Signatures of the superfluid to Mott-insulator transition in the excitation spectrum of ultracold atoms

We present a detailed analysis of the dynamical response of ultracold bosonic atoms in a one-dimensional optical lattice subjected to a periodic modulation of the lattice depth. Following the experimental realization by Stöferle et al (2004 Phys. Rev. Lett. 92 130403), we study the excitation spectrum of the system as revealed by the response of the total energy as a function of the modulation frequency Ω. By using the Time Evolving Block Decimation algorithm, we are able to simulate one-dimensional systems comparable in size to those in the experiment, with harmonic trapping and across many lattice depths ranging from the Mott-insulator (MI) to the superfluid (SF) regime. Our results produce many of the features seen in the experiment, namely a broad response in the SF regime, and narrow discrete resonances in the MI regime. We identify several signatures of the SF-MI transition that are manifested in the spectrum as it evolves from one limit to the other