Collective modes of ultracold fermionic alkaline-earth gases with SU(N) symmetry

Abstract

We calculate the collective modes of ultracold trapped alkaline-earth fermionic atoms, which possess an SU($N$) symmetry of the nuclear spin degree of freedom, and a controllable $N$, with $N$ as large as $10$. We calculate the breathing and quadrupole modes of two-dimensional and three-dimensional harmonically trapped gases in the normal phase. We particularly concentrate on two-dimensional gases, where the shift is more accessible experimentally, and the physics has special features. We present results as a function of temperature, interaction strength, density, and $N$. We include calculations across the collisionless to hydrodynamic crossover. We assume the gas is interacting weakly, such that it can be described by a Boltzmann-Vlasov equation that includes both mean-field terms and the collision integral. We solve this with an approximate scaling ansatz, taking care in two-dimensions to preserve the scaling symmetry of the system. We predict the collective mode frequency shifts and damping, showing that these are measurable in experimentally relevant regimes. We expect these results to furnish powerful tools to characterize interactions and the state of alkaline-earth gases, as well as to lay the foundation for future work, for example on strongly interacting gases and SU($N$) spin modes.

11 pages, 4 figures (including appendices)

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• Many-body Physics of Ultracold Alkaline-Earth atoms with SU($N$)-symmetric interactions
• Engineering infinite-range SU($n$) interactions with spin-orbit-coupled fermions in an optical lattice
• Effects of quantum fluctuations on the low-energy collective modes of two-dimensional superfluid Fermi gases from the BCS to the Bose Limit
• State selective cooling of $\mathrm{SU}(N)$ Fermi-gases
• Accelerating analysis of Boltzmann equations using Gaussian mixture models: Application to quantum Bose-Fermi mixtures
• Systematic large flavor fTWA approach to interaction quenches in the Hubbard model
• Degenerate Rabi spectroscopy of the Floquet engineered optical lattice clock