Non-Integrable Dynamics in a Trapped-Ion Quantum Simulator

Abstract

From the first demonstration of a quantum logic gate in 1995 to the actualizationof a “quantum advantage” over classical technology a few years ago, the field of quantum information has made remarkable progress during my lifetime. Multiple quantum technology platforms have developed to the point that companies and governments are investing heavily in the industry. A primary focus is the development of fault-tolerant error correction, a technology expected to be necessary for large-scale digital quantum computers. Meanwhile analog quantum simulators, a subclass of quantum computers that apply unitary evolutions instead of digitized gates, are at the forefront of controllable quantum system sizes. In place of algorithms, analog quantum simulators are naturally suited to study many-body physics and model certain materials and transport phenomena. In this thesis I discuss an analog quantum simulator based on trapped +Yb171 ions and its use for studying dynamics and thermalizing properties of the non-integrable long-range Ising model with system sizes near the limit of classical tractability. In addition to the technical properties of the simulator, I present three select experiments that I worked on during my PhD. The first is an observation of a phenomenon in nonequilibrium physics, a dynamical phase transition (DPT). While equilibrium phase transitions follow robust universal principles, DPTs are challenging to describe with conventional thermodynamics. We present an experimental observation and characterization of a DPT with up to 53 qubits. We also explore the system’s ability to simulate physics beyond its own by implementing a quasiparticle confinement Hamiltonian. Here we see that the natural long-range interactions present in the simulator induce an effective confining potential on pairs of domain-wall quasiparticles, which behave similarly to quarks bound into mesons. We measure post-quench dynamics to identify how confinement introduces low-energy bound states and inhibits thermalization. Lastly, we use the individual-addressing capabilities of our simulator to implement Stark many-body localization (MBL) with a linear potential gradient. Stark MBL provides a novel, disorder-free method for localizing a quantum system that would otherwise thermalize under evolution. We explore how the localized phase depends on the gradient strength and uncover the presence of correlations using interferrometric double electron-electron resonance (DEER) measurements. These experiments show the capability of our experiment to study complex quantum dynamics in systems near 50 qubits and above.