By exploiting the versatility of ultracold atoms experiments, a variety of many-body phe- nomena can be studied. Ferromagnetism in a trapped ultracold gas of repulsively interacting fermions is considered within a local-density approximation and beyond, where energetic sig- natures indicate its onset. Transport of a Bose-Einstein condensate is explored experimentally in a tunable double-well potential, and a crossover from hydrodynamic to Josephson transport is observed as the barrier between condensates is raised. To add a degree of freedom for the manipulation of ultracold gases, two schemes for species-specific optical lattices are developed theoretically.
By exploiting the versatility of ultracold atoms experiments, a variety of many-body phe- nomena can be studied. Ferromagnetism in a trapped ultracold gas of repulsively interacting fermions is considered within a local-density approximation and beyond, where energetic sig- natures indicate its onset. Transport of a Bose-Einstein condensate is explored experimentally in a tunable double-well potential, and a crossover from hydrodynamic to Josephson transport is observed as the barrier between condensates is raised. To add a degree of freedom for the manipulation of ultracold gases, two schemes for species-specific optical lattices are developed theoretically.
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].
This thesis is primarily a comprehensive discussion of the development of two experimental studies: the quantum transport and effects of heating of ultracold atoms. It specifically provides details of the manipulation and control of ultracold atoms in magnetic waveguides, optical lattices, and optical billiards. The design, construction, and implementation of experimental apparati are also outlined and additional experimental tests are summarized, including the realization of a macroscopic transport (> 20 cm) system for ultracold atoms and transmission of ultracold atoms through a random optical potential. The first experiment is a study of the quantum transport for atoms confined in a periodic potential. These results include a comparison made of thermal and BEC initial conditions. Here, observation of ballistic transport is made for all values of well depth and initial conditions, and the expansion rates for thermal atoms are shown to be in excellent agreement with a singleparticle model. For weak wells (V0/ER ≤ 6), the expansion of the BEC is also in excellent agreement with single-particle theory, using an effective temperature model based on single (non-interacting) particle theory. For deep wells (V0/ER ≥ 6), a crossover is observed to a new regime for the BEC case, indicating the importance of interactions on quantum transport. The second experiment is a study of the effect of different heating rates on a dilute Bose gas confined in a quasi-1D finite, leaky box. An optical kicked-rotor is used to transfer energy to the atoms while two repulsive optical beams are used to confine the atoms. The average energy of the atoms is localized after a large number of kicks and the system reaches a nonequilibrium steady state. A numerical simulation of the experimental data suggests that the localization is due to energetic atoms leaking over the barrier. Our data also indicates a correlation between collisions and the destruction of the BoseEinstein condensate fraction and an exponential decay in phase space density.
The study of ultracold trapped fermionic gases is a rapidly exploding subject [1-10] which is defining new directions in condensed matter and atomic physics. It has also captured the attention of physicists who study color superconducting quark matter as well as nuclear matter [11-13]. Indeed, it is hard, in recent times, to find a subfield of physics which appeals this broadly to the research community. As we come to understand the gases, experimentalists will move to address fermionic atoms in optical lattices; this will provide important insight to condensed matter physicists as analogue systems for “solving ” intractable many body problems. What makes these gases (and lattices) so important is their remarkable tunability and controllability. Using a Feshbach resonance, one can tune the attractive two-body interaction from weak to strong, and thereby make a smooth crossover from a BCS superfluid to a Bose-Einstein condensation (BEC) [14, 15]. Not only does this allow high transition temperatures Tc (relative to the Fermi energy EF) but it may also provide insights into the high temperature cuprate superconductivity [16-19]. Furthermore, one can tune the population of the two spin states, essentially at will, in this way, allowing exploration [20-22] of exotic polarized phases such as the FFLO [23-25] superfluids, of interest to condensed matter, nuclear and particle physicists. One will be able to tune the lattice parameters such as bandwidth, on-site repulsion, even random disorder, etc and thereby study the famous, and as yet, unsolved Hubbard model Hamiltonian. This paper will concentrate on those issues relating to the effects which are of current interest to experimentalists. In particular, we will study BCS-BEC crossover in atomic Fermi gases, looking at a wide range of different experiments. Our group has been principally interested in the effects of finite temperature [26, 17, 18] and in this review, we will discuss how temperature T enters into the standard crossover theory, and how temperature can be measured, and how temc○
Ultracold atomic Fermi gases close to Feshbach resonances represent the ideal platform to study strongly correlated fermionic states [1]. Up to now, most of the experimental efforts have been dedicated to the study of the famous BEC-BCS crossover, i.e. the transition from a Bose-Einstein condensate of tightly bound molecules to a BCS superfluid of long-range fermion pairs. However, such fermionic gases are the ideal environment to explore also the effects of strong, repulsive interactions. The interest in studying repulsive Fermi gases is manifold, since many phase transitions are driven by the strong repulsion between electrons in solids. One notable example is represented by the onset of itinerant ferromagnetism in metals, as envisioned by Stoner almost ninety years ago.
This thesis includes both experimental and theoretical investigations, presented in a series of eight papers. The experimental part ranges from the construction procedures of an apparatus for Bose-Einstein condensates, to full scale experiments using three different set-ups for ultracold atoms in optical lattices. As one of the main themes of the thesis, an experimental apparatus for production of Bose-Einstein Condensates is under construction. A magneto-optically trapped sample, hosting more than 200 million 87Rb atoms, have successfully been loaded into a magnetic trap with high transfer rate. The lifetime of the sample in the magnetic trap is in the range of 9 s, and the atoms have been shown to respond to evaporative cooling. The experiment is ready for optimization of the magnetic trap loading, and evaporative cooling parameters, which are the final steps for reaching Bose-Einstein condensation. The set-up is designed to host experiments including variable geometry optical lattices, and includes the possibility to align laser beams with high angular precision for this purpose. The breakdown of Bloch waves in a Bose-Einstein condensate is studied, attributed to the effect of energetic and dynamical instability. This experimental study is performed using a Bose-Einstein condensate in a moving one-dimensional optical lattice at LENS, Florence Italy. The optical lattice parameters, and the thermal distribution of the atomic sample required to trigger the instabilities, are detected, and compared with a theoretical model developed in parallel with the experiments. In close connection with these one-dimensional lattice studies, an experimental survey to characterize regimes of superradiant Rayleigh scattering and Bragg scattering is presented. Tunneling properties of repulsively bound atom pairs in double well potentials are characterized in an experiment at Johannes Gutenberg University, Mainz Germany. A three-dimensional optical lattice, producing an array of double wells with tunable properties is let to interact with a Bose-Einstein condensate. Pairs of ultracold atoms are produced on one side in the double wells, and their tunneling behavior, dependent on potential barrier and repulsion properties, is studied. A theoretical study of the crossover between one- and two-dimensional systems has been performed. The simulations were made for a two-dimensional array of atoms, where the behavior for different tunneling probabilities and atom-atom repulsion strengths was studied. Scaling relations for systems of variable sizes have been examined in detail, and numerical values for the involved variables have been found.
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.