Over recent years, exciting developments in the field of ultracold atoms confined in optical lattices have led to numerous theoretical proposals devoted to the quantum simulation of problems e.g. known from condensed matter physics. Many of those ideas demand experimental environments with non-cubic lattice geometries. In this paper, we report on the implementation of a versatile three-beam lattice allowing for the generation of triangular as well as hexagonal optical lattices. As an important step, the superfluid–Mott insulator (SF–MI) quantum phase transition has been observed and investigated in detail in this lattice geometry for the first time. In addition to this, we study the physics of spinor Bose–Einstein condensates (BEC) in the presence of the triangular optical lattice potential, especially spin changing dynamics across the SF–MI transition. Our results suggest that, below the SF–MI phase transition, a well-established mean-field model describes the observed data when renormalizing the spin-dependent interaction. Interestingly, this opens up new perspectives for a lattice-driven tuning of a spin dynamics resonance occurring through the interplay of the quadratic Zeeman effect and spin-dependent interaction. Finally, we discuss further lattice configurations that can be realized with our setup.
Over recent years, exciting developments in the field of ultracold atoms confined in optical lattices have led to numerous theoretical proposals devoted to the quantum simulation of problems e.g. known from condensed matter physics. Many of those ideas demand experimental environments with non-cubic lattice geometries. In this paper, we report on the implementation of a versatile three-beam lattice allowing for the generation of triangular as well as hexagonal optical lattices. As an important step, the superfluid–Mott insulator (SF–MI) quantum phase transition has been observed and investigated in detail in this lattice geometry for the first time. In addition to this, we study the physics of spinor Bose–Einstein condensates (BEC) in the presence of the triangular optical lattice potential, especially spin changing dynamics across the SF–MI transition. Our results suggest that, below the SF–MI phase transition, a well-established mean-field model describes the observed data when renormalizing the spin-dependent interaction. Interestingly, this opens up new perspectives for a lattice-driven tuning of a spin dynamics resonance occurring through the interplay of the quadratic Zeeman effect and spin-dependent interaction. Finally, we discuss further lattice configurations that can be realized with our setup.
The physics of quantum degenerate cold gases in optical lattices has rapidly grown to an extremely dynamic field over the past few years. In the experimental realizations, however, mainly cubic symmetries (or their two- and one-dimensional projections) are considered. We have implemented an optical lattice with an underlying triangular symmetry in order to investigate strongly correlated ultra-cold atoms in a novel experimental geometry. Exhibiting an explicit polarization dependence (compare figure 1) the optical lattice realized here should allow for the creation and analysis of thus far unexplored magnetic phases. Experiments attending to the quantum phase transition from a superfluid to a Mott-insulating state in a three- as well as in a two-dimensional system with triangular symmetry have been performed. Similarities as well as differences to the findings obtained in cubic lattices will be discussed and can be attributed to the inherent differences in the crucial lattice parameters such as tunneling energy J and on-site interaction U.
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.
An important new development in the field of ultracold atomic gases is the study of the properties of these gases in a so-called optical lattice. An optical lattice is a periodic trapping potential for the atoms that is formed by the interference pattern of a few laser beams. A reason for the interest in these systems is that the effects of the interatomic interactions can be strongly enhanced. More specifically, it has been shown in a beautiful experiment by Greiner et al. in 2002 that by loading a Bose-Einstein condensate into an optical lattice it is possible for the system to undergo a quantum phase transition to a new quantum phase of matter, the so-called Mott insulator phase. Within this Mott insulator phase each lattice site is occupied by exactly one atom. This makes the Mott insulator phase especially well suited for applications in the field of quantum computation and quantum information processing. We have theoretically investigated the above mentioned quantum phase transition and our formalism allows for a description of the Mott insulator phase at nonzero temperatures. Another important experimental development in the field of ultracold atomic gases is the use of Feshbach resonances to control the interatomic interactions. Such a resonance occurs whenever two colliding atoms form a long-lived molecule for some time. The crucial point of a Feshbach resonance is that the above mentioned molecule has a magnetic moment that is not equal to twice the magnetic moment of the atom. As a consequence the energy difference between the two atoms and the molecule and hence the interactions between the atoms can be controlled by using an external magnetic field. By combining these two techniques, i.e, by trapping ultracold atomic gases in an optical lattice and by tuning a magnetic field near a Feshbach resonance there can be a new quantum phase transition between two superfluid phases. We gave derived the the theory for the description of these Feshbach resonances in optical lattices and applied it to various systems. To be a bit more precise, if we tune the external magnetic field such that the energy difference between a molecule and two atoms is sufficiently negative, then the gas consists of a Bose-Einstein condensate of molecules. In contrast, if the energy difference is large enough and positive we have a gas that consists primarily of a Bose-Einstein condensate of atoms. It turns out that these two limits are separated by an Ising-like quantum phase transition. By using atomic Bose gases near a Feshbach resonance detailed experimental studies which test the theoretical predictions of the statistical and dynamical properties of these quantum phase transitions can be made.
