Radio-frequency spectroscopy and the dimensional crossover in interacting spin-polarized Fermi gases

Low-dimensional ultracold gases are created in the laboratory by confining three-dimensional (3D) gases inside highly anisotropic trapping potentials. Such trap geometries not only provide access to simulating 1D and 2D physics, but also can be used to study how the character of excitations cross over to three dimensions at higher energy. In this work we study the signature in radio-frequency (rf) spectroscopy for both the 1D-to-3D and the 2D-to-3D crossovers, in spin-polarized Fermi gases. We solve the two-body scattering $T$ matrix in the presence of strong harmonic confinement and use it to evaluate both the high-frequency rf transfer rate and the two-body bound-state energies. These general expressions are then compared both to the low-dimensional limit and to the 3D limit. We find that in order to understand the dimensional crossover for spin-polarized Fermi gases with $p$-wave interactions, one needs to take into account an emergent $s$-wave interaction.