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We consider the angular momentum of a harmonically trapped, noninteractingFermi gas subject to either rotation or to an artificial gauge field. Theangular momentum of the gas is shown to display oscillations as a function ofthe particle number or chemical potential. This phenomenon is analogous to thede Haas - van Alphen oscillations of the magnetization in the solid-statecontext. However, key differences exist between the solid-state and ultracoldatomic gases that we point out and analyze. We explore the dependence of thevisibility of these oscillations on the physical parameters and propose twoexperimental protocols for their observation. Due to the very strong dependenceof the amplitude of the oscillations on temperature, we propose their use as asensitive thermometer for Fermi gases in the low temperature regime.

Quantum oscillations in ultracold Fermi gases : realizations with rotating gases or artificial gauge fields