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 submillimeter 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 spindependent 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
From Physics Procedia 17 (2011) 4-9
III
Experimental setup (QBB)

As the neutron is
reflected by the
mirror its wavefunction shows
aspects of
quantum
interference

As the neutrons
are detected one
obtains the
probability
distribution of the
neutrons
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 frequency for the
transition:
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