Excitation spectra of strongly interacting bosons in the flat-band Lieb lattice

TL;DR

This paper investigates the excitation spectra of strongly interacting bosons in a Lieb lattice using the Bose-Hubbard model and Gutzwiller mean-field approach, revealing unique features of the Mott insulator and superfluid phases.

Contribution

It provides new insights into the excitation modes and oscillation behaviors of bosons in the Lieb lattice, including a method to distinguish superfluid regions via in-situ measurements.

Findings

Mott insulator phase exhibits gapped, particle or hole character excitations.

Superfluid phase shows gapless excitation spectrum.

Additional anti-crossings in dispersive bands due to lattice geometry.

Abstract

The strongly correlated bosons in flat band systems are an excellent platform to study a wide range of quantum phenomena. Such systems can be realized in optical lattices filled with ultracold atomic gases. In this paper we study the Bose-Hubbard model in the Lieb lattice by means of the time-dependent Gutzwiller mean-field approach. We find that in the Mott insulator phase the excitation modes are gapped and display purely particle or purely hole character, while in the superfluid phase the excitation spectrum is gapless. The geometry of the Lieb lattice leads to a non-uniform order parameter and non-uniform oscillation energy in the ground state. This results in additional anti-crossings between dispersive bands in the excitation spectra, while the flat bands remain insensitive to this effect. We analyze the oscillations of the order parameter on the sublattices as well as the particle-hole character of the excitations. For certain model parameters we find simultaneous pure phase and pure amplitude oscillations within the same mode, separated between the sublattices. Also, we propose a simple method to differentiate between the hole- and particle superfluid regions in the Lieb lattice by in-situ measurement of the atom population on the sublattices.