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Already a few bosons with contact interparticle interactions in small optical lattices feature a variety of quantum phases: superfluid, Mott-insulator and fermionized Tonks gases can be probed in such systems. To detect these phases -- pivotal for both experiment and theory -- as well as their many-body properties we analyze several distinct measures for the one-body and many-body Shannon information entropies. We exemplify the connection of these entropies with spatial correlations in the many-body state by contrasting them to the Glauber normalized correlation functions. To obtain the ground-state for lattices with commensurate filling (i.e. an integer number of particles per site) for the full range of repulsive interparticle interactions we utilize the multiconfigurational time-dependent Hartree method for bosons (MCTDHB) in order to solve the many-boson Schrodinger equation. We demonstrate that all emergent phases -- the superfluid, the Mott insulator, and the fermionized gas can be characterized equivalently by our many-body entropy measures and by Glaubers normalized correlation functions. In contrast to our many-body entropy measures, single-particle entropy cannot capture these transitions.
We report on high-resolution optical spectroscopy of interacting bosonic $^{174}$Yb atoms in deep optical lattices with negligible tunneling. We prepare Mott insulator phases with singly- and doubly-occupied isolated sites and probe the atoms using a
A correlated many-body calculation is presented to characterize the Shannon information entropy of trapped interacting bosons. We reformulate the one-body Shannon information entropy in terms of the one-body probability density. The minimum limit of
We study the out-of-equilibrium dynamics of bosonic atoms in a 1D optical lattice, after the ground-state is excited by a single spontaneous emission event, i.e. after an absorption and re-emission of a lattice photon. This is an important fundamenta
Periodically-driven quantum systems are currently explored in view of realizing novel many-body phases of matter. This approach is particularly promising in gases of ultracold atoms, where sophisticated shaking protocols can be realized and inter-par
We study a model of interacting bosons that occupy the first excited p-band states of a two-dimensional optical lattice. In contrast to the much studied single band Bose-Hubbard Hamiltonian, this more complex model allows for non-trivial superfluid p