Ultracold atoms in optical lattices provide a highly controllable environment for the clean experimental realization of various model Hamiltonians from condensed matter and statistical physics. For example, the two-component Bose-Hubbard model, which reduces to an anisotropic spin-1/2 Heisenberg model in a certain limit and thus allows for the study of quantum magnetism, can be implemented by using bosons with two different internal states that couple differently to an optical lattice potential. In this thesis, I present our first experiments with two-component hyperfine-state mixtures of ultracold 87Rb atoms in a state-dependent optical lattice, both in the strongly correlated regime and in the context of nonlinear atom optics. For the production of 87Rb Bose-Einstein condensates we have developed a moving-coil transporter apparatus featuring a magnetic TOP trap which serves as a 'phase-space funnel' to load a crossed optical dipole trap. The apparatus further incorporates a three-dimensional optical lattice setup with simultaneously usable hyperfine state-dependent and state-independent lattice beams of different spacing along the vertical axis. Internal state control is performed via rf and microwave Rabi pulses and Landau-Zener sweeps. As a first step towards studying strongly correlated two-component mixtures, we have realized a state-selective superfluid-to-Mott insulator transition, where one component enters the Mott insulator regime, while the other one stays superfluid. Using the state-dependent lattice we can tune the second component's properties from highly superfluid to strongly localized. At both extremes we find a reduction of the coherence of the primary component, i.e. a shift of the Mott transition to smaller values of the ratio U/t of interaction to tunneling. We ascribe this to a polaron-like dressing on the one hand, and a 'quantum emulsion' causing a disordered atomic background potential on the other hand. Further, we have observed and studied four-wave mixing of two-component matter waves. Using state-selective Kapitza-Dirac diffraction of a two-component BEC, we prepare seed and pump modes differing both in momentum and internal state. A novel collinear four-wave mixing process then populates the initially empty output modes. While this process can complicate studies of bosonic mixtures loaded into state-dependent optical lattices, it might prove useful for possible applications in quantum atom optics. | Ultracold atoms in optical lattices provide a highly controllable environment for the clean experimental realization of various model Hamiltonians from condensed matter and statistical physics. For example, the two-component Bose-Hubbard model, which reduces to an anisotropic spin-1/2 Heisenberg model in a certain limit and thus allows for the study of quantum magnetism, can be implemented by using bosons with two different internal states that couple differently to an optical lattice potential. In this thesis, I present our first experiments with two-component hyperfine-state mixtures of ultracold 87Rb atoms in a state-dependent optical lattice, both in the strongly correlated regime and in the context of nonlinear atom optics. For the production of 87Rb Bose-Einstein condensates we have developed a moving-coil transporter apparatus featuring a magnetic TOP trap which serves as a 'phase-space funnel' to load a crossed optical dipole trap. The apparatus further incorporates a three-dimensional optical lattice setup with simultaneously usable hyperfine state-dependent and state-independent lattice beams of different spacing along the vertical axis. Internal state control is performed via rf and microwave Rabi pulses and Landau-Zener sweeps. As a first step towards studying strongly correlated two-component mixtures, we have realized a state-selective superfluid-to-Mott insulator transition, where one component enters the Mott insulator regime, while the other one stays superfluid. Using the state-dependent lattice we can tune the second component's properties from highly superfluid to strongly localized. At both extremes we find a reduction of the coherence of the primary component, i.e. a shift of the Mott transition to smaller values of the ratio U/t of interaction to tunneling. We ascribe this to a polaron-like dressing on the one hand, and a 'quantum emulsion' causing a disordered atomic background potential on the other hand. Further, we have observed and studied four-wave mixing of two-component matter waves. Using state-selective Kapitza-Dirac diffraction of a two-component BEC, we prepare seed and pump modes differing both in momentum and internal state. A novel collinear four-wave mixing process then populates the initially empty output modes. While this process can complicate studies of bosonic mixtures loaded into state-dependent optical lattices, it might prove useful for possible applications in quantum atom optics. | 110 pages
Ultracold atoms in optical lattices provide a highly controllable environment for the clean experimental realization of various model Hamiltonians from condensed matter and statistical physics. For example, the two-component Bose-Hubbard model, which reduces to an anisotropic spin-1/2 Heisenberg model in a certain limit and thus allows for the study of quantum magnetism, can be implemented by using bosons with two different internal states that couple differently to an optical lattice potential. In this thesis, I present our first experiments with two-component hyperfine-state mixtures of ultracold 87Rb atoms in a state-dependent optical lattice, both in the strongly correlated regime and in the context of nonlinear atom optics. For the production of 87Rb Bose-Einstein condensates we have developed a moving-coil transporter apparatus featuring a magnetic TOP trap which serves as a 'phase-space funnel' to load a crossed optical dipole trap. The apparatus further incorporates a three-dimensional optical lattice setup with simultaneously usable hyperfine state-dependent and state-independent lattice beams of different spacing along the vertical axis. Internal state control is performed via rf and