Abstract Ultracold quantum gases in optical lattices can be used as novel model system for the exploration of strongly correlated many‐body phases of bosonic or fermionic particles. Here we report on the realization of metallic, Mott‐insulating and band insulating phases in ultracold spin mixtures of fermionic 40K atoms. The experimental results are compared to ab initio dynamical mean field theory (DMFT) calculations.
Abstract Ultracold quantum gases in optical lattices can be used as novel model system for the exploration of strongly correlated many‐body phases of bosonic or fermionic particles. Here we report on the realization of metallic, Mott‐insulating and band insulating phases in ultracold spin mixtures of fermionic 40K atoms. The experimental results are compared to ab initio dynamical mean field theory (DMFT) calculations.
Ultracold atoms in optical lattices provide an extremely clean and controllable setting to explore quantum many-body phases of matter. Here we give a brief review of the strong-correlation physics that has been realized using such ultracold atoms in optical lattices ranging from the realization of Hubbard models to studies of quantum magnetism and the detection of single atoms with lattice site resolution. All this has opened up fundamentally new opportunities for the investigation of quantum many-body systems. Introduction Over the past years, ultracold atoms in optical lattices have emerged as versatile new systems to explore the physics of quantum many-body systems. On the one hand, they can be helpful in gaining a better understanding of known phases of matter and their dynamical behavior; on the other hand, they allow one to realize completely novel quantum systems that have not been studied before in nature [1, 2, 3]. Commonly, the approach of exploring quantum many-body systems in such a way is referred to as “quantum simulations.” Examples of some of the first strongly interacting many-body phases that have been realized both in lattices and in the continuum include the quantum phase transition from a superfluid to a Mott insulator [4, 5, 6], fermionic Mott insulators [7, 8], the achievement of a Tonks- Girardeau gas [9, 10], and the realization of the Bose-Einsten condensate (BEC)– Bardeen-Cooper-Schrieffer (BCS) crossover (see also Chapter 12) in Fermi gas mixture [11] using Feshbach resonances [12]. In almost all of these experiments, detection was limited to time-of-flight imaging or more refined derived techniques that mainly characterized the momentum distribution of the quantum gas [2]. For several years, researchers in the field have therefore aspired to employ in situ single-particle detection methods for the analysis of ultracold quantum gases. Only recently has it become possible to implement such imaging techniques, marking a milestone for the characterization and manipulation of ultracold quantum gases [13, 14, 15, 16, 17]. In our discussion, we will focus on one of the most successful of these techniques based on high-resolution fluorescence imaging. Despite being a rather new technique, such quantum gas microscopy has already proven to be an enabling technology for probing and manipulating quantum many-body systems. For the first time, controllable and strongly interacting many-body systems, as realized with ultracold atoms, could be observed on a local scale [17, 16].
Ultracold quantum gases in optical lattices form almost ideal conditions to analyze the physics of strongly correlated quantum phases in periodic potentials. Such strongly correlated quantum phases are of fundamental interest in condensed matter physics, because they lie at the heart of topical quantum materials, such as high-Tc superconductors and quantum magnets, which pose a challenge to our basic understanding of interacting many-body systems. Quite generally, such strongly interacting quantum phases arise when the interaction energy between two particles dominates over the kinetic energy of the two particles. Such a regime can either be achieved by increasing the interaction strength between the atoms via Feshbach resonances or by decreasing the kinetic energy, such that eventually the interaction energy is the largest energy scale in the system. The latter can, for example, simply be achieved by increasing the optical lattice depth. This chapter tries gives an introduction into the field of optical lattices and the physics of strongly interacting quantum phases. A prominent example hereof is the superfluid-to-Mott insulator transition, which transforms a weakly interacting quantum gas into a strongly correlated many body system. Dominating interactions between the particles are in fact crucial for the Mott insulator transition and also for the realization of controlled interaction-based quantum gates, of which several have been successfully realized experimentally.
