Response of the Higgs amplitude mode of superfluid Bose gases in a three-dimensional optical lattice: effects of fluctuations and a trapping potential

The Higgs amplitude mode is a universal quasiparticle excitation on thermodynamic phases with spontaneous breaking of a continuous symmetry and with a particle-hole symmetry. In this work, we address a question of whether the Higgs mode can exist as a resonance peak or not, in particular, in three-dimensional (3D) optical-lattice systems. Specifically, we calculate the response functions of the 3D Bose-Hubbard model to the hopping strength and onsite-interaction strength modulations by means of the mapping to the effective pseudospin-one model near the insulator transition, finite-temperature Green’s function theory, and local density approximation. We show that a sharp resonance peak at the gap in the response functions survives in the presence of quantum and thermal fluctuations, and a parabolic potential [1].
[1] K. Nagao et al., arXiv:1710.00547