Response of the Higgs Mode in a Three Dimensional Optical Lattice

Abstract

In this chapter, we investigate responses of the Higgs mode in strongly-correlated Bose gases in a three-dimensional optical lattice. Our goal is to examine the detectability of the long-lived Higgs modes in real experiments of ultracold gases. In Sect. 4.1, we discuss time-dependent external perturbations to excite the Higgs mode in the optical lattice and formulate response functions within the linear-response theory. In Sect. 4.2, we generalize the effective model presented in Chap. 2 for the high-filling limit into low-filling cases, and derive interaction vertices among collective modes by identifying higher-order contributions of the Holstein–Primakoff expansion. In Sect. 4.3, we calculate the response functions using Feynman’s diagrammatic perturbation theory for a finite-temperature Green’s function. In Sect. 4.4, we numerically evaluate the analytical expressions obtained from the perturbative expansion and show that these exhibit a characteristic signal associated with the Higgs mode. In addition, we deal with a harmonic trap effect on the response functions within a local density approximation and discuss the detectability of the Higgs mode in typical experiments.