The Amplitude Mode in the Quantum Phase Model

TL;DR

This paper derives and analyzes collective excitations in the quantum phase model of lattice bosons, revealing a previously overlooked gapped mode relevant to ultracold atom experiments.

Contribution

It introduces a dynamical variational approach to identify a new gapped Higgs-like mode in the quantum phase model.

Findings

Recovery of the Goldstone mode as expected.

Identification of a gapped Higgs mode.

Predictions for experimental detection in lattice modulation experiments.

Abstract

We derive the collective low energy excitations of the quantum phase model of interacting lattice bosons within the superfluid state using a dynamical variational approach. We recover the well known sound (or Goldstone) mode and derive a gapped (Higgs type) mode that was overlooked in previous studies of the quantum phase model. This mode is relevant to ultracold atoms in a strong optical lattice potential. We predict the signature of the gapped mode in lattice modulation experiments and show how it evolves with increasing interaction strength.