The extreme tunability and control that atomic physics provides makes quantum gasesideal platforms for experimentally realizing novel synthetic materials beyond what istraditionally realizable in condensed matter experiments. In particular, the ability tocontrol interparticle interactions allows for the realization of long lived nonequilibriumstates, and strong periodic modulation of lattice potentials realizes novel Floquet matter.In this thesis I shall present a series of experiments studying the dynamics of ultracoldlithium in modulated and static one-dimensional optical lattices. First, I present anoverview of the experimental apparatus which includes a description of the generation ofour Bose-Einstein condensate and optical lattices. Then I step through four experimentswhich we conducted. The rst two involve studying spatial dynamics in static opticallattices in the ground and the excited bands which realize position-space Bloch oscillationsand a relativistic harmonic oscillator respectively. The third experiment studies transportin Floquet hybridized optical lattice Bloch bands, and the fourth experiment investigatesprethermalization in strongly modulated lattices with tunable interactions.
The extreme tunability and control that atomic physics provides makes quantum gasesideal platforms for experimentally realizing novel synthetic materials beyond what istraditionally realizable in condensed matter experiments. In particular, the ability tocontrol interparticle interactions allows for the realization of long lived nonequilibriumstates, and strong periodic modulation of lattice potentials realizes novel Floquet matter.In this thesis I shall present a series of experiments studying the dynamics of ultracoldlithium in modulated and static one-dimensional optical lattices. First, I present anoverview of the experimental apparatus which includes a description of the generation ofour Bose-Einstein condensate and optical lattices. Then I step through four experimentswhich we conducted. The rst two involve studying spatial dynamics in static opticallattices in the ground and the excited bands which realize position-space Bloch oscillationsand a relativistic harmonic oscillator respectively. The third experiment studies transportin Floquet hybridized optical lattice Bloch bands, and the fourth experiment investigatesprethermalization in strongly modulated lattices with tunable interactions.
Quantum emulation of extreme non-equilibrium phenomena is a natural application of the precision and control of ultracold atomic physics experiments. In particular, ``Floquet engineering" with an explicitly time-dependent Hamiltonian enables the creation of states of matter that can only exist in the presence of strong driving. In this work, we create and study such tunable strongly driven quantum systems. We use quantum degenerate lithium as a platform because of its light mass, fast tunneling rates, and broadly tunable Feshbach resonance, which allow the study of a wide variety of systems: noninteracting Bosons, strongly interacting many body systems, and bright solitons, to name a few. We describe the experimental setup used to create a 7Li Bose-Einstein condensate as an archetypal quantum platform, and then discuss three key results: the first direct measurement of position-space Bloch oscillations in a cold atom system, the creation of a massive relativistic harmonic oscillator, and finally the demonstration of a new method for controlled long-range quantum coherent transport enabled by Floquet band engineering.
Floquet engineering is a versatile tool that uses periodic driving of a quantum system to build novel many-body quantum states with drive-dependent properties. In this thesis I will detail experiments performed in the Weld group which explore a many-body Floquet system consisting of tunably-interacting ultracold atoms in an optical lattice amplitude-modulated at up to a thousand percent. I will discuss experiments in which we use Floquet engineering to coherently control long-range quantum transport in hybridized Floquet-Bloch bands. I will also discuss our use of a double quench protocol to experimentally control and quantitatively characterize Floquet prethermalization associated with a periodic generalized Gibbs ensemble.
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.