microwave Rabi pulses and Landau-Zener sweeps. As a first step towards studying strongly correlated two-component mixtures, we have realized a state-selective superfluid-to-Mott insulator transition, where one component enters the Mott insulator regime, while the other one stays superfluid. Using the state-dependent lattice we can tune the second component's properties from highly superfluid to strongly localized. At both extremes we find a reduction of the coherence of the primary component, i.e. a shift of the Mott transition to smaller values of the ratio U/t of interaction to tunneling. We ascribe this to a polaron-like dressing on the one hand, and a 'quantum emulsion' causing a disordered atomic background potential on the other hand. Further, we have observed and studied four-wave mixing of two-component matter waves. Using state-selective Kapitza-Dirac diffraction of a two-component BEC, we prepare seed and pump modes differing both in momentum and internal state. A novel collinear four-wave mixing process then populates the initially empty output modes. While this process can complicate studies of bosonic mixtures loaded into state-dependent optical lattices, it might prove useful for possible applications in quantum atom optics. | Ultracold atoms in optical lattices provide a highly controllable environment for the clean experimental realization of various model Hamiltonians from condensed matter and statistical physics. For example, the two-component Bose-Hubbard model, which reduces to an anisotropic spin-1/2 Heisenberg model in a certain limit and thus allows for the study of quantum magnetism, can be implemented by using bosons with two different internal states that couple differently to an optical lattice potential. In this thesis, I present our first experiments with two-component hyperfine-state mixtures of ultracold 87Rb atoms in a state-dependent optical lattice, both in the strongly correlated regime and in the context of nonlinear atom optics. For the production of 87Rb Bose-Einstein condensates we have developed a moving-coil transporter apparatus featuring a magnetic TOP trap which serves as a 'phase-space funnel' to load a crossed optical dipole trap. The apparatus further incorporates a three-dimensional optical lattice setup with simultaneously usable hyperfine state-dependent and state-independent lattice beams of different spacing along the vertical axis. Internal state control is performed via rf and microwave Rabi pulses and Landau-Zener sweeps. As a first step towards studying strongly correlated two-component mixtures, we have realized a state-selective superfluid-to-Mott insulator transition, where one component enters the Mott insulator regime, while the other one stays superfluid. Using the state-dependent lattice we can tune the second component's properties from highly superfluid to strongly localized. At both extremes we find a reduction of the coherence of the primary component, i.e. a shift of the Mott transition to smaller values of the ratio U/t of interaction to tunneling. We ascribe this to a polaron-like dressing on the one hand, and a 'quantum emulsion' causing a disordered atomic background potential on the other hand. Further, we have observed and studied four-wave mixing of two-component matter waves. Using state-selective Kapitza-Dirac diffraction of a two-component BEC, we prepare seed and pump modes differing both in momentum and internal state. A novel collinear four-wave mixing process then populates the initially empty output modes. While this process can complicate studies of bosonic mixtures loaded into state-dependent optical lattices, it might prove useful for possible applications in quantum atom optics. | 110 pages
Quantum degenerate atomic gases offer a unique platform for the exploration of a wide variety of interacting many-body systems in a pristine environment, based on a set of powerful tools for the coherent control of the atoms' internal and external degrees of freedom. Here, we present experimental studies of strongly interacting bosonic mixtures in one-dimensional (1D) systems, in which the mobilities of the two species are independently controlled with a state-selective optical lattice. In a first experiment, we freeze out the tunneling of one species from a binary mixture, and study the formation of ``quantum emulsion'' states, where immobile atoms serve as a static, random disorder for a more mobile species. We investigate the 1D superfluid-to-insulator transition in the presence of this disorder, and make comparisons to the effects of quasi-disorder from an incommensurate optical lattice. We observe enhanced localization in the more random potential, highlighting the important role of correlations in disordered systems. Through a combined measurement of transport, localization, and excitation spectra, we are able to obtain strong evidence for observation of a disordered, insulating quantum phase, the 1D Bose glass. In a second experiment, we introduce a new experimental technique for the characterization of ultracold gases held in optical lattices. In analogy to neutron diffraction from solids, we use atomic de Broglie waves to non-destructively probe the spatial structure of 1D Mott insulators through elastic Bragg diffraction, and to probe inelastic band-structure excitations of more weakly interacting 1D Bose gases. Furthermore, we use the diffraction of matter waves to detect the formation of forced-antiferromagnetic ordering in a crystalline atomic spin mixture. Lastly, we study the dynamical response of matter waves to a periodically pulsed, incommensurate optical lattice, a situation that realizes a system of two coupled kicked quantum rotors. We observe that the coupling induces a suppression of energy growth at quantum resonances, and a localization-to-delocalization transition in momentum space for off-resonant driving. Our observations confirm a long-standing theoretical prediction for the two-rotor system, and illustrate how classical behavior can emerge from the evolution of a simple quantum system. | 193 pages
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.
