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 Stoferle 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 Omega. 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.