Cold bosons in optical lattices: a tutorial for exact diagonalization

Bosons in Rotating Optical Lattices

Date The final copy of this thesis has been examined by the signatories, and we find that both the content and the form meet acceptable presentation standards of scholarly work in the above mentioned discipline. The fractional Quantum Hall effect (FQHE) has been predicted in a cloud of bosons rotating at a frequency equal to that of the confining harmonic potential. Achieving this regime experi...

Studies of bosons in optical lattices in a harmonic potential

We present a theoretical study of bose condensation and specific heat of non-interacting bosons in finite lattices in harmonic potentials in one, two, and three dimensions. We numerically diagonalize the Hamiltonian to obtain the energy levels of the systems. Using the energy levels thus obtained, we investigate the temperature dependence, dimensionality effects, lattice size dependence, and ev...

Searching for a supersolid in cold-atom optical lattices

Cold atoms in double-well optical lattices

Cold atoms, loaded into an optical lattice with double-well sites, are considered. Pseudospin representation for an effective Hamiltonian is derived. The system in equilibrium displays two phases, ordered and disordered. The second-order phase transition between the phases can be driven either by temperature or by changing the system parameters. Collective pseudospin excitations have a gap disa...

Ultra-cold fermions in optical lattices

We summarize recent theoretical results for the signatures of strongly correlated ultra-cold fermions in optical lattices. In particular, we focus on collective mode calculations, where a sharp decrease in collective mode frequency is predicted at the onset of the Mott metal–insulator transition; and correlation functions at finite temperature, where we employ a new exact technique that applies...