Clock shift in a strongly interacting two-dimensional Fermi gas

TL;DR

This paper derives universal relations for rf spectroscopy in a 2D Fermi gas, revealing how the clock shift and high-frequency tail depend on the contact and scattering lengths, with implications for understanding strongly interacting quantum gases.

Contribution

It introduces universal relations for rf spectroscopy in 2D Fermi gases, including the dependence of the clock shift and tail behavior on scattering lengths and contact.

Findings

High-frequency tail decreases as $1/(^2 ^2 ^2)$ with logarithmic scaling violations.

Clock shift is proportional to the contact and logarithm of scattering length ratio.

Cancellation effects occur when the logarithm of the scattering length ratio is large.

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 $\ln^2(a_{2D}'/a_{2D})$, where $a_{2D}$ and $a_{2D}'$ are the 2-dimensional scattering lengths associated with initial-state and final-state interactions. The clock shift is proportional to the contact and to $\ln(a_{2D}'/a_{2D})$. If $|\ln(a_{2D}'/a_{2D})| \gg 1$, the clock shift arises as a cancellation between much larger contributions proportional to $\ln^2(a_{2D}'/a_{2D})$ from bound-bound and bound-free rf transitions.