extends the techniques of Purcel, Rabi and Ramsey to neutron quantum states in the gravity potential of the Earth [Abe10]. We named the new technique Gravity Resonance Spectroscopy (GRS) in close analogy to Magnetic Resonance Spectroscopy (MRS). Here a neutron in the gravity potential of the Earth is placed on a reflecting mirror and transitions between the gravitational quantum states are performed by applying mechanical oscillations of the mirror with the proper transition frequency, whereas in MRS technique, an atom, a molecule or a nucleus with a magnetic moment is placed in an outer magnetic field and transitions between the magnetic Zeeman splitting are performed by applying proper oscillations of radiofrequency fields. Resonant transitions between several of the lowest quantum states are observed for the first time. Similarly to the 3-region Rabi setup for molecules, we have established a 3-region GRS experiment. The measurements deliver severe restrictions on cosmology and any gravity-like interaction within the level of sensitivity of 1.410-15 eV. If some yet undiscovered particles of Dark Matter or Dark Energy interact with a neutron, the result is a measurable energy shift in the observed quantum states, devoid of electromagnetic perturbations. These measurements allow to restrict the parameter space for a chameleon field, hypothetically being responsible for the accelerated expansion of the universe, by seven orders of magnitude, and, makes it possible to find or exclude this field in full parameter space. Another example is the pseudo-scalar interaction of an axion field, a prominent candidate for the unknown Dark Matter, which would provide a force between the spin of the neutron and the neutron mirror. Limits on axion fields are improved by a factor of 30.