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An Apparatus for Dynamical Quantum Emulation Using Ultracold Lithium

Zachary A. Geiger

Published Jan 1, 2017• 1 citation
OpenAlex

Abstract

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.

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•Jul 26, 2017•0 citations
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.
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.
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.
Ultracold quantum gases offer a versatile platform to study a wide range of open questions in condensed matter physics and beyond. In particular, their controllability, isolation from noisy thermal environments, and evolution on experimentally-accessible timescales make them a natural choice to probe the effects of driving on time evolution and energy. This thesis details the construction of two cold-atom apparatuses, a lithium machine and a strontium machine, for quantum emulation experiments studying driven systems. Initial numerical simulations along two experimental lines are briefly discussed, and results from the first two experiments on the strontium machine are then presented. In the first, a strontium Bose-Einstein condensate in an optical trap is strongly driven to emulate ultrafast photoionization processes; in a series of proof-of-principle experiments measuring the momenta and energy of particles ejected from the trap, we demonstrate the viability of this technique to study open questions in strong-field physics. The second experiment realizes a tunable quasicrystal, the energy structure for which is described by the multifractal Hofstadter butterfly. Quasiperiodic structures host not only phonons, but also a higher-dimension analogue called phasons. In the experiment, we demonstrate phasonic spectroscopy for the first time by directly driving one of these modes; we characterize the coupling to the resulting excitations, and directly map a slice of the Hofstadter energy spectrum.
Weakly-interacting atoms in a Bose-Einstein condensate coherently occupy the ground-state of their container. This phenomenon, coupled with the technical ability to produce precise, isolated and dynamically-tunable trapping potentials, makes ultracold atoms a versatile platform for simulating quantum mechanical systems. This thesis details the construction of two apparatus at the University of California, Santa Barbara for the production of Bose-Einstein condensates of lithium and strontium atoms respectively. Results of the first experiment performed on the strontium apparatus, a quantum simulation of ultrafast dynamics, are presented. In this experiment, driven cold atoms simulate ultrafast ionization dynamics in attosecond laser pulses, counter-intuitively emulating some of the fastest processes in atomic physics with some of the slowest. A sequence of experiments which demonstrate the correspondence with ultrafast science are described, including the direct observation of carrier-envelope-phase dependent sub-cycle unbinding dynamics. Preliminary results from a second experiment, studying phasonic excitations in a quasiperiodic lattice, are also discussed.
This thesis highlights the versatility of ultracold atoms as quantum simulators by utilizing Bose gases and engineered light-induced Hamiltonians to investigate quantum phenomena across multiple areas of physics.As a high-energy simulator, an analog experiment simulating particle–antiparticle pair creation from the quantum vacuum, emulated these strong-field effects at energy scales accessible in the laboratory. The Dirac picture of particle-antiparticle vacuum and the concept of optical lattice band theory was the foundation of our approach. In this framework, we readily measured pair creation and demonstrated that this high-field phenomenon is well-characterized by Landau-Zener tunneling. Within condensed matter physics, ultracold atoms were employed to study topological dynamics of periodically driven Floquet systems. Using a Floquet “switching” protocol in a one-dimensional bipartite magnetic lattice, we realized a periodically driven Su–Schrieffer–Heeger model that maps onto a massless Dirac Hamiltonian. By alternating between two lattice configurations with near-optimal timing, we observed spin–momentum–locked transport characterized by well-defined drift velocities and with spatial displacement linearly increasing over many Floquet periods, establishing a platform for exploring topological band dynamics. The culminating focus of this thesis is localization physics in Rb-87 Bose-Einstein condensates subjected to disordered artificial gauge fields over a range of energy and time scales, in both equilibrium and out-of-equilibrium settings. The effective Hamiltonian was implemented by driving two-photon Raman transitions with laser fields, while disordered vector potential landscapes were independently generated using tunable intensity patterns projected by a digital micromirror device (DMD). By varying the experimental protocols—including the turn on times of the Raman coupling and disorder, as well as the disorder strength—we obtained insight into quantum dynamics in the presence of disordered gauge fields. The resulting dynamics revealed rich behavior: including spatially inhomogeneous magnetization for high-energy dynamics and increases in the condensate width after time-of-flight for pulsed disorder in lower energy and near-equilibrium conditions; lastly, signatures of localization, in the form of damped oscillations, were observed as the system was driven out-of-equilibrium.
The present thesis is devoted to quantum simulation of strongly interacting systems of ultra-cold atoms in optical lattices. It is a theoretical work which focuses on the possibility to employ strong time-periodic forcing for the coherent control of these system. This form of quantum engineering is called Floquet engineering. Experimentally, time-periodic forcing has been successfully applied to realize a variety of physical models and phenomena, especially in the regime of weak interactions. We describe two novel proposals for interesting phenomena in the regime of strong interactions that rely on lattice shaking: melting of a Mott-insulator into an excited-state superfluid via coherent coupling of Bloch bands and the creation of 1D lattice anyons. Furthermore, the role of multiphoton excitations in a driven lattice is analyzed since these processes can lead to unwanted heating and thereby impeding of successful Floquet engineering in the experiment. The introductory Chapter 1 gives an overview over the field of quantum simulations with ultra-cold atoms in optical lattices and describes the experimental progress that has been made in the recent years. In Chapter 2, Floquet theory is reviewed, which provides an excellent framework to deal with time-periodic Hamiltonians and which is the basis of the analysis presented in the following chapters. Chapter 3 deals with the proposal of coherently coupling Bloch bands of an optical lattice via resonant lattice shaking. In particular, the orbital-driven phase transition from a Mott insulating to a superfluid ground state is described in detail. In Chapter 4, a proposal of realizing 1D lattice anyons from strongly interacting bosons in a shaken and tilted lattice is worked out. Furthermore, Friedel oscillations are proposed to provide a measurable real-space signature for the anyonization. Finally, in Chapter 5 multiphoton excitations to higher Bloch bands are analyzed for the cases of a shaken and an amplitude-modulated lattice. The strength and the location of resonances, which are associated with heating, are described theoretically and numerically.