In various experiments within the qBounce project, two essential methods to investigate gravitationally bound quantum states of ultra-cold neutrons were developed. The first one enables us to map the probability distribution of the „Quantum Bouncing Ball“ and with the second, the so-called gravity-resonance-spectroscopy-method, we are able to probe the eigenenergies of bound states in the gravitational potential. 

Gravity-resonance-spectroscopy

1. State preparation
   The first step to perform experiments in the quantum regime is to prepare the system of interest in a well-defined state. At qBounce, we prepare the system in the lower bound states by sending a beam of ultra-cold neutrons through a system of two neutron mirrors.
   They are arranged on top of each other with a distance of ca. 30 µm and an upper, rough surface. Neutrons in high energetic states are scattered out of the system, thus only the lowest states are populated.
2. State transition
   To excite neutrons in higher states, the neutron mirrors are vibrated with a frequency ω_pq. Because of the vibrating surfaces, the boundary conditions of the system change periodically so that the Hamiltonian is time dependent and allows state transitions. By applying ω₁₃ one can drive transitions from state |1> to state |3> and thus effectively measure the energy difference between the two states by measuring the applied frequency.
3. State analysis
   By repetition of region I, the occupation of state |1> may be analyzed.
4. Time-resolved neutron detection
   To check if a transition frequency is met one measures the population of state |1>. If the applied frequency was resonant, there should be a drop in transmission. So one only has to measure the neutron flow for different applied frequencies. This is realized by a proportional counter, that works by converting neutrons to ionizing radiation by a boron coated aluminum foil and intensify the signal by collisions with gas behind the foil.

Quantum Bouncing Ball with neutrons

1. Velocity selection (not in picture 3)
   Neutrons with a too high velocity are blocked from the experiment by an aperture system so that the horizontal velocity distribution is restricted to a convenient region.
2. State preparation
   Two neutron mirrors prepare the neutrons in a superposition of the lowest states. This happens similar to the method that was used for the gravity-resonance-spectroscopy.
3. The prepared superposition passes a step at the transition to region [III] of several ten microns and evolves further on in time.
4. Spatially resolved neutron detection
   To map the probability distribution of the „Quantum Bouncing Ball“, track detectors of Boron-coated CR-39 plastics were used. Ultra-cold neutrons hitting the boron layer initiate a nuclear reaction that leads to two decay products. One of those enters the plastics and leaves a track of defects, which can be enlarged by etching to the point of easy visibility.

[1]  J. Felber, R. Gähler, and C. Rausch, Matter waves at a vibrating surface: Transition from quantum-mechanical to classical behavior, opens an external URL in a new window, Physical Review A Vol. 53 Nr. 1

[2]  Tobias Jenke, qBounce - vom Quantum Bouncer zur Gravitationsresonanzspektroskopie, Dissertation (2011)