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.
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.
Periodic driving is a powerful tool for engineering tunable many-body quantum states. Such Floquet engineering relies on the existence of a localized prethermal regime, a state which remains incompletely understood. We report experiments on a many-body Floquet system consisting of ultracold atoms in an optical lattice subjected to sign-changing amplitude modulation. A double-quench protocol enables measurement of an inverse participation ratio quantifying the degree of prethermal localization as a function of continuously tunable drive parameters and interactions. Following the time evolution of the driven system, we observe the sequential formation of two localized prethermal plateaux, interaction-driven delocalization, and strongly frequency-dependent dynamics of departure from the prethermal state. The experimental control and quantitative characterization of Floquet prethermalization opens new possibilities for dynamical quantum engineering.
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.
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.
The use of periodic driving for synthesizing many-body quantum states depends crucially on the existence of a prethermal regime, which exhibits drive-tunable properties while forestalling the effects of heating.This dependence motivates the search for direct experimental probes of the underlying localized nonergodic nature of the wave function in this metastable regime.We report experiments on a many-body Floquet system consisting of atoms in an optical lattice subjected to ultrastrong sign-changing amplitude modulation.Using a double-quench protocol, we measure an inverse participation ratio quantifying the degree of prethermal localization as a function of tunable drive parameters and interactions.We obtain a complete prethermal map of the drive-dependent properties of Floquet matter spanning four square decades of parameter space.Following the full time evolution, we observe sequential formation of two prethermal plateaux, interaction-driven ergodicity, and strongly frequency-dependent dynamics of long-time thermalization.The quantitative characterization of the prethermal Floquet matter realized in these experiments, along with the demonstration of control of its properties by variation of drive parameters and interactions, opens a new frontier for probing far-from-equilibrium quantum statistical mechanics and new possibilities for dynamical quantum engineering.
We report Floquet band engineering of long-range transport and direct imaging of Floquet-Bloch bands in an amplitude-modulated optical lattice. In one variety of Floquet-Bloch bands we observe tunable rapid long-range high-fidelity transport of a Bose condensate across thousands of lattice sites. Quenching into an opposite-parity Floquet-hybridized band allows Wannier-Stark localization to be controllably turned on and off using modulation. A central result of this work is the use of transport dynamics to demonstrate direct imaging of a Floquet-Bloch band structure. These results demonstrate that transport in dynamical Floquet-Bloch bands can be mapped to transport in quasistatic effective bands, opening a path to cold atom quantum emulation of ultrafast multiband electronic dynamics.