Clock shift in a strongly interacting two-dimensional Fermi gas

Abstract

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

4 pages, 1 figure