Goh, Matthew
Description
Ultracold atomic Fermi gases are the leading platform
for analogue quantum simulation, and provide a promising avenue
to study the origin of high-temperature superconductivity in
cuprates. However, current experimental approaches to cooling
Fermi gases use evaporative cooling, which is limited by poor
thermalisation properties of fermions and is
non-number-conserving. This prevents the creation of useful
analogue simulators of many collective phenomena. This...[Show more] thesis is
the first theoretical investigation into the use of
continuous-measurement feedback control as an alternative means
of cooling an atomic Fermi gas. Since tractable simulation of
Fermi gas dynamics requires simplifications to the full quantum
field theory, we derive and simulate a fermionic equivalent to
the Gross-Pitaevskii equation, generalising a model of
feedback-controlled BECs by Haine et al. to multimode ultracold
atomic Fermi gases. We demonstrate that in the absence of
measurement effects, a suitable control can drive an interacting
Fermi gas arbitrarily close to its ground state. However,
although control schemes based upon damping spatial density
fluctuations work well for single-spatial-mode BECs, we show that
they perform poorly for Fermi gases with a large number of atoms
due to counter-oscillation of multiple spatial modes, which must
exist due to Pauli exclusion. We generalise a
feedback-measurement model of BECs by Szigeti et al. to a
multimode atomic Fermi gas, and perform stochastic simulations of
measured, feedback-controlled fermions in the single-atom and
many-atom mean-field limits. The effects of measurement
backaction are an important consideration, since in a realistic
experiment knowledge of the system state used for feedback must
be obtained from measurement, leading to competition between
measurement-induced heating and feedback cooling. We show that
weaker and less precise measurements cool the system to a lower
equilibrium excitation energy, but are unable to place practical
lower bounds on measurement strength due to the lack of a
system-filter separation. When measurement-induced heating is
accounted for, we find that the equilibrium energy per particle
scales superlinearly, suggesting that existing control schemes
which work well for bosons would not be effective for fermions.
In light of this, we propose several avenues of future
investigation to overcome this limitation, leaving open the
possibility of feedback control of atomic Fermi gases as a
pathway to analogue quantum simulation.
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