Quantum simulation is emerging as an ambitious and active subfield of atomic physics. This thesis describes progress towards the goal of simulating condensed matter sys-tems, in particular the physics of the Fermi-Hubbard model, using ultracold Lithium atoms in an optical lattice. A major goal of the quantum simulation program is to observe phase transitions of the Hubbard model, into Néel antiferromagnetic phases and d-wave superfluid phases. Phase transitions are generally accompanied by a change in an underlying correlation in a physical system. Such correlations may be most amenable to probing by looking at fluctuations in the system. Experimental techniques for probing density and magnetization fluctuations in a variety of atomic Fermi systems are developed. The suppression of density fluctuations (or atom “shot noise”) in an ideal degenerate Fermi gas is observed by absorption imaging of time-of-flight expanded clouds. In-trap measurements of density and magnetization fluctuations are not easy to probe with absorption imaging, due to their extremely high attenuation. A method to probe
Quantum simulation is emerging as an ambitious and active subfield of atomic physics. This thesis describes progress towards the goal of simulating condensed matter sys-tems, in particular the physics of the Fermi-Hubbard model, using ultracold Lithium atoms in an optical lattice. A major goal of the quantum simulation program is to observe phase transitions of the Hubbard model, into Néel antiferromagnetic phases and d-wave superfluid phases. Phase transitions are generally accompanied by a change in an underlying correlation in a physical system. Such correlations may be most amenable to probing by looking at fluctuations in the system. Experimental techniques for probing density and magnetization fluctuations in a variety of atomic Fermi systems are developed. The suppression of density fluctuations (or atom “shot noise”) in an ideal degenerate Fermi gas is observed by absorption imaging of time-of-flight expanded clouds. In-trap measurements of density and magnetization fluctuations are not easy to probe with absorption imaging, due to their extremely high attenuation. A method to probe
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].
Recent advances in using microscopes in ultracold atom experiment have allowed experimenters for the first time to directly observe and manipulate individual atoms in individual lattice sites. This technique enhances our capability to simulate strongly correlated systems such as Mott insulator and high temperature superconductivity. Currently, all ultracold atom experiments with high resolution imaging capability use bosonic atoms. In this thesis, I present our progress towards creating the fermionic version of the microscope experiment which is more suitable for simulating real condensed matter systems. Lithium is ideal due to the existence of both fermionic and bosonic isotopes, its light mass, which means faster experiment time scales that suppresses many sources of technical noise, and also due to the existence of a broad Feshbach resonance, which can be used to tune the inter-particle interaction strength over a wide range from attractive, non-interacting, and repulsive interactions. A high numerical aperture objective will be used to image and manipulate the atoms with single lattice site resolution. This setup should allow us to implement the Hubbard hamiltonian which could describe interesting quantum phases such as antiferromagnetism, d-wave superfluidity, and high temperature superconductivity. I will also discuss the feasibility of the Raman sideband cooling method for cooling the atoms during the imaging process. We have also developed a new electronic control system to control the sequence of the experiment. This electronic system is very scalable in order to keep up with the increasing complexity of atomic physics experiments. Furthermore, the system is also designed to be more precise in order to keep up with the faster time scale of lithium experiment.
One of the most active areas in atomic, molecular and optical physics is the use of ultracold atomic gases in optical lattices to simulate the behaviour of electrons in condensed matter systems. The larger mass, longer length scale, and tuneable interactions in these systems allow the dynamics of atoms moving in these systems to be followed in real time, and resonant light scattering by the atoms allows this motion to be probed on a microscopic scale using site-resolved imaging. This book reviews the physics of Hubbard-type models for both bosons and fermions in an optical lattice, which give rise to a rich variety of insulating and conducting phases depending on the lattice properties and interparticle interactions. It also discusses the effect of disorder on the transport of atoms in these models, and the recently discovered phenomenon of many-body localization. It presents several examples of experiments using both density and momentum imaging and quantum gas microscopy to study the motion of atoms in optical lattices. These illustrate the power and flexibility of ultracold-lattice analogues for exploring exotic states of matter at an unprecedented level of precision.
One of the most active areas in atomic, molecular and optical physics is the use of ultracold atomic gases in optical lattices to simulate the behaviour of electrons in condensed matter systems. The larger mass, longer length scale, and tuneable interactions in these systems allow the dynamics of atoms moving in these systems to be followed in real time, and resonant light scattering by the atoms allows this motion to be probed on a microscopic scale using site-resolved imaging. This book reviews the physics of Hubbard-type models for both bosons and fermions in an optical lattice, which give rise to a rich variety of insulating and conducting phases depending on the lattice properties and interparticle interactions. It also discusses the effect of disorder on the transport of atoms in these models, and the recently discovered phenomenon of many-body localization. It presents several examples of experiments using both density and momentum imaging and quantum gas microscopy to study the motion of atoms in optical lattices. These illustrate the power and flexibility of ultracold-lattice analogues for exploring exotic states of matter at an unprecedented level of precision.
Ultracold atomic gases provide a fantastic platform to implement quantum simulators and investigate a variety of models initially introduced in condensed matter physics or other areas. One of the most promising applications of quantum simulation is the study of strongly correlated Fermi gases, for which exact theoretical results are not always possible with state-of-the-art approaches. Here, we review recent progress of the quantum simulation of the emblematic Fermi–Hubbard model with ultracold atoms. After introducing the Fermi–Hubbard model in the context of condensed matter, its implementation in ultracold atom systems, and its phase diagram, we review landmark experimental achievements, from the early observation of the onset of quantum degeneracy and superfluidity to the demonstration of the Mott insulator regime and the emergence of long-range anti-ferromagnetic order. We conclude by discussing future challenges, including the possible observation of high- T c superconductivity, transport properties, and the interplay of strong correlations and disorder or topology.
Abstract : Ultracold atoms confined in optical lattice potentials provide an ideal platform to address some of the most outstanding questions in quantum many-body physics, that are difficult or impossible to study using conventional solid state systems. During this DARPA program, progressin several important directions has been made. We have developed cooling techniques suitable for a lattice system and cooled fermionic lithium atoms confined in a three-dimensional (3D) cubic lattice to unprecedented low temperatures, very close to the Neel temperature. We employed Bragg scattering of near-resonant light to observe the antiferromagnetic correlations. We have mapped the phase diagram overthe entire BEC-BCS crossover for a trapped 3D gas with imbalanced numbers of spin-up and spin-down atoms, and have also observed the crossover from a 1D to a 3D spin-imbalanced Fermi gas. We have investigated dynamics, rethermalization and out-of-equilibrium phenomena in strongly correlated lattice systems, as well as in disordered lattice systems. These studies greatly deepened our understanding of quantum phases of matter in lattice potentials.