Feedback control of atomic Fermi gases

Abstract

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 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.