Wigley, Paul Benjamin
Description
Bose-Einstein condensates (BECs), a quantum state of matter
formed when bosonic atoms
are cooled close to absolute zero, have become the premier
platform for investigating
fundamental physics with atomic vapours. Experiments on
Bose-Einstein condensates
now achieve exquisite control over many aspects of the system,
including interactions,
trapping potential, and dynamics. This has precipitated a new
wave of research into
many-body quantum...[Show more] phenomena and, in particular, solitons. These
structures are fundamental
excitations of an interacting non-linear medium, of interest to a
multitude of
scientific disciplines from non-linear optics to financial
markets. The highly controllable
environment of BECs form an attractive playground for the study
of solitons allowing
the non-linearity to be dynamically tuned, facilitating deeper
investigations into these
structures.
Consistently generating and analysing solitons in BEC experiments
continues to be
problematic. In particular, the non-linear dynamics of BECs,
though required for the
generation of solitons, produce particularly challenging control
and optimization problems.
These control problems must be solved before further
investigations into the fundamental
physics of soliton dynamics can be answered. This thesis makes
three important
advances in the control and measurement of BECs that will lead to
better generation and
observation of solitons. (1) a theoretical model for a control
scheme capable of highly
precise wavefunction engineering, (2) the experimental
implementation of a machine
learning algorithm for online optimisation, and (3) a continuous
non-destructive imaging
system capable of directly observing soliton dynamics in
real-time. Together, these advances
provide a suite of tools for manipulating and exploiting solitons
in Bose-Einstein
condensates.
A novel technique was developed theoretically, offering control
of the macroscopic
wavefunction of a Bose-Einstein condensate with unprecedented
spatial resolution and
speed. The ability to control the atomic wavefunction at the
fundamental length scale
is key to the advancement of many quantum technologies such as
quantum simulators.
The magnetic resonance control scheme is demonstrated through
simulation of a 87Rb
condensate with the exemplar model generating a single dark
soliton with corresponding
π phase kink. The soliton represents a structure at the
fundamental length scale of
the system, and demonstrates the potential of the scheme for
precision state engineering.
The scheme is extended to generate higher-order soliton modes
which are yet to be
experimentally realised.
A machine learning algorithm based on Gaussian processes was
developed and implemented
on the evaporative cooling stage of the production of a 87Rb
Bose-Einstein
condensate, successfully demonstrating fast optimisation to
condensation. The Gaussian
process develops a statistical model based on the data that
enables the characterisation of
the relationship between the experimental controls and resultant
quality of the BEC. This
relationship is often obfuscated through technical details of the
apparatus, frustrating the
use of theoretical models to design optimal evaporation ramps.
These models often only
consider ergodic dynamics with two-body s-wave interactions and
no other loss rates
with better ramps likely exploiting more complex interactions.
The internal model generated from the Gaussian process utilised
uncertainty in measured
data, making the optimisation more robust to experimental noise
than alternate
methods. The algorithm is shown to produce high quality
Bose-Einstein condensates in
10 times fewer experimental iterations than previously used
online optimisation techniques.
By exploiting information on the sensitivity of each control, the
model can be
used to aid experimental design. The convergence of the
optimisation is further improved
by eliminating a superfluous parameter identified by the model.
The general
usefulness of machine learning compared with bespoke optimisation
algorithms has seen
machine learning approach ubiquity.
Finally, an experimentally straightforward technique for
continuous non-destructive
imaging of matter-wave solitons was developed and implemented,
facilitating measurements
of stochastic phenomena. The technique is readily practicable on
any ultracold
atom experiment with an existing absorption imaging system,
simply requiring the probe
laser be far-detuned from resonance. With a signal-to-noise of
∼ 33 at 1.25 GHz detuning,
the technique is capable of producing 100 images with no
observable heating or atom
loss. Coupled with a fast optical phase locked loop, the
technique can be used in conjunction
with absorption imaging to generate a series of non-destructive
images followed by
a final high signal-to-noise absorption image solely through
moving the laser on resonance
for the final image. The high performance and utility of this
imaging setup make
it a powerful tool for ultra-cold atom experiments.
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