Abstract
A system of ultracold atoms in an optical lattice has been regarded as an ideal quantum simulator for a Hubbard model with extremely high controllability of the system parameters. While making use of the controllability, a comprehensive measurement across the weakly to strongly interacting regimes in the Hubbard model to discuss the quantum many-body state is still limited. Here we observe a great change in the excitation energy spectra across the two regimes in an atomic Bose–Hubbard system by using a spectroscopic technique, which can resolve the site occupancy in the lattice. By quantitatively comparing the observed spectra and numerical simulations based on sum rule relations and a binary fluid treatment under a finite temperature Gutzwiller approximation, we show that the spectra reflect the coexistence of a delocalized superfluid state and a localized insulating state across the two regimes.
Highlights
A system of ultracold atoms in an optical lattice has been regarded as an ideal quantum simulator for a Hubbard model with extremely high controllability of the system parameters
Ultracold atoms confined in an optical lattice potential offer a novel way to study quantum many-body physics[1,2]
To understand the excitation spectrum quantitatively, we develop a numerical method for calculating the spectrum, which is based on a finite temperature Gutzwiller approximation and formally derived sum rule relations[22]
Summary
A system of ultracold atoms in an optical lattice has been regarded as an ideal quantum simulator for a Hubbard model with extremely high controllability of the system parameters. We can tune the difference of the on-site interactions |dU0| 1⁄4 |Uge,[0] À Ugg| sufficiently large compared with the other energy scales in the Hubbard Hamiltonian[27], such as Ugg, the hopping term Jg and the site-dependent inhomogeneous trapping potential Vg(e),i (Fig. 1b).
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