Response of the Higgs amplitude mode of superfluid Bose gases in a three dimensional optical lattice

TL;DR

This paper investigates the Higgs amplitude mode in superfluid Bose gases within a 3D optical lattice, analyzing its response to modulations and effects of trapping potentials, proposing detection methods for experimental observation.

Contribution

The study introduces a perturbative approach using an effective pseudospin model to analyze Higgs mode responses, including quantum and thermal fluctuations, in a trapped 3D lattice.

Findings

Higgs mode appears as a sharp resonance at zero trapping potential.

Global trapping potential broadens the resonance peak.

Partial modulation can reveal a sharp Higgs resonance.

Abstract

We study the Higgs mode of superfluid Bose gases in a three dimensional optical lattice, which emerges near the quantum phase transition to the Mott insulator at commensurate fillings. Specifically, we consider responses of the Higgs mode to temporal modulations of the onsite interaction and the hopping energy. In order to calculate the response functions including the effects of quantum and thermal fluctuations, we map the Bose-Hubbard model onto an effective pseudospin-one model and use a perturbative expansion based on the imaginary-time Green's function theory. We also include the effects of an inhomogeneous trapping potential by means of a local density approximation. We find that the response function for the hopping modulation is equal to that for the interaction modulation within our approximation. At the unit filling rate and in the absence of a trapping potential, we show that the Higgs mode can exist as a sharp resonance peak in the dynamical susceptibilities at typical temperatures. However, the resonance peak is significantly broadened due to the trapping potential when the modulations are applied globally to the entire system. We suggest that the Higgs mode can be detected as a sharp resonance peak by partial modulations around the trap center.