Session F2: Topology and Localization in Floquet Systems

Floquet States: Anomalous topological phases and steady state engineering

Periodically driven quantum systems provide a novel and versatile platform for realizing topological phenomena. In my talk I'll provide a brief introduction to the Floquet path to topological behavior. Next, I will concentrate on a remarkable Floquet state that has no static analog: A 2d system which has chiral edge states, alongside fully localized bulk orbitals. This unique situation serves as the basis for a new topologically-protected non-equilibrium transport phenomenon: quantized non-adiabatic charge pumping. We identify the bulk topological invariant that characterizes this new phase,which we dub the 'anomalous Floquet Anderson Insulator'. In the second part of my talk, I will discuss recent results on stabilizing desired steady states in periodically driven fermionic semiconducting systems using bosonic and fermionic bath engineering.   

When do Floquet systems fail to heat?

Periodically driven quantum systems do not have a conserved energy. Thus, statistical mechanical lore holds that if they thermalize, it must be to infinite temperature. I will first show this holds in undriven systems that satisfy the eigenstate thermalization hypothesis. I will then present two counter-examples to infinite temperature heating. The first is the bosonic O(N) model at infinite N, in which the steady states are paramagnetic and have non-trivial correlations. The second is the Clifford circuit model, which can fail to heat depending on the choice of circuit elements. The resulting steady states can then be localized or delocalized but not ergodic. Such models shed light on the nature of interacting Floquet localization.   

Floquet thermodynamics--nature of ensembles and order under periodic driving

We study the long-time behaviour of many-body Floquet systems--closed quantum systems under temporally periodic driving, arguably the simplest deviation from equilibrium. We begin by showing that generically such interacting systems heat up and discuss the microcopic mechanism by which this happens. We then discuss two ways to prevent this: integrability and disorder. In the integrable case, a "periodic Gibbs ensemble" may be derived by maximising the entropy and shown to exactly describe the long-time steady state, while in the interacting disordered (many-body localised, or MBL) case, we identify the regime under which driving does not delocalise the system. We conclude by discussing the nontrivial steady-states achieved in interacting Floquet systems.   

Floquet engineering with ultracold fermions: From Haldane's model of topological bands to spin-dependent lattices

Periodically driving a system of ultracold fermionic atoms in an optical lattice allows for implementing a large variety of effective Hamiltonians through Floquet engineering. Using this concept we realize the Haldane model which is a fundamental example of a Hamiltonian exhibiting topologically distinct phases of matter. By loading non-interacting degenerate fermions in a periodically modulated honeycomb lattice we can implement and characterize the topological band structure. We explore the resulting Berry-curvatures of the lowest band and map out topological phase transitions connecting distinct regimes. \\ \\ Such a technique may be extended to also address internal degrees of freedom. By periodically modulating a magnetic field gradient we tune the relative amplitude and sign of the tunneling for different internal states. Thereby we experimentally realize spin-dependent effective Hamiltonians where one state can be pinned to the lattice, while the other remains itinerant. For each spin state, the differing band structure can be characterized either by measuring the expansion of an atomic cloud in the lattice, or by a measurement of the effective mass through dipole oscillations. Furthermore we use the tunability of ultracold atoms to investigate the role of interactions.   

Localization effects in periodically driven many-body systems

In this talk, I will discuss the emergence of quasi, or sometimes strictly, conserved quantities in periodically driven many-body quantum systems. In the particular case of a many-body localized Hamiltonian, characterized by a full set of local integral of motions (LIOMs), I will show that the driven system itself admits a full set of strictly conserved LIOMs, if the driving frequency is high enough. Moreover, I will show that the ideas developed in the context of driven systems can be generalized to describe the emergence of “pre-thermal” behavior in a wide class of both closed and driven systems.