Ultra-cold atom system provides novel technology to simulate traditional solid state physics, including boson and fermion particles. Due to the flexibility of tuning pa- rameters, people can further understand basic physics behind strongly correlated effects, especially mechanism of unconventional density wave and superfluidity. Using weak cou- pling renormalization group method, we propose and study several models which can be realized in experiments. Ranging from most well-known extended Hubbard model, to spin- polarized Fermi Hubbard model and multi-flavor Fermi-Fermi mixture, we establish solid theories to explain the origin of new states of matter, and the experimental techniques to exploit them. The effects of lattice structure and particle density in fermionic system play important roles for determining phase diagram in low energy scale. Due to the presence of lattice, these systems have insulator phase at half-filled. The density imbalance, however, prevents formation of conventional density wave state, and the screening interaction dra- matically affects other species's behavior. The interplay between screening interaction and square lattice is key ingredient of unconventional density wave and superfluidity. Our studyvishows that the unconventional density wave and superfluidity can be realized and detected in ultra-cold atom experiments.
Ultra-cold atom system provides novel technology to simulate traditional solid state physics, including boson and fermion particles. Due to the flexibility of tuning pa- rameters, people can further understand basic physics behind strongly correlated effects, especially mechanism of unconventional density wave and superfluidity. Using weak cou- pling renormalization group method, we propose and study several models which can be realized in experiments. Ranging from most well-known extended Hubbard model, to spin- polarized Fermi Hubbard model and multi-flavor Fermi-Fermi mixture, we establish solid theories to explain the origin of new states of matter, and the experimental techniques to exploit them. The effects of lattice structure and particle density in fermionic system play important roles for determining phase diagram in low energy scale. Due to the presence of lattice, these systems have insulator phase at half-filled. The density imbalance, however, prevents formation of conventional density wave state, and the screening interaction dra- matically affects other species's behavior. The interplay between screening interaction and square lattice is key ingredient of unconventional density wave and superfluidity. Our studyvishows that the unconventional density wave and superfluidity can be realized and detected in ultra-cold atom experiments.
The present thesis is devoted to the study of physical phenomena emerging from strong correlations in strongly interacting quantum many-body systems with several components. Hubbard models are widely used as minimal models which take into account the interactions between particles and they have been studied in relation to phenomena such as Mott localization, unconventional superconductivity, quantum magnetism and many others. All of these striking phenomena share their origin from the strong correlations among fermions induced by their mutual interactions. Furthermore, condensed matter models are usually realized only in an approximate fashion in actual solid-state systems, making the situation all the more puzzling and hard to be treated analytically or numerically. Therefore, a great effort has been performed to simulate Hubbard models in a system of atoms cooled down to ultra low temperatures and trapped in optical lattices. The most peculiar feature of cold atoms experiments consists in the possibility of tuning relevant physical parameters of the systems, as the density or the interactions among atoms, using laser and/or magnetic fields. This paved the way to the observation of fundamental quantum states of matter as the weakly interacting Bose-Einstein condensate, the super fluid to Mott insulator transition, the super fluid BEC-BCS crossover, the Mott transition in systems of composite fermions and so on. Hence, it is considered of great interest establishing connections between the quantum simulations cold atomic toolbox and systems realized in solid-state physics...
The advent of ultracold alkaline-earth atoms in optical lattices has established a platform for investigating correlated quantum matter with SU(N) symmetry, offering highly tunable model parameters that allow experiments to access phenomena that are unavailable in conventional materials. Understanding the ground-state physics of SU(N) Fermi-Hubbard models away from the Heisenberg limit and from the spin-flavor balanced setting is important, as examining the flavor imbalance reveals new physics in Fermi-Hubbard models and shows how SU(N) phases react to practical experimental imperfections in optical lattices. In this study, mean-field phase diagrams are presented for the unit-density SU(3) Fermi-Hubbard model at two sets of flavor densities, (31−δ,31+δ,31) and (41−δ,41+δ,21), with the flavor imbalance introduced as δ. Novel phases are identified at moderate interaction strengths for both densities and their robustness is investigated in the presence of flavor imbalance. Furthermore, we provide microscopic explanations of the phases found and their stability. Analysis of thermal ensembles of random mean-field solutions indicate that, at temperatures accessible in state-of-the-art cold atom experiments, some spin orders are hard for conventional scattering or local observable measurements to detect, but can be more accessible with quantum gas microscopy in optical lattice experiments. This work also shows that nesting and Mottness, intertwined in the usual SU(2) Hubbard model in stark contrast to generic materials, can be tuned in the SU(3) model and play distinct roles. The resulting phase diagrams not only deepen our understanding of SU(N) Fermi-Hubbard models but also inform future experimental search for new phases.
