Many-body physics in the radio frequency spectrum of lattice bosons

TL;DR

This paper calculates the radio-frequency spectrum of cold bosonic atoms in an optical lattice, revealing features that indicate superfluidity and correlations, using an approach valid in certain limits and including interactions.

Contribution

It introduces a method to compute RF spectra of lattice bosons that accounts for interactions, obeys conservation laws, and applies to various lattice configurations.

Findings

Spectra reveal superfluid and correlation signatures.

Method is exact in deep Mott and superfluid limits.

Includes effects of final state interactions and spin-dependent lattices.

Abstract

We calculate the radio-frequency spectrum of a trapped cloud of cold bosonic atoms in an optical lattice. Using random phase and local density approximations we produce both trap averaged and spatially resolved spectra, identifying simple features in the spectra that reveal information about both superfluidity and correlations. Our approach is exact in the deep Mott limit and in the deep superfluid when the hopping rates for the two internal spin states are equal. It contains final state interactions, obeys the Ward identities (and the associated conservation laws), and satisfies the $f$-sum rule. Motivated by earlier work by Sun, Lannert, and Vishveshwara [Phys. Rev. A \textbf{79}, 043422 (2009)], we also discuss the features which arise in a spin-dependent optical lattice.