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Previous studies of gravitationally bound states of ultracold neutrons showed the quantization of energy levels, and confirmed quantum mechanical predictions for the average size of the two lowest energy states wave functions. Improvements in position-like measurements can increase the accuracy by an order of magnitude only. We therefore develop another approach, consisting in accurate measurements of the energy levels. The GRANIT experiment is devoted to the study of resonant transitions between quantum states induced by an oscillating perturbation. According to Heisenbergs uncertainty relations, the accuracy of measurement of the energy levels is limited by the time available to perform the transitions. Thus, trapping quantum states will be necessary, and each source of losses has to be controlled in order to maximize the lifetime of the states. We discuss the general principles of transitions between quantum states, and consider the main systematical losses of neutrons in a trap.
Observation time is the key parameter for improving the precision of measurements of gravitational quantum states of particles levitating above a reflecting surface. We propose a new method of long confinement in such states of atoms, anti-atoms, neu
The UCN$tau$ experiment is designed to measure the lifetime $tau_{n}$ of the free neutron by trapping ultracold neutrons (UCN) in a magneto-gravitational trap. An asymmetric bowl-shaped NdFeB magnet Halbach array confines low-field-seeking UCN within
The GRANIT project is the follow-up of the pioneering experiments that first observed the quantum states of neutrons trapped in the earths gravitational field at the Institute Laue Langevin (ILL). Due to the weakness of the gravitational force, these
The arithmetic problem of factoring an integer $N$ can be translated into the physics of a quantum device, a result that supports Polyas and Hilberts conjecture to prove Riemanns hypothesis. The energies of this system, being univocally related to th
We present the status of the development of a dedicated high density ultra-cold neutron (UCN) source dedicated to the gravitational spectrometer GRANIT. The source employs superthermal conversion of cold neutrons to UCN in superfluid helium. Tests ha