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.
We study density wave instabilities in a doubly degenerate Fermi-Fermi mixture with $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)$ symmetry on a square lattice. For sufficiently large on-site inter-species repulsion, when the two species of fermions are both at half-filling, two conventional (s wave) number density waves are formed with a $\ensuremath{\pi}$-phase difference between them to minimize the interspecies repulsion. Upon moving one species away from half-filling, an unconventional density wave with dxy-wave symmetry emerges. When both species are away from the vicinity of half-filling, superconducting instabilities dominate. We present results of a functional renormalization-group calculation that maps out the phase diagram at weak couplings. Also, we provide a simple explanation for the emergence of the dxy-density wave phase based on a four-patch model. We find a robust and general mechanism for dxy-density-wave formation that is related to the shape and size of the Fermi surfaces. The density imbalance between the two species of fermions in the vicinity of half-filling leads to a phase-space discrepancy for different interspecies umklapp couplings. Using a phase-space argument for leading corrections in the one-loop renormalization-group approach to fermions, we show that the phase-space discrepancy in our system causes opposite flows for the two leading intraspecies umklapp couplings and that this triggers the dxy-density-wave instability.
Two models are discussed here to illustrate the quantum many-body phenomena in mixtures of ultra-cold atoms in optical lattices. The first model describes a mixture of two species of bosonic atoms of equal masses in optical lattices and the second describes a mixture of heavy bosonic atoms and light fermionic atoms in optical lattices. For both models, we assume the trap is present and use parameters typical in experiment. For the first model, the discussion is aimed at providing a thorough description of the collective behavior of the binary mixture in various interaction regions, with emphasis on two many-body phenomena, pairing and anti-pairing, as a result of the inter-species interaction. The pairing leads to a new type of superfluid order, called the paired superfluid (PSF) and the anti-pairing leads to another type of superfluid order, called the counter-flow superfluid (CFSF). In addition, we discuss the coexistence of charge density wave order with the three superfluid orders in the strong interaction region. We use both Luttinger liquid theory and the time evolving block decimation (TEBD) method to study this model in one dimension. The discussion is organized in three parts: the phase diagram and the correlation functions; the noise correlation functions; and the transport properties. Two phase diagrams are constructed to map the different orders in the parameter space. The correlation functions, include noise correlations, are carefully examined for the determination of the orders and for possible detection methods. In the end, the transport properties of the PSF and CFSF orders are studied through the dipole oscillation induced by trap displacement. For the second model, examining a mixture of heavy bosons and light fermions, the discussion is oriented toward determining the thermal properties of the mixture for attractive inter-species interactions. This work is motivated by experiments creating artificial molecules through optical and magnetic control of ultra-cold atoms. We use the strong coupling (SC) expansion method to evaluate the density profile, the onsite inter-species correlations, the density fluctuations and the entropy per particle. Analytical expressions are derived for all the quantities above as well as the partition function. To benchmark the accuracy, the SC calculations are compared with inhomogeneous dynamical mean field theory (IDMFT) and Monte Carlo (MC) simulation. From the calculations, we find that 1) the efficiency of creating pre-formed molecules is significantly increased by confining the mixtures onto optical lattices; 2) the temperature of the mixtures in optical lattices can be reliably estimated through the density gradient and the density fluctuations.
Ultra-cold fermionic atoms trapped in optical lattices may be a candidate for the discovery of new novel phenomena in condensed matter systems.Experiments afford the creation of virtually any lattice geometry, and physicalparameters of tight binding type lattice models can be acurately and easily tuned. Although some theoretical work has been conducted, few have used the power of the functional renormalization group method to unearth rigorous methods for determining collective many-body phases in this regime. Motivated byrecent theoretical achievements, we investigate novel condensed matter systemsinvolving interacting fermions which are engineered to be confined in differentdimensions. In this sense, we seek low energy effective theories for low-dimensional fermionic lattice systems embedded into higher dimensional lattice systems, and show how tuning physical quantities, such as the fillingor density, can have dramatic effects on the behavior of the lower dimensionalsystem.