Seminario
"Analytical Phase Diagram for the Current-Carrying States of the Quantum Phase Model"

## Aula Feynman 30 Ottobre 2012 ore 16.30

 Abstract A gas of (bosonic) alkhali atoms can be spatially confined, cooled down to virtually zero temperature and trapped in a "crystal of light" periodic potential. Under suitable conditions a tight-binding approximation applies, and the system can "simulate" the bosonic Hubbard model with a high degree of ideality and control over the parameters. Besides the superfluid-insulator transition taking place in the ground-state at a critical value of the effective interaction, a transition to a "dynamical insulator" has been observed for the current-carrying excited states of the model. The interaction-dependent critical momentum $p_{\rm c}$ for such transition interpolates between the value for the modulational instability in the semiclassical dynamics of the model, $p_c=\pi/2$ in the noninteracting limit, and $p_c=0$ at the critical interaction for the ground-state. We analyze the properties of the current-carrying states in the Quantum Phase Model, which is equivalent to the Bose-Hubbard model for strong interactions and large average occupation numbers. A variational approach based on a simple Gutzwiller trial state allows us to derive the critical lines in the phase diagram of the system analytically. raffaella.burioni@fis.unipr.it