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Quantum states of neutrons in the Earth's gravitational field


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 atoms16, and quantum states of nucleons in a strong nuclear field give rise to the structure of atomic nuclei17. 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 theory1,2,3.

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Figure 1: Wavefunctions of the quantum states of neutrons in the potential well formed by the Earth's gravitational field and the horizontal mirror.
Figure 2: Layout of the experiment.
Figure 3: The neutron throughput N versus the absorber height.
Figure 4: The neutron throughput versus the absorber height at low height values.


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We are grateful to our colleagues who were interested in this research and contributed to its development, in particular K. Ben-Saidane, D. Berruyer, Th. Brenner, J. Butterworth, D. Dubbers, P. Geltenbort, T. M. Kuzmina, A. J. Leadbetter, B. G. Peskov, S. V. Pinaev, K. Protasov, I. A. Snigireva, S. M. Soloviev and A. Voronin. The work was supported by INTAS.

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Correspondence to Valery V. Nesvizhevsky.

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Nesvizhevsky, V., Börner, H., Petukhov, A. et al. Quantum states of neutrons in the Earth's gravitational field. Nature 415, 297–299 (2002).

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