Cold atoms trapped in optical lattices (crystals of light) provide a pristine platform for exploring quantum many body physics. Motivated by several recent experiments, this thesis examines the equilibrium and non-equilibrium dynamics of a Bose-Einstein condensate (BEC) loaded in a low dimensional optical lattice in order to realize novel quantum phases. There are two main research directions in this thesis. The first one involves the possibility that exotic order spontaneously forms when two-component bosons are trapped in a honeycomb lattice. My studies on this theme is motivated by the observation of a “twisted superfluid” state in Prof. Klaus Sengstock’s group at Hamburg (Soltan-Panahi et al., Nat. Phys. 8, 71 (2012)). A twisted superfluid involves Bose-Einstein condensation into a state whose order parameter has a spatially varying phase. In chapter 3, I study the stability of a Bose-Einstein condensate towards forming a twisted superfluid within the framework of mean field theory. Despite a exhaustive numerical search I do not find a parameter regime with a twisted superfluid. This search involved all experimentally relevant parameter regimes and therefore mean field theory predicted that the experimentalists should not observe a twisted superfluid. I conclude that the experimental observations were either a manifestation of counter superfluidity or due to interactions during time-of-flight. Subsequent experiments showed that the observations were an artifact of the measurement process. The second research direction in this thesis is an exploration of the stability of periodically driven quantum systems (also known as Floquet systems). Floquet systems can be used to realize exotic non-equilibrium quantum phases which do not have a counterpart in static systems. However, the driving can cause these systems to heat up which presents a major obstacle to creating exotic states. To explore this issue in a concrete example, I model an experiment (Parker, Ha, and Chin, Nat. Phys. 9, 769 (2013)) where a Bose-Einstein condensate loaded in an optical lattice is subjected to periodic shaking. I investigate the stability of this Floquet BEC to interactions. This research direction consists of 3 studies. In chapter 4, I first do this analysis for a purely one-dimensional system and identify a large parameter regime where the BEC is stable. In the next two chapters, I go beyond 1D and consider the role of transverse degrees of freedom. This is because the shaken lattice experiments that I model involves a 1D array of pancakes. I find that this geometry leads to much more dissipation than a purely 1D system. This extra dissipation arises because interactions can transfer energy between different directions. In chapter 5, I consider the extreme case where there is no transverse confinement. I find that in the absence of transverse confinement, a one-dimensional Floquet BEC is generically unstable. Finally, in chapter 6, I consider harmonic transverse confinement modeling the crossover between chapters 4 and 5. I find that as the transverse confinement is made stronger, the atom loss rate initially increases, but beyond a critical transverse confinement, the atom loss disappears due to unavailability of phase space for scattering. I also predict that if the transverse confinement is tuned to the vicinity of certain magic values, the heating rate exhibits a sharp drop. I perform similar analyses for a shaken square lattice and find that generically a low-dimensional Floquet BEC can be stabilized by suitably designing the transverse confinement.
Quantum gases in optical lattices allow for fundamental studies in atomic and condensed-matter physics and the exploration of novel effects. After a brief introduction to the fundamentals of quantum gas experiments in optical lattices, we discuss two recent experiments focusing on driven matter waves in a one-dimensional optical lattice. The first experiment uses a tilted bichromatic optical lattice to investigate the interplay of disorder and collisional interactions in the accelerated transport of a Bose-Einstein condensate. Here, a screening effect is observed, in which the interactions effectively cancel the damping of Bloch oscillations induced by a (quasi-)disordered potential. This effect can be understood through a modification of the underlying band structure by the interactions. The second experiment studies the dynamics of a weakly trapped condensate resonantly coupled to the orbitals of a strongly confining state-selective lattice. We observe momentum distributions that correspond to matter wave diffraction from a periodic structure; however, the diffractive dynamics remain strongly linked to the internal-state Rabi oscillations. In the regime investigated, which we call the nonadiabatic regime, no diffracting potential can be defined. We show how only for much stronger coupling, the internal and external dynamics decouple, transitioning from nonadiabatic diffraction to the well-studied Kapitza-Dirac diffraction. We further investigate prospects for realizing dissipative spin models in our ultracold atomic gas experiment. To this end, we develop and test in the laboratory several possible implementations of effective spins with differential coupling to a superfluid background and examine their viability for a realization of the spin-boson model. | 94 pages
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.