A Fabry–Pérot Cavity for Rare-Earth-Ion-Doped Nanocrystals

Abstract

This thesis work contributes to the effort of detecting single rare earth ions doped into crystals,
an operation crucial for the development of rare earth quantum computer hardware. Doping
crystals with rare earth elements, their trivalent ions substitute some of the crystal’s original
bonds. These ions have a partially filled 4f shell, protected by the full 5s and 5p shell from the
environment which makes them good candidates for qubits.
Because not every ion experiences the same electric field from the imperfect crystal, their total
linewidth is inhomogeneously broadened. If the doping is sufficiently low and the crystal sufficiently small, each ion undergoes a different optical shift and can thus be addressed separately.
Communication between ions happens due to their permanent dipole moments which change
according to their energy level.
So far no single ions could be detected in Lund because highly doped bulk crystals were used.
It was nevertheless tried to construct quantum logic gates using qubits that consisted of an
ensemble of ions. Constructing logic gates with these means that every single ion of one qubit
needs to be able to communicate with every single ion of another qubit, a method that becomes
increasingly difficult when more and more qubits are to be entangled. Connecting as many
qubits as possible is a crucial step in building a quantum computer that could outperform
classical computers and this could be facilitated if every qubit consisted of only one ion which
is the reason for the recent explorations towards nano crystals. This development also makes
it possible to address another problem of rare earth ions, their low probability of spontaneous
emission.
Placing nano crystals into an optical cavity promises the enhancement of spontaneous emission
by the Purcell effect. Ideal cavities are Fiber Fabry-Pérot resonators of which one side consists
of a mirror coated fiber tip and the other of a plane mirror functioning as the substrate for the
nano crystals. It was the aim of this thesis to build a cryostat holder that would bring these two
mirrors together with high stability and would allow for vertical and horizontal scanning.

Popular Abstract

How a Quantum Computer could be built using Rare Earth Ions

Quantum Computers have the potential to transform how research is done in many different
fields. Analogously to classical computers whose fundamental unit is a binary value, the
”bit”, quantum computers can run calculations using ”qubits”. Instead of taking either value
0 or 1, qubits can also be in between. Practically, this could mean that an atom exists in two
different energy levels at the same time, a state which is predicted by quantum theory and
can be achieved experimentally using laser light and really cold temperatures. This property
makes certain calculations much more efficient than on any classical computer because many
different calculations can be run simultaneously. A quantum computer’s prediction could for
example revolutionize how we use molecules in pharmaceutical research.
The approach to this subject in Lund is based on rare earth ions, yttrium (element 39) and everything
from lanthanum (element 57) to lutetium (element 71). Doped into crystals, it is exactly the above
mentioned superposition of energy states that is treated as the qubit. At close to the absolute zero
temperature (achieved using liquid helium), this superposition can be held alive for a very long
time. This property, referred to as long coherence time, makes the rare earths especially suitable
for quantum computers because the computations cannot happen instantaneously. At the same
time, short coherence times are needed when the result of the computation is to be read out. The
dilemma is therefore that long coherence times are needed for the computation to run but short
coherence times are necessary for reading out the result.
This enigma is on its way to being solved by incorporating a second type of rare earth ion into
the crystals. By interacting with neighboring atoms, it communicates with the qubit ions but would
itself not be involved in the calculations, only being used for reading out the final state. But because
it also has a non negligible coherence time, another trick needs to be employed based on a quantum
effect named after its discoverer ”Purcell”. This can be achieved by placing the crystals between
two mirrors that form a cavity. At sufficiently small mirror distances the coherence time is reduced
by the Purcell effect. Hence, using nano crystals it should be possible to decrease the coherence
time of the read out ion.
One of the mirrors of the cavity can be made extremely small when an optical fiber is used as base
material. On its tip a curvature can be molded and then a mirror coating can be applied onto it.
This is exactly what has been done by a German research group and they have also tested the cavity
effects at really cold temperatures. However, their cooling system differs from the one available at
Lund University such that their approach could not easily be reproduced in our group. It was the
task of this thesis to built a holder for the fiber to be placed in. In addition to fitting into our cooling
system, the requirements for the holder were the ability for the fiber to move in all three directions
but to be very stable once an appropriate position is found.
If successful, this method opens a new chapter for the quantum computing research in Lund and all
over the world

• author: Nüsslein, Andre
• supervisor: Andreas Walther
• organization: Atomic Physics; Department of Physics
• course: FYSK02 20182
• year: 2019
• type: M2 - Bachelor Degree
• subject: Physics and Astronomy
• keywords: Quantum Computer, Rear Earth Ions, Cavity, Laser, Cavity Quantum Electrodynamics, QED, Solidworks
• language: English
• id: 8971718
• date added to LUP: 2019-02-25 11:27:08
• date last changed: 2019-02-25 11:27:08