Tuning phase coherence in optical lattices

The high degree of control in cold atoms has allowed to explore quantum phase transitions with unprecedented freedom and many states of matter breaking U(1) symmetry and establishing phase coherence have been realised. In this talk I will first discuss the realisation of an extended Hubbard model with density-dependent hopping terms by employing time-dependent driving forces and I will show that this model supports unconventional superconductivity (eta-superconductivity) in one-dimension. Local Cooper pairs with finite lattice momentum Pi are responsible of the off-diagonal long-range order and exist because of a charge SU(2) symmetry of the Hamiltonian. Moreover, spin and charge degrees of freedom show incommensurate quasi long-range order. In the second part of the talk I will discuss the loss of phase coherence in a bipartite Bose-Hubbard model. The experimental data show that a moderate distortion of the unit cell obtained by detuning neighbour wells in the optical potential are able to fully destroy coherence and superfluidity.
We perform mean-field calculations using a variational ansatz for the many-body wave function (Gutzwiller) to quantitatively understand the mechanism behind this phenomenon. We also study the asymptotic regime at large detuning using a perturbative approach and compare our findings with the experimental data.