Floquet engineering offers exhilarating opportunities for controlling the dynamics of quantum many body systems and realizing new nonequilibrium phases of matter. However, generic interacting Floquet systems tend to heat up due to energy absorption from the drive, washing away the desired behavior. In this work, the authors characterize the steady states of an interacting electronic system, coupled to a phonon heat bath. They determine the regimes where the system-bath coupling stabilizes Floquet-insulator-like states, an important prerequisite for realizing topological states through Floquet engineering.
Floquet engineering offers exhilarating opportunities for controlling the dynamics of quantum many body systems and realizing new nonequilibrium phases of matter. However, generic interacting Floquet systems tend to heat up due to energy absorption from the drive, washing away the desired behavior. In this work, the authors characterize the steady states of an interacting electronic system, coupled to a phonon heat bath. They determine the regimes where the system-bath coupling stabilizes Floquet-insulator-like states, an important prerequisite for realizing topological states through Floquet engineering.
Floquet engineering is an important tool for realizing topologically nontrivial band structures for charge-neutral atoms in optical lattices. However, the preparation of a topological-band-insulator-type state of fermions, with one nontrivial quasi-energy band filled completely and the others empty, is challenging as a result of both driving induced heating as well as imperfect adiabatic state preparation (with the latter induced by the unavoidable gap closing when passing the topological transition). An alternative procedure that has been proposed is to prepare such states dissipatively, i.e. as a steady state that emerges when coupling the system to reservoirs. Here we discuss a concrete scheme that couples the system to a weakly interacting Bose condensate given by second atomic species acting as a heat bath. Our strategy relies on the engineering of the potential for the bath particles, so that they occupy weakly coupled tubes perpendicular to the two-dimensional system. Using Floquet-Born-Markov theory, we show that the resulting nonequilibrium steady state of the driven-dissipative system approximates a topological insulator. We even find indications for the approximate stabilization of an anomalous Floquet topological insulator, a state that is impossible to realize in equilibrium.
Floquet engineering, the control of a quantum system by means of time-periodic driving, allows to modify the properties of a system so that it is described by an approximate effective time-independent Hamiltonian. However, in the presence of interactions the stabilization of interesting many-body ground states of such effective Hamiltonians is possible only on a certain time scale, beyond which Floquet heating sets in, as it results from unwanted driving induced resonant excitation. Moreover, the preparation of the ground state of such Floquet engineered effective Hamiltonians usually has to be accomplished adiabatically, which is another source of heating, especially when a phase transition has to be passed in a large system. Here, we propose a general dissipative strategy for the preparation and stabilization of effective ground states that are protected by an energy gap, such as topologically ordered states. It is scalable and relies on coupling the driven system to a thermal bath, the properties of which are chosen so that it both suppresses Floquet heating and guides the system into a non-equilibrium steady state with a large occupation of the effective ground-state. The small residual occupations of effective excited states are non-thermal, reflecting the non-equilibrium nature of the scheme. We use the Floquet-Born-Markov master equation to verify the proposed strategy. In particular, we discuss the preparation of both a one-dimensional Mott insulator and a two-dimensional fractional Chern insulator in strongly driven Bose-Hubbard systems.
Periodically-driven (Floquet) quantum systems are ubiquitous in science and technology. For example, when a laser illuminates a material or an AC voltage is applied to a device, the system is well-described by a time-periodic Hamiltonian. In recent years, periodic driving has been proposed, not just as a tool to excite and probe devices, but actually as a mechanism of engineering new phases of matter, some of which have no equilibrium analog. However, with this promise comes a serious problem. Intuitively, if energy is injected into and distributed throughout a system, it is no surprise that it tends to heat up indefinitely to infinite temperature. In this thesis, we study the mechanisms of heating, i.e. the process of thermalization, in Floquet systems and propose methods to control them. Specifically, for non-interacting Floquet systems that are coupled to external bosonic and fermionic baths (e.g. laser-driven electrons in a semiconductor that interact with phonons and an external lead), we classify the relevant scattering processes that contribute to cooling/heating in the Floquet bands and suggest methods to suppress heating via bandwidth-restrictions on the baths. We find that is possible, with appropriate dissipative engineering, to stabilize a controlled incompressible nonequilibrium steady-state resembling a ground state - a state we term the "Floquet insulator." We extend this analysis to include short-range interactions that contribute additional heating processes and show, under the same framework, that heating can be controlled with dissipation. In the process, we develop a simple effective model for the Floquet band densities that captures the essence of all the Floquet scattering processes and that is useful for ballparking experimentally-relevant estimates of heating. Next, we turn our attention to strongly-interacting closed Floquet systems and study how heating emerges through a proliferation of resonances. We find a novel integrable point governing the strong-interaction limit of the Floquet system and examine the breakdown of integrability via the proliferation of resonances. We observe two distinct scaling regimes, attributed to non-thermal and thermal behavior, and discover a power-law scaling of the crossover between them as a function of system size. The lingering ergodicity-breaking effects of the conserved quantities in the vicinity (in parameter space) of the integrable point at finite size is a phenomena we term "near-integrability." These results suggest that small quantum systems, which are accessible currently in many platforms (e.g. trapped ions, cold atoms, superconducting devices), intrinsically host non-thermal states that one may be able to utilize to avoid heating. Furthermore, our results suggest a "dual" interpretation, in the thermodynamic limit, that a periodically-driven system exhibits prethermalization as a power-law in interaction strength.
We review methods for using time-periodic fields (e.g., laser or microwave fields) to induce non-equilibrium topological phenomena in quantum many-body systems. We discuss how such fields can be used to change the topological properties of the single particle spectrum, and key experimental demonstrations in solid state, cold atomic, and photonic systems. The single particle Floquet band structure provides a stage on which the system's dynamics play out; the crucial question is then how to obtain robust topological behaviour in the many-particle setting. In the regime of mesoscopic transport, we discuss manifestations of topological edge states induced in the Floquet spectrum. Outside the context of mesoscopic transport, the main challenge of inducing stable topological phases in many-body Floquet systems is their tendency to absorb energy from the drive and thereby to heat up. We discuss three routes to overcoming this challenge: long-lived transient dynamics and prethermalization, disorder-induced many-body localization, and engineered couplings to external baths. We discuss the types of phenomena that can be explored in each of these regimes, and their experimental realizations.
Floquet engineering of closed quantum systems can lead to the formation of long-lived prethermal states that, in general, eventually thermalize to infinite temperature. Coupling these driven systems to dissipative baths can stabilize such states, establishing a true nonequilibrium steady state. We demonstrate that, in a certain strongly interacting lattice model coupled to a bath and driven by an electric field, such steady states can have the remarkable property that the cycle-averaged rate of energy transfer between the lattice and the baths vanishes. Despite this, we show that these states retain a clear nonequilibrium nature.
Floquet driving underlies Hamiltonian and gate engineering, and produces dynamical orders with no equilibrium counterpart. These phenomena are, however, transient in well-isolated systems. We show that statically coupled dissipative auxiliaries cool the system toward low-energy states of the Floquet-engineered Hamiltonian, stabilizing orders in the steady state. The excess energy density is controllably small at high drive frequency and weak coupling and is captured by rate theory based on Fermi's Golden Rule. We numerically confirm robust cooling in a Floquet-engineered transverse-field Ising chain in both phases, and demonstrate discrete time-crystalline order, with a period-doubled magnetization response, in the steady state of a long-range Ising chain. Our results provide a rare analytical handle on the steady states of driven dissipative systems.