Novel Non-Equilibrium Steady States and Phases in Periodically Driven and Measured Quantum Systems

The advent of phases of matter which are inherently and explicitly quantum mechanical has made it possible to create devices with exciting capabilities that would otherwise be completely impossible.
Recently, experimental advancements are beginning to make it feasible to not just create such quantum materials, but actually manipulate microscopic details in these systems to engineer their properties on demand. Furthermore, by externally interacting with quantum systems, it is possible to induce phases of matter (such as time crystals and materials exhibiting anomalous topological properties) that are forbidden for isolated systems in equilibrium. In this dissertation, we introduce a variety of new classes of physically realizable, non-equilibrium models with a focus on systems which are periodically driven or subjected to a periodic protocol of quantum measurements. We leverage this driving and these quantum measurements to induce non-trivial steady states and phases of matter with surprising and appealing novel properties.

We first examine free fermionic lattice systems subject to quantum measurements (as well as other quantum operations such as particle injection). For example, we consider the effect of a measurement device (along with a variety of other kinds of disturbances) which is dragged through a Fermi sea. The device induces a wake pattern (in analogy with a boat moving through water) which is characterized by the speed at which the probe is moved through the system and its direction with respect to the lattice. Furthermore, stark contrasts emerge between the wake geometry of a quantum disturbance (such as a measurement) and classical disturbances (such as a potential). These effects are especially prominent at half-filling where the the density wake due to measurements disappears and the wake from a moving particle extractor is temperature invariant.

We also introduce a model where lattice fermions are subjected to a periodic sequence of measurements which break the time reversal symmetry of the original free hopping evolution. We show that this protocol induces chiral edge transport in the system that is protected against perturbations and deformations of the boundary at high measurement rates. This model shows that it is possible to induce chiral edge modes in an analogous way to those in anomalous Floquet topological insulators via measurements alone. On the other hand, the measurement-induced model also exhibits novel, distinct features due to the non-unitary nature of the evolution.

Finally, we turn to consider exotic non-equilibrium dynamics which may be induced via a combination of periodic driving and interactions, instead of through a protocol of measurements. Namely, we introduce a broad class of interacting Floquet models which exhibit special points in parameter space where the dynamics becomes exactly solvable. Additionally, at other interaction strengths and driving frequencies, we show that the system exhibits Hilbert space fragmentation with some subspaces corresponding to a (complex) permutation of number states while others may be non-integrable and thermalize. When disorder is added to the system, it is shown that this dynamics is stabilized within finite regions of parameters space (thereby corresponding to true dynamical phases of matter) instead of just at finely tuned parameter values. Importantly, the phases realizable in this fashion include many of the uniquely non-equilibrium materials which are currently the focus of active interest including, for example, time crystals and anomalous Floquet topological insulators. In this way, we show how our introduction and analysis of this broad class of interacting Floquet models allows for new insights into these non-equilibrium phases as well as provides a framework upon which to systematically search for and examine other completely novel non-equilibrium steady states.