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.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.

arXiv:1111.0999Physical Review LettersFeb 9, 201249 citations

Theory of RF Spectroscopy in Strongly Interacting Fermi Gases

Erich J. Mueller

Bulletin of the American Physical SocietyMar 13, 20080 citations

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.