We demonstrate that the transition from a superfluid to a Mott insulator in the Bose-Hubbard model can be induced by an oscillating force through an effective renormalization of the tunneling matrix element. The mechanism involves adiabatic following of Floquet states, and can be tested experimentally with Bose-Einstein condensates in periodically driven optical lattices. Its extension from small to very large systems yields nontrivial information on the condensate dynamics.

We investigate the scattering of a quantum matter wave soliton on a barrier in a one dimensional geometry and we show that it can lead to mesoscopic Schrödinger cat states, where the atomic gas is in a coherent superposition of being in the half-space to the left of the barrier and being in the half-space to the right of the barrier. We propose an interferometric method to reveal the coherent nature of this superposition and we discuss in details the experimental feasibility.PACS numbers: 03.75. Gg, 03.75.Lm, It is now possible to control the strength of the atomic interaction in a gas, with Feshbach resonances. This has allowed the observation of single matter wave bright solitons with thousands of atoms [1] or a train of solitons [2] with 7 Li atoms trapped in a one-dimensional (1D) geometry. These solitons are quantum bound states of a mesoscopic gas, which opens up fascinating possibilities: Apart from testing mean field predictions in these systems [3], one can address truly quantum problems, issuing from the quantum nature of the gas center of mass.In particular, it was recently proposed to use a BoseEinstein condensate in interferometric experiments to test the existence of decoherence mechanisms not predicted by usual quantum mechanics and that would show up for very massive particles [4]. Experiments have succeeded in observing interferences with molecules as big as fullerenes and there is a need for more massive interferometric objects [5]. A soliton with a small number of 100 7 Li atoms has the same mass as C 60 , with appealing new features: It does not have internal bound states other than its ground state, it can be reversibly dissociated in an unbound atomic gas via a Feshbach resonance, and it allows the exploration of a new regime, in which the center of mass kinetic energy of the interfering object is of the same order as the binding energy of its constituents.Furthermore, thanks to the extremely low temperatures accessible in atomic gases, down to 0.45nK [6], and the weak decoherence present in these systems [7], one may hope to split the center of mass wavefunction of the solitonic gas in two wavepackets that would keep their mutual coherence over mesoscopic distances, say a fraction of a millimeter, much larger than the size of the soliton. The gas would then have simultaneously non-zero probability amplitudes of being in two different spatial locations, thus forming a mesoscopic Schrödinger cat in real space. One may then ascertain the presence of a cat state by recombining and interfering these two mesoscopically different quantum states of the gas. This would constitute a generalization to many atoms of the oneion experiment of [8]. While mesoscopic Schrödinger cat states have been reported for radiation fields [9] they have not been reported yet with ultracold atoms, and atom optics with a quantum soliton is a promising alternative to existing ideas for cat production in these systems [10].The dynamics of the center of mass wavepacket during the scattering of the soliton on a barrier ra...