In this thesis I report on experiments that enter a new regime in the many body physics of ultracold atomic gases. A Bose-Einstein condensate is loaded into a three-dimensional optical lattice potential formed by a standing wave laser light field. In this novel quantum system we have been able to both realize a quantum phase transition from a superfluid to a Mott insulator, and to observe the collapse and revival of a macroscopic matter wave field. Quantum phase transitions are driven by quantum fluctuations and occur, even at zero temperature, as the relative strength of two competing energy terms in the underlying Hamiltonian is varied across a critical value. In the first part of this work I report on the observation of such a quantum phase transition in a Bose-Einstein condensate with repulsive interactions, held in a three-dimensional optical lattice potential. In the superfluid ground state, each atom is spread-out over the entire lattice, whereas in the Mott insulating state, exact numbers of atoms are localized at individual lattice sites. We observed the reversible transition between those states and detected the gap in the excitation spectrum of the Mott insulator. A Bose-Einstein condensate is usually described by a macroscopic matter wave field. However, a quantized field underlies such a "classical" matter wave field of a Bose-Einstein condensate. The striking behavior of ultracold matter due to the field quantization and the nonlinear interactions between the atoms is the focus of the second part of this work. The matter wave field of a Bose-Einstein condensate is observed to undergo a series of collapses and revivals as time evolves. Furthermore, we show that the collisions between individual pairs of atoms lead to a fully coherent collisional phase shift in the corresponding many-particle state, which is a crucial cornerstone of proposed novel quantum computation schemes with neutral atoms. With these experiments we enter a new field of physics with ultracold quantum gases. In this strongly correlated regime, interactions between atoms dominate the behavior of the many-body system such that it can no longer be described by the usual theories for weakly interacting Bose gases. This novel quantum system offers the unique possibility to experimentally address fundamental questions of modern solid state physics, atomic physics, quantum optics, and quantum information.
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].
In this dissertation we focus on many-body phenomena on a quantum level. In particular fermionic quantum gases in a temperature regime approaching absolute zero. Ultracold quantum gases have proven to be a versatile framework for Theorists and Experimentalists to probe many-body quantum mechanics. They also serve to quantum simulate solid state problems in a clean and controllable environment. The use of optical lattices include the advantage of tuning the required lattice structure nearly at will and lack the experimental shortcomings compared to the solid state, like the presence of lattice dislocations. The relevant lattice parameters can be easily tuned without changing the setup. In recent years many goals within theory and experiments of ultracold quantum gases in optical lattices were achieved. This emphasizes the significance of ongoing research with ultracold quantum gases on optical lattices. We present two aspects of modern theory of ultracold quantum gases in optical lattices. On the one hand, we implement orbital physics in a setup of optical lattices and on the other, we find elusive Majorana fermions in a setup with ultracold fermionic gases. Both aspects are well-known in solid state systems, but did not make the step towards ultracold quantum gases so far. We propose and investigate setups to quantum simulate these challenges in the framework of optical lattices. The first part of this work concerns the implementation of orbital physics in optical lattices. The orbital structure of atoms reveals novel phenomena in solid state systems. This raises the interest in creating optical lattice systems exhibiting analog behavior, as dictated by the orbitals in the solid state. We derive the microscopic Hamiltonian for a p-orbital system and investigate it in detail. For this Hamiltonian we perform a mean-field treatment and discover novel phase transitions including a possible tricritical point. In the analysis of the strong coupling regime we find an additional phase transition towards an antiferromagnet and then extend the mean-field phase diagram. Concluding the investigations is a proposal of an experimental setup to achieve orbital physics with state-of-the-art experimental tools. The second part of this work considers Majorana modes and p-wave superfluids. Majorana modes are not only present in high-energy physics, but also in condensed matter systems. Here we demonstrate a setup in order to simulate Majorana modes and p-wave superfluids in optical lattices. We derive an effective Hamiltonian and investigate it on a mean-field level as well as give the mean-field phase diagram. It contains a rich manifold of different p-wave phases. In addition, we extend our investigations to topological properties of our system and provide the topological phase diagram. We discover the special phenomena that the mean-field and topological phase transitions are decoupled in our system. The proposed system is suited to have Majorana modes at vortices and dislocations, which are injected into the system in controllable experimental manner. We conclude the considerations by giving a protocol for braiding in order to demonstrate non-Abelian statistics of Majorana modes.