Advances in pure optical trapping techniques now allow the creation of degenerate Bose gases with internal degrees of freedom. Systems such as $^{87}\mathrm{Rb},\phantom{\rule{0.16em}{0ex}}^{39}\mathrm{K}$, or $^{23}\mathrm{Na}$ in the $F=1$ hyperfine state offer an ideal platform for studying the interplay of superfluidity and quantum magnetism. Motivated by the experimental developments, we study ground-state phases of a two-component Bose gas loaded on an optical lattice. The system is described effectively by the Bose-Hubbard Hamiltonian with on-site and near-neighbor spin-spin interactions. An important feature of our investigation is the inclusion of interconversion (spin-flip) terms between the two species, which has been observed in optical lattice experiments. Using mean-field theory and quantum Monte Carlo simulations, we map out the phase diagram of the system. A rich variety of phases is identified, including antiferromagnetic (AF) Mott insulators and ferromagnetic and AF superfluids.
Advances in pure optical trapping techniques now allow the creation of degenerate Bose gases with internal degrees of freedom. Systems such as 87Rb,39K, or 23Na in the F=1 hyperfine state offer an ideal platform for studying the interplay of superfluidity and quantum magnetism. Motivated by the experimental developments, we study ground-state phases of a two-component Bose gas loaded on an optical lattice. The system is described effectively by the Bose-Hubbard Hamiltonian with on-site and near-neighbor spin-spin interactions. An important feature of our investigation is the inclusion of interconversion (spin-flip) terms between the two species, which has been observed in optical lattice experiments. Using mean-field theory and quantum Monte Carlo simulations, we map out the phase diagram of the system. A rich variety of phases is identified, including antiferromagnetic (AF) Mott insulators and ferromagnetic and AF superfluids.
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 . . . . . . . . .
Abstract Motivated by recent experimental processes, we systemically investigate strongly correlated spin-1 ultracold bosons trapped in a three-dimensional optical lattice in the presence of an external magnetic field. Based on a recently developed bosonic dynamical mean-field theory (BDMFT), we map out complete phase diagrams of the system for both antiferromagnetic and ferromagnetic interactions, where various phases are found as a result of the interplay of spin-dependent interaction and quadratic Zeeman energy. For antiferromagnetic interactions, the system demonstrates competing magnetic orders, including nematic, spin-singlet and ferromagnetic insulating phase, depending on longitudinal magnetization, whereas, for ferromagnetic case, a ferromagnetic-to-nematic-insulating phase transition is observed for small quadratic Zeeman energy, and the insulating phase demonstrates the nematic order for large Zeeman energy. Interestingly, at low magnetic field and finite temperature, we find an abnormal multi-step condensation of the strongly correlated superfluid, i.e. the critical condensing temperature of the m F = −1 component with antiferromagnetic interactions demonstrates an increase with longitudinal magnetization, while, for ferromagnetic case, the Zeeman component m F = 0 demonstrates a local minimum for the critical condensing temperature, in contrast to weakly interacting cases.
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.
We derive the ground-state phase diagram of antiferromagnetic spin-1 bosons trapped in a square optical lattice in the limit of large negative quadratic Zeeman interaction, i.e., a limit where only two spin components σ=↑,↓ are involved. The system thus reduces to an interacting binary Bose gas. Our quantum Monte Carlo simulations reveal a phase transition from a x−y ferromagnetic-order to a spin insulator without symmetry breaking, inside the Mott insulating phase with two particles per site. This 3D-XY transition is characterized by the establishment of a finite local magnetic moment along the z-axis and by counterflow superfluidity inside the Mott phase. When increasing the spin-spin interaction amplitude U2, this transition merges with the Mott-superfluid transition and becomes first-order. We derive the phase diagram of the spin-charge separation with respect to U2 parameter.
Two-component coupled Bose gas in a 1D optical lattice is examined. In addition to the postulated Mott insulator and superfluid phases, multiple bosonic components manifest spin degrees of freedom. Coupling of the components in the Bose gas leads to substantial changes in the previously observed spin phases, giving rise to a new effective spin Hamiltonian and unraveling remarkable spin correlations. The system in the absence of coupling exhibits ferromagnetic and nonferromagnetic spin phases for on-site intracomponent interaction stronger than intercomponent interaction. Upon introduction of coupling, the phase transition switches from first to second order. For comparable on-site inter- and intracomponent interactions, with coupling, instead of one, two spin phases emerge with a second-order phase transition. Exact diagonalization and variational Monte Carlo with stochastic minimization on the entangled-plaquette state bestow a unique and enhanced perspective on the system beyond the scope of a mean-field treatment.
Ultracold atomic gases may be the ultimate quantum simulator.These isolated systems have the lowest temperatures in the observable universe, and their properties and interactions can be precisely and accurately tuned across a full spectrum of behaviors, from few-body physics to highly-correlated many-body effects.The ability to impose potentials on and tune interactions within ultracold gases to mimic complex systems mean they could become a theorist's playground.One of their great strengths, however, is also one of the largest obstacles to this dream: isolation.This thesis touches on both of these themes.First, methods to characterize phases and quantum critical points, and to construct finite temperature phase diagrams using experimentally accessible observables in the Bose Hubbard model are discussed.Then, the transition from a weakly to a strongly interacting Bose-Fermi mixture in the continuum is analyzed using zero temperature numerical techniques.Real materials can be emulated by ultracold atomic gases loaded into optical lattice potentials.We discuss the characteristics of a single boson species trapped in an optical lattice (described by the Bose Hubbard model) and the hallmarks of the quantum critical region that separates the superfluid and the Mott insulator ground states.We propose a method to map the quantum critical region using the single, experimentally accessible, local quantity R, the ratio of compressibility to local number fluctuations.The procedure to map a phase diagram with R is easily generalized to inhomogeneous systems and generic many-body Hamiltonians.We illustrate it here using quantum Monte Carlo simulations of the 2D Bose Hubbard model.Secondly, we investigate the transition from a degenerate Fermi gas weakly coupled List of Tables Table Page 2.1 Techniques to Probe Atoms in Optical Lattices . . . . . .