Clock Shift in a Strongly Interacting Two-Dimensional Fermi Gas

Abstract

We derive universal relations for the rf spectroscopy of a two-dimensional Fermi gas consisting of two spin states interacting through an $S$-wave scattering length. The rf transition rate has a high-frequency tail that is proportional to the contact and displays logarithmic scaling violations, decreasing asymptotically like $1/({\ensuremath{\omega}}^{2}{ln}^{2}\ensuremath{\omega})$. Its coefficient is proportional to ${ln}^{2}({a}_{2\mathrm{D}}^{\ensuremath{'}}/{a}_{2\mathrm{D}})$, where ${a}_{2\mathrm{D}}$ and ${a}_{2\mathrm{D}}^{\ensuremath{'}}$ are the two-dimensional scattering lengths associated with initial-state and final-state interactions. The clock shift is proportional to the contact and to $\mathrm{ln}({a}_{2\mathrm{D}}^{\ensuremath{'}}/{a}_{2\mathrm{D}})$. If $|\mathrm{ln}({a}_{2\mathrm{D}}^{\ensuremath{'}}/{a}_{2\mathrm{D}})|\ensuremath{\gg}1$, the clock shift arises as a cancellation between much larger contributions proportional to ${ln}^{2}({a}_{2\mathrm{D}}^{\ensuremath{'}}/{a}_{2\mathrm{D}})$ from bound-bound and bound-free rf transitions.