Our work concerns the effects of strong correlations of ultracold atoms in optical lattices in three different scenarios. First we analyze the influence of dissipative processes on the superfluid-Mott insulator transition in the Bose-Hubbard model, observing a shift of the well-known phase transition. In a second setup atoms are trapped in state-dependent lattices; we show that any asymmetry in the contact interaction produces a form of correlated hopping, which results in a pair superfluid phase, with interesting correlation properties that differentiate it from an ordinary atomic Bose-Einstein condensate. Finally we investigate a two-species Bose-Hubbard model including a conversion term, which can be implemented experimentally through a Feshbach resonance producing long-lived bound states. We are particularly interested in the exotic incompressible, yet superfluid “super-Mott” phase.
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.
Ultracold atoms in optical lattices can be used to model condensed matter systems. They provide a clean, tuneable system which can be engineered to reach parameter regimes that are not accessible in condensed matter systems. Furthermore, they provide different techniques for probing the properties of these systems.This thesis presents an experimental and theoretical study of ultracold atoms in optical lattices for quantum simulation of two-dimensional systems.The first part of this thesis describes an experiment with a Bose-Einstein condensate of 87Rb loaded into a two-dimensional optical lattice. The beams that generate the optical lattice are controlled by acousto-optic deflection to provide a flexible optical lattice potential. The use of a dynamic ‘accordion’ lattice with ultracold atoms, where the spacing of the lattice is increased in both directions from 2.2 to 5.5 μm, is described. This technique allows an experiment such as quantum simulations to be performed with a lattice spacing smaller than the resolution limit of the imaging system, while allowing imaging of the atoms at individual lattice sites by subsequent expansion of the optical lattice. The optical lattice can also be rotated, generating an artificial magnetic field. Previous experiments with the rotating optical lattice are summarised, and steps to reaching the strongly correlated regime are discussed.The second part of this thesis details numerical techniques that can be used to describe strongly correlated two-dimensional systems. These systems are challenging to simulate numerically, as the exponential growth in the size of the Hilbert space with the number of particles means that they can only be solved exactly for very small systems. Recently proposed correlator product states [Phys. Rev. B 80, 245116 (2009)] provide a numerically efficient description which can be used to simulate large two-dimensional systems. In this thesis we apply this method to the two-dimensional quantum Ising model, and the Bose-Hubbard model subject to an artificial magnetic field in the regime where fractional quantum Hall states are predicted to occur.
Ultracold atoms in optical lattices can be used to model condensed matter systems. They provide a clean, tuneable system which can be engineered to reach parameter regimes that are not accessible in condensed matter systems. Furthermore, they provide different techniques for probing the properties of these systems.This thesis presents an experimental and theoretical study of ultracold atoms in optical lattices for quantum simulation of two-dimensional systems.The first part of this thesis describes an experiment with a Bose-Einstein condensate of 87Rb loaded into a two-dimensional optical lattice. The beams that generate the optical lattice are controlled by acousto-optic deflection to provide a flexible optical lattice potential. The use of a dynamic ‘accordion’ lattice with ultracold atoms, where the spacing of the lattice is increased in both directions from 2.2 to 5.5 μm, is described. This technique allows an experiment such as quantum simulations to be performed with a lattice spacing smaller than the resolution limit of the imaging system, while allowing imaging of the atoms at individual lattice sites by subsequent expansion of the optical lattice. The optical lattice can also be rotated, generating an artificial magnetic field. Previous experiments with the rotating optical lattice are summarised, and steps to reaching the strongly correlated regime are discussed.The second part of this thesis details numerical techniques that can be used to describe strongly correlated two-dimensional systems. These systems are challenging to simulate numerically, as the exponential growth in the size of the Hilbert space with the number of particles means that they can only be solved exactly for very small systems. Recently proposed correlator product states [Phys. Rev. B 80, 245116 (2009)] provide a numerically efficient description which can be used to simulate large two-dimensional systems.
In this thesis we apply this method to the two-dimensional quantum Ising model, and the Bose-Hubbard model subject to an artificial magnetic field in the regime where fractional quantum Hall states are predicted to occur.