DEVELOPING A STRONG DRIVING TOOLKIT FOR FLOQUET SYSTEMS WITH SUPERCONDUCTING QUBITS

Abstract

Simple systems such as a spin 1/2 particle driven by periodic drives can exhibit surprisingly rich physics. These systems can be described as lattices in phase space, in analogy with spatially periodic systems. By varying the phase and amplitude of the drives one can synthesize arbitrary complex hopping terms where the dimensionality of the effective lattice is set by the number of drives. In this thesis, we explore how to construct a 2-dimensional synthetic lattice with a topological band structure and study the effect of dissipation on the steady state of a strongly driven system.

Topological band structures are well known to produce symmetry-protected chiral edge modes which transport particles unidirectionally. The half-BHZ (Bernevig–Hughes–Zhang) model, defined as a 2-d lattice of two-level systems, exhibits edge modes in the limit that the hopping exceeds the on-site energy splitting. We synthesize this model by coupling a qubit to a cavity and driving it with a large external effective magnetic field. In the limit of strong driving, the Floquet lattice can be topologically non-trivial, where the analog of a topologically protected edge state is a topologically protected energy pump. We have developed a toolkit for generating and characterizing the large synthetic magnetic fields required to reach the topological regime.

In the second part of the thesis, we explore a surprising result discovered in the process of characterizing the large synthetic fields: the stabilization of Floquet states in the presence of dissipation. While dissipation generally leads to errors in quantum systems, it can also lead to the stabilization of specific states of a driven system. This concept has been extensively studied in the context of optical pumping in atomic systems to drive systems to a pure ground state. Here we show that cavity-induced loss can have the dramatic and unexpected consequence of purifying a mixed state to a dynamically driven Floquet state.