# History

**1969:** Independently from each other, ultra-cold neutrons are produced for the first time at the Joint Institute for Nuclear Research in Dubna, Russia [1] and at the Forschungsreaktor München [2].

Ultra-cold neutrons have a kinetic energy in the order of 300 neV corrsponding to a velocity of 10 m/s. Therefore, they are reflected from certain materials under all angles of incidence.

**1971/1974:** Langhoff [3] and Gibbs [4] publish the solution of a quantum particle in the linearized gravity potential as a simple example for teaching quantum mechanics.

**1978/1991:** Lushchikov and Frank [5] propose to search for ultra-cold neutrons that are bound in the gravitational potential over a horizontal surface. Wallis et al. publish an extensive theoretical analysis of a gravitationally bound atom over a concave mirror [6].

Bound states in the linearized gravitational potential can be described by airy-functions, see Fig. 1 [12]. For this description the eigenenergies depend only on the acceleration of free fall g, the neutron mass and the Planck constant.

**1994:** We have demonstrated that cold atoms can be retroreflected from a ferromagnetic surface by the Stern-Gerlach effect. This work has been done at the atomic physics group of E. Hinds at Yale University. [13]

**2002:** A collaboration between us, at that time at the University of Heidelberg, the Institute Laue-Langevin in Grenoble/France, the Petersburg Nuclear Physics Institut in Gatchina/Russia and the Joint Institut for Nuclear Research in Dubna/Russia demonstrated bound quantum states of ultra-cold neutrons in the gravity potential of the earth, see Fig. 5 (setup) and Fig. 6 (results) [7].

## The qBounce experiment:

**2007:** The qBounce project constitutes a seamless advancement of the previous realizations.

Its first main emphasis was put on the direct observation of the time evolution of the Quantum Bouncing Ball, involving track detectors with an excellent spatial resolution.

As in 2002, a mirror is placed on top of another one, with the surface of the upper one being roughened. Their separation, together with a convenient choice of the collimating plates, prepares the neutron in the first two bound states. Then, the neutron falls down onto a third mirror which has been carefully placed a few ten microns below the previous mirror. This creates the effect of the so-called “quantum bouncing ball”.

The probability density of the neutron has been recorded for different mirror lengths in region II with the use of track detectors with a spatial resolution in the micron range.

This allows the realization of a Quantum Bouncing Ball with ultra-cold neutrons as well as the study of its time evolution [8,9].

Varying the frequency allows the observation of a reduced flux when the excitation is resonant. The theoretical dependency of the transmission on the excitation amplitude could be predicted theoretically. The observed transitions are |1> -> |3> [10], |1> -> |2> as well as |2> -> |3> [11].

[1] V. I. Lushchikov, Yu. N. Pokotilovskii, A. V. Strelkov, F. L. Shapiro, *Observation of Ultracold Neutrons*, ZhETF Pis. Red. 9, No. 1, 40-45 (1969)

[2] A. Steyerl,* Measurments of total cross sections for very slow Neutrons with velocities from 100 m/sec to 5 m/sec*, Physics Letters Volume 29B, number 1 (1969)

[3] P. W. Langhoff, *Schrödinger Particle in a Gravitational Well*, AJP Volume 39/955, August 1971

[4] R. L. Gibbs, *The Quantum Bouncer*, AJP Volume 43/25, January 1975

[5] V. Lushchikov, A. Frank, *Quantum effects occuring when ultracold neutrons are stored on a plane*, JETP Letter (1978).

[6] H. Wallis, J. Dalibard, and C. Cohen-Tannoudji, *Trapping Atoms in a Gravitational Cavity,* Appl. Phys. B 54, 407-419 (1992)

[7] V. Nesvizhevsky, H. Abele et al., *Quantum states of neutrons in the Earth's gravitational field*, Nature 415 6869 (2002).

[8] H. Abele, T. Jenke, D. Stadler, P. Geltenbort, *QuBounce: the dynamics of ultra-cold neutrons falling in the gravity potential of the Earth*, Nuclear Physics A, Volume 827, Issues 1-4

[9] Tobias Jenke, David Stadler, Hartmut Abele, Peter Geltenbort,* Q-BOUNCE— Experiments with quantum bouncing ultracold neutrons*, Nuclear Instruments and Methods in Physics Research A, Volume 611, Issues 2-3, (2009)

[10] Tobias Jenke, Peter Geltenbort, Hartmut Lemmel, Hartmut Abele,* Realization of a gravity-resonance-spectroscopy technique*, Nature Physics 7, 468–472

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

[12] H. Abele, T.Jenke, H.Leeb, J.Schmiedmayer, *Ramsey’s method of separated oscillating fields and its application to gravitationally induced quantum phase shifts*, Phys. Rev. D 81, 065019 (2010)

[13] T. Roach, H. Abele et al., *Realization of a Magnetic Mirror for Cold Atoms*, Phys. Rev. Lett. 75 630 (1995)