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We study cold atomic gases with a contact interaction and confined into one-dimension. Crossing the confinement induced resonance the correlation between the bosons increases, and introduces an effective range for the interaction potential. Using the mapping onto the sine-Gordon model and a Hubbard model in the strongly interacting regime allows us to derive the phase diagram in the presence of an optical lattice. We demonstrate the appearance of a phase transition from a Luttinger liquid with algebraic correlations into a crystalline phase with a particle on every second lattice site.
We investigate the dynamics of the rate function and of local observables after a quench in models which exhibit phase transitions between a superfluid and an insulator in their ground states. Zeros of the return probability, corresponding to singula
We show that ultracold two-component fermionic dipolar gases in an optical lattice with strong two-body on-site loss can be used to realize a tunable effective spin-one model. Fermion number conservation provides an unusual constraint that $sum_i (S^
One of the most striking features of the strong interactions between Rydberg atoms is the dipole blockade effect, which allows only a single excitation to the Rydberg state within the volume of the blockade sphere. Here we present a method that spati
We demonstrate clear collective atomic recoil motion in a dilute, momentum-squeezed, ultra-cold degenerate fermion gas by circumventing the effects of Pauli blocking. Although gain from bosonic stimulation is necessarily absent because the quantum ga
We study the exact solution for two atomic particles in an optical lattice interacting via a Feshbach resonance. The analysis includes the influence of all higher bands, as well as the proper renormalization of molecular energy in the closed channel.