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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, neutrons and other particles possessing a magnetic moment. The earth gravitational field and a reflecting mirror confine particles in the vertical direction. The magnetic field originating from electric current passing through a vertical wire confines particles in the radial direction. Under appropriate conditions, motions along these two directions are decoupled to a high degree. We estimate characteristic parameters of the problem, and list possible systematic effects that limit storage times due to the coupling of the two motions.

The discrete quantum properties of matter are manifest in a variety of phenomena. Any particle that is trapped in a sufficiently deep and wide potential well is settled in quantum bound states. For example, the existence of quantum states of electrons in an electromagnetic field is responsible for the structure of atoms 16 , and quantum states of nucleons in a strong nuclear field give rise to the structure of atomic nuclei 17 . In an analogous way, the gravitational field should lead to the formation of quantum states. But the gravitational force is extremely weak compared to the electromagnetic and nuclear force, so the observation of quantum states of matter in a gravitational field is extremely challenging. Because of their charge neutrality and long lifetime, neutrons are promising candidates with which to observe such an effect. Here we report experimental evidence for gravitational quantum bound states of neutrons. The particles are allowed to fall towards a horizontal mirror which, together with the Earth's gravitational field, provides the necessary confining potential well. Under such conditions, the falling neutrons do not move continuously along the vertical direction, but rather jump from one height to another, as predicted by quantum theory 1 , 2 , 3 .

We measured the temperature dependence of the probability of small heating and total losses of UCNs on the PFPE Fomblin Y surface with various molecular mass \\[M_{{\\bar{W}}}\\] (2800, 3300, 6500 amu) in the temperature range of 100–300 K. The probability of small heating sharply decreases with increasing \\[M_{{\\bar{W}}}\\] and decreasing temperature. The probability of total loss weakly decreases with decreasing temperature and takes the minimum value at \\[M_{{\\bar{W}}} =3300 \\, \\hbox {amu}\\]. As this oil provides a homogeneous surface with minimal probabilities of small heating and total losses of UCNs, it is the preferred candidate for experiments on measuring the neutron lifetime.

We have studied neutron quantum states in the potential well formed by the earth’s gravitational field and a horizontal mirror. The estimated characteristic sizes of the neutron wave functions in the two lowest quantum states correspond to expectations with an experimental accuracy. A position-sensitive neutron detector with an extra-high spatial resolution of \\(\\sim 2 \\mathrm{\\mu} \\)m was developed and tested for this particular experiment, to be used to measure the spatial density distribution in a standing neutron wave above a mirror for a set of some of the lowest quantum states. The present experiment can be used to set an upper limit for an additional short-range fundamental force. We studied methodological uncertainties as well as the feasibility of improving further the accuracy of this experiment.

GBAR is a project aiming at measuring the free-fall acceleration of gravity for antimatter, namely antihydrogen atoms ( H ¯ ). The precision of this timing experiment depends crucially on the dispersion of initial vertical velocities of the atoms as well as on the reliable control of their distribution. We propose to use a new method for shaping the distribution of the vertical velocities of H ¯ , which improves these factors simultaneously. The method is based on quantum reflection of elastically and specularly bouncing H ¯ with small initial vertical velocity on a bottom mirror disk, and absorption of atoms with large initial vertical velocities on a top rough disk. We estimate statistical and systematic uncertainties, and we show that the accuracy for measuring the free fall acceleration g ¯ of H ¯ could be pushed below 10 - 3 under realistic experimental conditions.

Different experiments are ongoing to measure the effect of gravity on cold neutral antimatter atoms such as positronium, muonium, and antihydrogen. Among those, the project GBAR at CERN aims to measure precisely the gravitational fall of ultracold antihydrogen atoms. In the ultracold regime, the interaction of antihydrogen atoms with a surface is governed by the phenomenon of quantum reflection which results in bouncing of antihydrogen atoms on matter surfaces. This allows the application of a filtering scheme to increase the precision of the free fall measurement. In the ultimate limit of smallest vertical velocities, antihydrogen atoms are settled in gravitational quantum states in close analogy to ultracold neutrons (UCNs). Positronium is another neutral system involving antimatter for which free fall under gravity is currently being investigated at UCL. Building on the experimental techniques under development for the free fall measurement, gravitational quantum states could also be observed in positronium. In this contribution, we report on the status of the ongoing experiments and discuss the prospects of observing gravitational quantum states of antimatter and their implications.

We consider the feasibility of observing the gravitational quantum states of positronium. The proposed scheme employs the flow-throw technique used for the first observation of this effect with neutrons. Collimation and Stark deceleration of Rydberg positronium atoms allow selecting the required velocity class. If this experiment could be realized with positronium, it would lead to a determination of g for this matter-antimatter system at the few % level. As discussed in this contribution, most of the required techniques are currently available but important milestones have to be demonstrated experimentally before such an experiment could become reality. Those are the efficient focusing of a bunched positron beam, Stark deceleration of Rydberg positronium, and its subsequent excitation into states with large angular momentum. We provide an estimate of the efficiencies we expect for these steps and assuming those could be confirmed we calculate the signal rate.

The aim of the GBAR experiment is to measure the gravitational acceleration of antihydrogen by observing the free fall of ultracold anti-atoms. The experiment is installed at CERN’s Antiproton Decelerator/ELENA facility. Positrons are produced by a low energy (9 MeV) linear electron accelerator and captured in a modified Surko (buffer gas) trap. We have recently implemented a silicon carbide-based trapping scheme that replaces the routinely used nitrogen gas with a high quality silicon carbide single crystal in the first phase of the trap. The new setup has been providing stable and efficient positron trapping for more than a year. After a short accumulation in the buffer gas trap, the particles are transported to a high-field (5 T) Penning-Malmberg trap, where a high number of pulses can be collected in a deep potential well. We discuss the performance of the improved positron line and the present status of the experiment.

We report analysis of rough mirrors used as the gravitational state selectors in neutron beam and similar experiments. The key to mirror properties is its roughness correlation function (CF) which is extracted from the precision optical scanning measurements of the surface profile. To identify CF in the presence of fluctuation-driven fat tails, we perform numerical experiments with computer-generated random surfaces with the known CF. These numerical experiments provide a reliable identification procedure which we apply to the actual rough mirror. The extracted CF allows us to make predictions for ongoing GRANIT experiments. We also propose a radically new design for rough mirrors based on Monte Carlo simulations for the 1D Ising model. The implementation of this design provides a controlled environment with predictable scattering properties.

Quantum states in the earth’s gravitational field have been observed, with ultra-cold neutrons falling under gravity. The experimental results can be described by the quantum mechanical scattering model presented here. We also discuss other geometries of the experimental setup, which correspond to the absence or the reversion of gravity. Since our quantum mechanical model quantitatively describes, particularly, the experimentally realized situation of reversed gravity, we can practically rule out alternative explanations of the quantum states, in terms of pure confinement effects.