Quantum phase transition in vortex lattices and mobile impurity in mixed-dimension mixtures - Chaviguri, Jhonny Richard Huamani (2021)
The most recent advances in the ultracold atoms experimental techniques allowed the production of the ultracold gases mixtures in the laboratory. Motivated by these developments, in this project we study systems involving two ultracold atoms mixtures. In the first part, we consider a Bose-Einstein condensate (BEC) with a vortex lattice weakly interacting with another utracold dilute bosonic gas. We apply the Bose-Hubbard (BH) model to describe the atoms of the minority species trapped in the vortex lattice. As occurs in a static optical lattice, we predict the quantum phase transition between the Mott insulator to superfluid phases, which now can be controlled by changing the intra and inter-species scattering length. Considering the intrinsic lattice dynamics, the Tkachenko modes of the vortex lattice, we derive an extended BH Hamiltonian and analyzed new properties in the phase diagram that arise from a long-range attractive potential and density-dependent hopping. In the second part, we study the properties of a mobile impurity living in two dimensions and interacting with a 2D and 3D BEC cloud. The resulting impurity-bath interaction leads to the formation of a polaron (particle dressed by the phonon excitations of the BEC), which is characterized by its spectral function. We determine the energy dispersion, spectral weight, effective mass and lifetime of the polaron. These analysis allowed us to identify a dissipative regime for higher impurity velocities, with an increasing scattering rate of phonons. In addition, we observe a self-localization regime for lower impurity velocities which may be a signature for molecular formation. In spite of qualitatively similar results obtained for the 2D and 3D bath, we had differences related to the self-localization and dissipation limits, that allowed us to conclude that a 2D BEC bath would be a better candidate to observe stable quasi-particle properties.