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HUAMANI CHAVIGURI, J. R. Quantum phase transition of 2D system in a vortex lattice. 2016. 101 p. Dissertação (Mestrado em Ciências) Instituto de Física de São Carlos, Universidade de São Paulo, São Carlos, 2016. In this work we consider a two dimensional system composed of two condensed atomic species, one containing a vortex lattice. Analogously to the model used to describe ultracold atoms in optical lattices, we mapped our system Hamiltonian in the Hamiltonian of the Bose-Hubbard (BH) model, with the periodic lattice potential arising from the meanfield interaction between the two species. The variation of the atomic scattering length allow us to change the properties of the confining potential, to induce the quantum phase transition in the species trapped in the vortices. The new aspect brought by the vortex lattice comes with its low energy normal modes, the Tkachenko modes. We considered the effects of such dynamic potential over the confined species thought an effective BH model, with new values for the local interaction and tunneling parameters, besides an additional long-range interaction term mediated by the lattice modes. Our theoretical proposal goes beyond the studies with static optical lattice. Additionally, it has great feasibility in the current context of ultra-cold atoms experimental techniques.

Transição de fase quântica de sistema 2D em rede de vórtices