The fermionic Hubbard model plays a fundamental role in the description of strongly correlated materials. We have realized this Hamiltonian in a repulsively interacting spin mixture of ultracold (40)K atoms in a three-dimensional (3D) optical lattice. Using in situ imaging and independent control of external confinement and lattice depth, we were able to directly measure the compressibility of the quantum gas in the trap. Together with a comparison to ab initio dynamical mean field theory calculations, we show how the system evolves for increasing confinement from a compressible dilute metal over a strongly interacting Fermi liquid into a band-insulating state. For strong interactions, we find evidence for an emergent incompressible Mott insulating phase. This demonstrates the potential to model interacting condensed-matter systems using ultracold fermionic atoms.
Ultracold atoms in optical lattices have proven to be a versatile model system in which strong correlation effects in a many-body quantum system can be studied [1]. The tunability and control over almost all underlying system parameters makes them rather unique and allows one to switch between different ground states of the underlying many-body quantum system. One of the most prominent effects in this respect is the quantum phase transition (QPT) from a superfluid (SF) to a Mott insulator (MI) that started the field of strong-correlation physics with ultracold gases. First theoretically proposed by Fisher et al. [2], the Bose-Hubbard model (BHM) was introduced into the field of ultracold atoms by Jaksch et al. [3], eventually being realized in subsequent experiments [4-7]. This article focuses on giving a brief summary of the main results achieved in the SF-MI transition with ultracold bosons in optical lattices. A brief introduction into the setup of optical lattices is followed by a discussion of key results such as the coherence properties, the density profiles, transport properties and SF characteristics across the QPT.
Ultracold atomic gases in optical lattices provide an unique framework to study quantum phenomena in strongly correlated systems. In addition to the precise control over all relevant parameters in the experiment, these experiments can be mapped to a fundamental model from solid-state physics. For the bosonic version of this model, the so-called Bose-Hubbard model, a phase transition from a superfluid to a Mott insulator was theoretically predicted and later experimentally observed in an ultracold gas of Rb-87 atoms in three-dimensional as well as in one-dimensional optical lattices. Apart from homogeneous optical lattices one can introduce more complex lattice topologies such as two-color superlattices which give rise to a rich phase diagram including more exotic phases like the Bose-glass. We employ various powerful many-body techniques like exact diagonalization in complete and truncated Hilbert spaces and the Density-Matrix Renormalization Group (DMRG) algorithm to study the phase diagrams of the one-dimensional Bose-Hubbard and the one-dimensional Bose-Fermi-Hubbard Hamiltonian. Most theoretical studies of these systems discuss the phase diagrams with respect to the generic parameters of the Hubbard model. These Hubbard parameters, however, depend non-trivially on the control parameters used in experiments. The focus of this work is on the ab-initio calculation of the phase diagram of ultracold Rb-87 in one-dimensional optical superlattices starting directly from the experimental setup. To this end, we first employ band-structure calculations to extract the Hubbard parameters from the experimental parameters. Then, we use state-of-the-art DMRG techniques to solve the many-body problem for realistic particle numbers and lattice sizes that occur in experiments. Our results show that by using the intensities of the two laser fields forming the two-color superlattice as control parameters while keeping all other experimental parameters fixed, it is possible to access all relevant quantum phases of the system. Furthermore, we found out that the critical values of the laser intensities for the different phase transitions depend strongly on a third parameter that has to be included for a realistic description of the experiment. This third parameter is the strength of a harmonic trapping potential which accounts for the Gaussian shape of the laser fields and an additional magnetic potential used to confine the atoms in the center of the trap.
We show that ultracold atoms can be controlled in multi-band optical lattices through spatially periodic Raman pulses for investigation of a class of strongly correlated physics related to the Kondo problem. The underlying dynamics of this system is described by a spin-dependent fermionic or bosonic Kondo-Hubbard lattice model even if we have only spin-independent atomic collision interaction. We solve the bosonic Kondo-Hubbard lattice model through a mean-field approximation, and the result shows a clear phase transition from the ferromagnetic superfluid to the Kondo-singlet insulator at the integer filling.