This dissertation discusses the experimental study of strong fermionic interactions in an optical lattice. Ultracold samples of
40K are prepared in an intricate experimental platform using the combination of various optical and evaporative cooling techniques. The atoms are adiabatically loaded into an optical lattice to realize isolated pair states. Various tools for the coherent manipulation of spin and orbital degrees of freedom of the atoms in the lattice are developed. The inter-particle interactions between pairs are tuned using magnetic Feshbach resonances. Spectroscopic measurements of resonantly enhanced and controllable s-wave and p-wave interaction energies are reported. The measurements extend to the unitary limit of interactions characterized by diverging scattering lengths and universal observables. These measurements show excellent agreements to an exact solution for two harmonically confined atoms interacting via a pseudopotential and numerical solutions using an \textit{ab initio} interaction potential. For p-wave interactions, exquisite experimental control is demonstrated by measuring Rabi oscillations between non-interacting and strongly interacting atomic pairs, which are used to accurately measure highly sensitive properties such as the two-body wavefunction overlap. With the full suppression of three-body loss processes, the lifetime of p-wave interacting pairs is investigated. The experiments demonstrate that losses of p-wave interacting pairs are limited by the intrinsic lifetime of the free-space molecular dimer, resulting in the observation of lifetimes that are fifty times larger than previous measurements in
40K. The observation, control, and comprehensive understanding of strong fermionic interactions demonstrated in this thesis illuminate a path towards the assembly of new many-body states of matter.
We investigate the e↵ect of a spherical cuto↵ in the single particle momentum on the lattice calculations of unitary fermions, and use this to explore the ground state configuration. The unitarity limit, corresponding to an infinite s-wave scattering length and zero interaction range, is achieved by tuning the lattice coupling of four-fermi interactions to reproduce the scattering phase shift of σ = π/2 in the continuum. We particularly compute the ground state energies of three unitary fermions at zero and non-zero net momenta. We show that in the continuum limit the spherical cuto↵ does not a↵ect the results, while it violates the unitarity for a boosted pair of fermions. Our findings suggest that the pair of fermions in the ground state of three unitary fermions has zero momentum, while the total net momentum of the system is carried by the unpaired fermion.
We investigate the e↵ect of a spherical cuto↵ in the single particle momentum on the lattice calculations of unitary fermions, and use this to explore the ground state configuration. The unitarity limit, corresponding to an infinite s -wave scattering length and zero interaction range, is achieved by tuning the lattice coupling of four-fermi interactions to reproduce the scattering phase shift of σ = π/2 in the continuum. We particularly compute the ground state energies of three unitary fermions at zero and non-zero net momenta. We show that in the continuum limit the spherical cuto↵ does not a↵ect the results, while it violates the unitarity for a boosted pair of fermions. Our findings suggest that the pair of fermions in the ground state of three unitary fermions has zero momentum, while the total net momentum of the system is carried by the unpaired fermion.