We describe an experimental protocol for introducing spin-dependent lattice structure in a cold atomic Fermi gas using lasers. It can be used to realize Hubbard models whose hopping parameters depend on spin and whose interaction strength can be controlled with an external magnetic field. We suggest that exotic superfluidities will arise in this framework. An especially interesting possibility is a class of states that support coexisting superfluid and normal components, even at zero temperature. The quantity of normal component varies with external parameters. We discuss some aspects of the quantum phase transition that arises at the point where it vanishes.
We describe an experimental protocol for introducing spin-dependent lattice structure in a cold atomic Fermi gas using lasers. It can be used to realize Hubbard models whose hopping parameters depend on spin and whose interaction strength can be controlled with an external magnetic field. We suggest that exotic superfluidities will arise in this framework. An especially interesting possibility is a class of states that support coexisting superfluid and normal components, even at zero temperature. The quantity of normal component varies with external parameters. We discuss some aspects of the quantum phase transition that arises at the point where it vanishes.
We propose a scheme to simulate the t–J–U model and investigate the quantum phase transitions using cold atoms confined in a two-dimensional optical lattice. By adjusting the parameters of external laser fields, we find a phase transition from antiferromagnetic phase to Gossamer superfluid. The Gossamer superfluid has a d-wave or mixed d- and s-wave symmetry, depending on the hopping parameters which can be adjusted by tuning the laser field. Experimental protocol to observe these new phenomena for future experiments has also been briefly discussed.
A major focus in condensed matter physics is to study the origin of exotic quantum phases such as coexistent and inhomogeneous phases, quantum criticality, and secondary ordered phases close to quantum critical points. Exotic phenomena in strongly correlated systems occur due to competing complex interactions of spin, charge, lattice, and orbital degrees of freedom. Complex quantum phases in strongly correlated systems are challenging, but they might be very useful due to their possible functionality to make advance devices. In order to understand, utilize, and optimize such behaviors, we need to improve our understanding of these systems. Studies in cold atom systems are of interest since cold atom experiments provide a control on model parameters. In this thesis, we use novel analytical and computational techniques to treat strongly interacting bosonic systems. Taking advantage of the very versatile quantum Monte Carlo Stochastic Green Function algorithm, we studied several interesting problems. First, we explore a recently developed new confining method for cold atoms on optical lattices. Atoms are confined via a hopping integral that decreases as a function of the distance from the center of the lattice. This method might lead to lower temperatures than existing diagonal confinement methods. Next, we study the ground state phase diagram of interacting bosons on a ring-shape lattice with a region of weak hopping integrals. The model, an extension of the well known Bose-Hubbard model, develops a novel local Mott phase in addition to the usual Mott and superfluid phases in the homogeneous system. This might provide a new insight to the description of atomtronics applications. Finally, we study the two species Bose Hubbard model in a two-dimensional lattice. This model presents novel phases due to the complexity associated with multiple species. Its phase diagram shows ordered and coexistence phases including a ferromagnetic phase separated phase with high entropy. This phase might be accessible experimentally. The novel phases found from our studies are linked to experiments on ultra-cold atoms trapped by laser beams.
For systems of interacting, ultracold spin-zero neutral bosonic atoms, harmonically trapped and subject to an optical lattice potential, we derive an Extended Bose Hubbard (EBH) model by developing a systematic expansion for the Hamiltonian of the system in powers of the lattice parameters and of a scale parameter, the lattice attenuation factor. We identify the dominant terms that need to be retained in realistic experimental conditions, up to nearest-neighbor interactions and nearest-neighbor hoppings conditioned by the on-site occupation numbers. In the mean field approximation, we determine the free energy of the system and study the phase diagram both at zero and at finite temperature. At variance with the standard on site Bose Hubbard model, the zero-temperature phase diagram of the EBH model possesses a dual structure in the Mott insulating regime. Namely, for specific ranges of the lattice parameters, a density wave phase characterizes the system at integer fillings, with domains of alternating mean occupation numbers that are the atomic counterparts of the domains of staggered magnetizations in an antiferromagnetic phase. We show as well that in the EBH model, a zero-temperature quantum phase transition to pair superfluidity is, in principle, possible, but completely suppressed at the lowest order in the lattice attenuation factor. Finally, we determine the possible occurrence of the different phases as a function of the experimentally controllable lattice parameters.
Since the experimental realization of Bose-Einstein condensation in 1995, the field of ultracold atoms has expanded rapidly, and has become an important arena for exploring diverse quantum many-body physics, as highlighted by the experimental observation of quantum phase transitions in the system of bosons in a periodic potential, which is described by the Bose-Hubbard model.Recently, ultracold atoms with spin degrees of freedom are actively studied because the coupling between the internal spin degrees of freedom and the spatial degrees of freedom can give rise to novel and interesting physics.A minimal model for studying such physics is the spin-1 Bose-Hubbard model, which describes spin-1 bosons in a periodic potential.The model has a spin-dependent interaction, which can be ferromagnetic or antiferromagnetic, and it is known that although the ferromagnetic model resembles the spinless counterpart, the antiferromagnetic model exhibits totally different features, which make the model much more intensively studied compared with the ferromagnetic one.However, the presence of an external magnetic field can change the situation, because the positive quadratic Zeeman energy competes with the ferromagnetic interaction, which can give rise to rich phases.In this thesis, we explore the ground-state and nonzero-temperature phase diagrams of the spin-1 Bose-Hubbard model under an external magnetic field.To analyze the model, we use an approximation method called the decoupling approximation, or equivalently, the Gutzwiller variational ansatz.It is shown that, in addition to the Mott insulator phase, the model possesses two superfluid phases.Moreover, for large values of a spin-dependent interaction, the phase transitions between the two superfluid phases can be discontinuous.Such discontinuous phase transitions are shown to survive at nonzero but sufficiently low temperature.The discontinuous phase transitions are in clear contrast to the mean-field theory of weakly interacting spin-1 bosons without a lattice, which predicts that the corresponding phase transition is continuous, signifying the importance of the effect of strong interactions on the interplay between the spatial and spinor degrees of freedom. 4.1.2The grand Hamiltonian . . . . . . . . .
We study a two-leg fermionic Hubbard ladder model with a state-dependent hopping. We find that, contrary to the case without a state-dependent hopping, for which the system has a superfluid nature regardless of the sign of the interaction at incommensurate filling, in the presence of such a hopping a spin-triplet superfluid, spin-density wave, and charge-density wave phases emerge. We examine our results in the light of recent experiments on periodically driven optical lattices in cold atoms. We give protocols allowing us to realize the spin-triplet superfluid elusive in the cold atoms.
The dynamics of an ultracold dilute gas of bosonic atoms in an optical lattice can be described by a Bose-Hubbard model where the system parameters are controlled by laser light. We study the continuous (zero temperature) quantum phase transition from the superfluid to the Mott insulator phase induced by varying the depth of the optical potential, where the Mott insulator phase corresponds to a commensurate filling of the lattice (``optical crystal''). Examples for formation of Mott structures in optical lattices with a superimposed harmonic trap and in optical superlattices are presented.