1. qBOUNCE: a quantum bouncing ball gravity spectrometer
Presentation by Lucas van Sloten (s ) & Jelle Thole (s ), adaption of the talk of Hartmut Abele at the QU7 Symposium

2. Outline Introduction Theory Experimental Setup Results & Discussion
Conclusion

3. Introduction
qBOUNCE is an experiment of the University of Vienna, which uses Ultra Cold Neutrons (UCN) to probe the laws of gravity at the micron-scale
These UCNs are used to do spectroscopy, which is the indirect measurement of energies through frequencies

4. Introduction
Spectroscopy has in general been restricted to electromagnetic interactions (e.g. Atomic Clocks, Rabi Spectroscopy)
Here instead of radiofrequency magnetic fields, mechanics is used
From:

5. Motivation
Newton's gravitational law has not been tested at the sub- millimeter level, the qBOUNCE experiment allows for this
This new test of Newton’s gravitational law grants possible insights into new physics
UCNs allow for a very precise test of these physics

6. Motivation Fifth forces/String Theories The Equivalence Principle
Possible Neutron Electric Charge
Dark Matter
Dark Energy

7. Fifth forces/String Theories
Fifth forces that are only effective at small scales or folded up string-type extra dimensions at these scales can modify Newton’s potential in the following way:
This alpha can be measured through a shift in the energy levels of the experiment

8. Weak Equivalence principle
Using the two type of experiments of qBOUNCE we can measure both the characteristic energy and length scale of the experiment
This allows for a test whether inertial mass and gravitational mass are the same, thus testing the weak equivalence principle

9. Dark matter
Very light bosonic dark matter candidates can be detected through the macroscopic forces they mediate
This force would show itself by a deviation from Newton’s law at short distances
qBOUNCE looks for particles that mediate a spin- dependent force, axions in particular, directly
These particles would induce an energy shift

10. Dark Energy
Dark energy might be some kind of cosmological constant or it might be a quintessence type of scalar field
A kind of scalar field that qBOUNCE looks for are chameleon fields
Chameleon fields couple to matter, it is this coupling that qBOUNCE can test directly, through a shift in energy levels

11. Theory
So basically we have these UCNs, which are subject to a linear gravity potential, leading to the following Schrödinger equation:
Solutions of this Schrödinger equations are the Airy functions:

12. Airy Functions
Now the Airy Functions for this gravitational potential have the following characteristic length, energy and time scale:
The discrete quantum states this airy function solution has are the ones qBOUNCE uses for the spectroscopy

13. Quantum States
From: arXiv

14. Two possible experiments
Gravity Resonance Spectroscopy (GRS)
Can be used to determine the energy differences between the states with high precision
Quantum Bouncing Ball (QBB)
Can be used to determine the distance scale of the wave packet

15. Ultra-Cold Neutron Source
A reactor provides the neutrons due to a fission process
Fast neutrons cant get through the bends, while neutrons that are too slow cant overcome gravity
From:

16. Why neutrons? Neutrons are insensitive to electric fields
The energy eigenstates are non-equidistant, this allows for resonance spectroscopy
The lowest states are in the range of several pico-eV’s, giving very high accuracy

17. Experimental setup (GRS)
I : Prepare system in lower bound states
II : Excite the system with vibrating mirror
III : Remove higher energy states again
IV : Measure the surviving neutrons
From arXiv

18. Experimental setup (GRS)
Converts an energy measurement into a frequency measurement, which can be done with very high precision.
The GRS method is analogous to Rabi’s method for measuring nuclear magnetic moments
From arXiv

19. Simularities of GRS and Rabi’s magnetic resonance spectroscopy
Rabi’s magnetic spectroscopy
Gravity Resonance Spectroscopy

20. Experimental setup (QBB)
I: Prepares the neutrons in a superposition of the lowest states
II: The neutrons fall down a step which converts them into a superposition of higher states, which evolves in time
III: The neutrons are detected with a position sensative detector I II
III
From Physics Procedia 17 (2011) 4-9

21. Experimental setup (QBB)
As the neutron is reflected by the mirror its wave- function shows aspects of quantum interference
As the neutrons are detected one obtains the probability distribution of the neutrons
Region I
Region II
Simulated probability distribution of the QBB (From: arXiv )

22. Experimental difficulties
The effects of the rough surface of the upper glass mirror on the quantum states are difficult to predict
The QBB experiment requires position-sensitive detectors with high spatial resoltution and low background
The step between the two mirrors in the QBB experiment needs to be very stable for several days
The accuracy of the experiments is restricted by the strength of the UCN sources.

23. Results & Discussion
From: arXiv

24. Axion Exclusion

25. Results & Discussion
From: arXiv

26. Results & Discussion Transition frequency fore the transition:
Transition frequency for the transition:

27. Fifth Force & Chameleon Fields Exclusion

28. Results & Discussion
From: arXiv

29. From: arXiv

30. Quantum Bouncing Ball
Up to now not enough precision to give definite results
There is a need for more data analysis, which in oncoming years will probably give conclusive evidence on the weak equivalence principle

31. Conclusion/outlook
The GRS and QBB experiments can contribute in answering a wide range of scientific questions
Stronger UCN sources and better detectors will likely improve the accuracy in the future