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/(ω2ln2ω). Its coefficient is proportional to ln2'(a'(2D)/a(2D)), where a(2D) and a'(2D) are the two-dimensional scattering lengths associated with initial-state and final-state interactions. The clock shift is proportional to the contact and to ln(a'(2D)/a(2D)). If |ln(a'(2D)/a(2D))| >> 1, the clock shift arises as a cancellation between much larger contributions proportional to ln2(a'(2D)/a(2D)) from bound-bound and bound-free rf transitions.