Phase Transition Of Two-Component Ultra-Cold Atoms In Optical Lattices

The study of phase transitions of ultra-cold atoms in optical lattices has made great progress both theoretically and experimentally in the last decades. Two-species bosons in optical lattices described by the two-component Bose-Hubbard model may exhibit rich behaviour,opening the door to controlled studies of quantum magnetism.On the other hand,the interactions between atoms can be tuned by Feshbach resonance which enables the study of multiband occupied systems.Firstly,we investigate the ground-state properties of an equal mixture of two species of bosons in its Mott-insulator phase at a filling factor of two per site.One novel of spin triplet-singlet transition is identified through the competition of the ground state.For a weak on-site interaction the two particles prefer to stay in the lowest band and with weak tunneling between neighboring sites the system is mapped into an effective spin-1 ferromagnetic exchange Hamiltonian.When the interaction is tuned by a Feshbach resonance to be large enough,the higher band will be populated.Due to the orbital coupling term S~+S~- in the Hamiltonian,the two atoms in different orbits on a site would form an on-site singlet.For a non-SU(2) symmetric model,easy-axis or easy-plane ferromagnetic spin exchange models may be realized,corresponding to phase separation or counterflow superfluidity, respectively.Secondly,we develop a general scheme for detecting spin correlations inside a two-component lattice gas of bosonic atoms,stimulated by the recent theoretical and experimental advances on analogous systems for a single component quantum gas.Within a linearized theory for the transmission spectra of the cavity mode field,different magnetic phases of a two-component(spin 1/2) lattice bosons become clearly distinguishable.In the Mott-insulating(MI) state with unit filling for the two-component lattice bosons,three different phases:antiferromagnetic,ferromagnetic,and the XY phases are found to be associated with drastically different cavity photon numbers.Our suggested study can be straightforwardly implemented with current cold atom experiments.