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We conduct a theoretical study of SU(N ) fermions confined by a one-dimensional harmonic potential. Firstly, we introduce a numerical approach for solving the trapped interacting few-body problem, by which one may obtain accurate energy spectra across the full range of interaction strengths. In the strong-coupling limit, we map the SU(N ) Hamiltonian to a spin-chain model. We then show that an existing, extremely accurate ansatz − derived for a Heisenberg SU(2) spin chain − is extendable to these N -component systems. Lastly, we consider balanced SU(N ) Fermi gases that have an equal number of particles in each spin state for N = 2, 3, 4. In the weak-and strong-coupling regimes, we find that the ground-state energies rapidly converge to their expected values in the thermodynamic limit with increasing atom number. This suggests that the many-body energetics of N -component fermions may be accurately inferred from the corresponding few-body systems of N distinguishable particles. arXiv:1707.07781v2 [cond-mat.quant-gas] 1 May 2018

The orbital Feshbach resonance (OFR) is a novel scheme for magnetically tuning the interactions in closed-shell fermionic atoms. Remarkably, unlike the Feshbach resonances in alkali atoms, the open and closed channels of the OFR are only very weakly detuned in energy. This leads to a unique effect whereby a medium in the closed channel can Pauli block -or frustrate -the twobody scattering processes. Here, we theoretically investigate the impact of frustration in the fewand many-body limits of the experimentally accessible three-dimensional 173 Yb system. We find that by adding a closed-channel atom to the two-body problem, the binding energy of the ground state is significantly suppressed, and by introducing a closed-channel Fermi sea to the many-body problem, we can drive the system towards weaker fermion pairing. These results are potentially relevant to superconductivity in solid-state multiband materials, as well as to the current and continuing exploration of unconventional Fermi-gas superfluids near the OFR. arXiv:1908.04495v1 [cond-mat.quant-gas]

We consider the problem of three distinguishable fermions confined to a quasi-two-dimensional (quasi-2D) geometry, where there is a strong harmonic potential in one direction. We go beyond previous theoretical work and investigate the three-body bound states (trimers) for the case where the two-body short-range interactions between fermions are unequal. Using the scattering parameters from experiments on ultracold 6 Li atoms, we calculate the trimer spectrum throughout the crossover from two to three dimensions. We find that the deepest Efimov trimer in the 6 Li system is unaffected by realistic quasi-2D confinements, while the first excited trimer smoothly evolves from a three-dimensional-like Efimov trimer to an extended 2D-like trimer as the attractive interactions are decreased. We furthermore compute the excited trimer wave function and quantify the stability of the trimer against decay into a dimer and an atom by determining the probability that three fermions approach each other at short distances. Our results indicate that the lifetime of the trimer can be enhanced by at least an order of magnitude in the quasi-2D geometry, thus opening the door to realizing long-lived trimers in three-component Fermi gases.arXiv:1803.02529v2 [cond-mat.quant-gas] 1 May 2018