Second-order response theory of radio-frequency spectroscopy for cold atoms

TL;DR

This paper develops a second-order response theory to describe rf spectroscopy in cold fermionic gases, accounting for energy resolution and inhomogeneities, and explores how final-state interactions influence spectral line shapes.

Contribution

It introduces a theoretical framework based on second-order response theory for rf spectroscopy, incorporating effects of pulse envelope, inhomogeneities, and final-state interactions.

Findings

Inhomogeneities' effects can be reduced by final-state interactions.

Finite lifetime effects are significant at low temperature and density.

The formalism helps interpret rf spectra in cold atom experiments.

Abstract

We present a theoretical description of the radio-frequency (rf) spectroscopy of fermionic atomic gases, based on the second-order response theory at finite temperature. This approach takes into account the energy resolution due to the envelope of the rf pulse. For a noninteracting final state, the momentum- and energy-resolved rf intensity depends on the fermion spectral function and pulse envelope. The contributions due to interactions in the final state can be classified by means of diagrams. Using this formalism, as well as the local density approximation in two and three dimensions, we study the interplay of inhomogeneities and Hartree energy in forming the line shape of the rf signal. We show that the effects of inhomogeneities can be minimized by taking advantage of interactions in the final state, and we discuss the most relevant final-state effects at low temperature and density, in particular the effect of a finite lifetime.