The extreme tunability and control that atomic physics provides makes quantum gases

ideal platforms for experimentally realizing novel synthetic materials beyond what is

traditionally realizable in condensed matter experiments. In particular, the ability to

control interparticle interactions allows for the realization of long lived nonequilibrium

states, 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 ultracold

lithium in modulated and static one-dimensional optical lattices. First, I present an

overview of the experimental apparatus which includes a description of the generation of

our Bose-Einstein condensate and optical lattices. Then I step through four experiments

which we conducted. The rst two involve studying spatial dynamics in static optical

lattices in the ground and the excited bands which realize position-space Bloch oscillations

and a relativistic harmonic oscillator respectively. The third experiment studies transport

in Floquet hybridized optical lattice Bloch bands, and the fourth experiment investigates

prethermalization in strongly modulated lattices with tunable interactions.

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.

Quantum degenerate gases, in the form of Bose-Einstein condensates, are ideal objects for probing fundamental quantum mechanical phenomena. These platforms are highly isolated, and enable coherent control and manipulation of quantum matter with exquisite precision. The work presented in this thesis utilizes quantum degenerate gases of bosonic $^7$Li which have tunable interactions, allowing for studies of both single-particle and many-body physics. By subjecting these gases to periodic driving, a rich and diverse landscape of physical phenomena is unlocked. I will first describe our work realizing a thermodynamic engine with a quantum degenerate working fluid, achieved via slow periodic driving, and the effect of quantum degeneracy on engine performance. In the regime of fast driving, I will then propose a scheme for a noise-tolerant continuously-trapped atom interferometer.

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.