qBOUNCE: a quantum bouncing ball gravity spectrometer Presentation by Lucas van Sloten (s2297604) & Jelle Thole (s2183110), adaption of the talk of Hartmut Abele at the QU7 Symposium

Outline Introduction Theory Experimental Setup Results & Discussion Conclusion

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

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: https://www.khanacademy.org

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

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

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

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

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

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

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:

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

Quantum States From: arXiv 1510.03078

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

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: www.ILL.eu

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

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 1512.09314

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 1512.09314

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

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

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 1510.03078)

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.

Results & Discussion From: arXiv 1510.03078

Axion Exclusion

Results & Discussion From: arXiv 1512.09134

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

Fifth Force & Chameleon Fields Exclusion

Results & Discussion From: arXiv 1510.03078

From: arXiv 1510.03078

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

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