RF Spectra: Multiple Peaked Spectrum in a Homogeneous System

Abstract

This chapter will discuss RF spectroscopy of lattice bosons from a point of view complementary to that of Chap. 4. That chapter looked at things from the vantage of sum rules assuming a single, narrow spectral line, one common approach in the literature. This chapter is more closely related to another common approach in the literature: taking the RF spectra to be (convolutions of) the single particle spectral functions, perhaps with shifts of lines due to final state interactions. This naturally leads to a two-peaked structure in the superfluid: there are gapless Goldstone modes (superfluid phonons) and gapped order parameter amplitude modes (Higgs modes). After constructing an approximation sufficient to capture the global physics, we will reconcile the two points of view. In addition to giving a global calculation for the spectrum of bosons in an optical lattice, the reconciliation provides a new general lesson for interpreting RF spectra of many-body systems, showing how standard viewpoints emerge in special limits of the proper calculation.

This chapter was adapted from “Many-body physics in the radio-frequency spectrum of lattice bosons” by Kaden. R. A. Hazzard and Erich. J. Mueller, published in Physical Review A 81, 033404 (2010).