Suppressing Floquet thermalization is an important goal in the field of Floquet engineering. Here, we propose a driving transparency mechanism to suppress the Floquet thermalization in periodically driven tilted lattices of interacting spinless fermions. By leveraging the interplay between the tilting and interaction, the system can be engineered to prevent direct energy absorption from the driving at particular frequencies. We analytically determine these driving transparency frequencies through the Floquet time-dependent perturbation theory. The system is near-integrable at the driving transparency frequencies. The suppression of thermalization by the driving transparency is demonstrated numerically by the violation of the Floquet eigenstate thermalization hypothesis, the retention of the initial state, and the logarithmic growth of entanglement entropy. Our work provides an intuitive way to suppress Floquet thermalization and offers an opportunity to engineer exotic nonequilibrium Floquet states in tilted lattice systems.
Suppressing Floquet thermalization is an important goal in the field of Floquet engineering. Here, we propose a driving transparency mechanism to suppress the Floquet thermalization in periodically driven tilted lattices of interacting spinless fermions. By leveraging the interplay between the tilting and interaction, the system can be engineered to prevent direct energy absorption from the driving at particular frequencies. We analytically determine these driving transparency frequencies through the Floquet time-dependent perturbation theory. The system is near-integrable at the driving transparency frequencies. The suppression of thermalization by the driving transparency is demonstrated numerically by the violation of the Floquet eigenstate thermalization hypothesis, the retention of the initial state, and the logarithmic growth of entanglement entropy. Our work provides an intuitive way to suppress Floquet thermalization and offers an opportunity to engineer exotic nonequilibrium Floquet states in tilted lattice systems.
This work presents a theoretical investigation of dynamic stabilization in interacting quantum many-body systems via high-frequency periodic driving. Using Floquet theory and the Magnus expansion, we derive the effective time-independent Hamiltonian governing the slow dynamics of a driven spin chain. We show that the external field induces a parametric renormalization of the transverse tunneling terms through a zeroth-order Bessel function dependence, leading to a critical drive amplitude at which transport is strongly suppressed. This suppression of the lowest-order hopping term gives rise to a long-lived prethermal regime in which many-body thermalization is significantly delayed. The resulting dynamics exhibit a sharp reduction in the short-to-intermediate time entanglement entropy growth rate. The framework is consistent with known results in Floquet engineering and coherent destruction of tunneling, and provides a unified interpretation of transport suppression and delayed scrambling in periodically driven systems. A falsifiable experimental protocol using ultracold atoms in optical lattices is proposed to validate the predicted threshold behavior and prethermal stabilization mechanism.
Abstract We demonstrate the existence of exact Floquet flat bands in a class of non-integrable quantum many-body Hamiltonians leading to strong violation of the eigenstate thermalization hypothesis in the presence of a two-tone drive characterized by frequencies Ω1 and Ω 2 = ν Ω 1 , where ν is an integer. We provide the exact analytic condition for this phenomenon to occur for a generic protocol. A small departure from the flat band conditions leads to suppression of heating over a long prethermal timescale in an otherwise ergodic many-body system away from integrable or perturbative regimes; we elucidate the central role of the flat band behind such heating suppression. Our analysis indicates the existence of a perturbative Floquet Hamiltonian, away from high drive frequency/amplitude limit, which controls the dynamics of the driven system near such flat bands. We demonstrate this phenomenon by exact numerical studies of Floquet bandwidth, spectral form factor, entanglement and Shannon entropies, heat absorption, and correlation functions of a driven Rydberg chain. We also study the corresponding micromotion which exhibits coherent reversal of excitations reminiscent of echoes; in addition, it harbors an exact reflection symmetry about t = T 1 / 2 , where T 1 = 2 π / Ω 1 , which we elucidate. We discuss experiments which can test our theory.
Conventional wisdom suggests that the long time behavior of isolated interacting periodically driven (Floquet) systems is a featureless maximal entropy state characterized by an infinite temperature. Efforts to thwart this uninteresting fixed point include adding sufficient disorder to realize a Floquet many-body localized phase or working in a narrow region of drive frequencies to achieve glassy non-thermal behavior at long time. Here we show that in clean systems the Floquet eigenstates can exhibit non-thermal behavior due to finite system size. We consider a one-dimensional system of spinless fermions with nearest-neighbor interactions where the interaction term is driven. Interestingly, even with no static component of the interaction, the quasienergy spectrum contains gaps and a significant fraction of the Floquet eigenstates, at all quasienergies, have non-thermal average doublon densities. We show that this non-thermal behavior arises due to emergent integrability at large interaction strength and discuss how the integrability breaks down with power-law dependence on system size.
We demonstrate the existence of exact Floquet flat bands implying strong violation of the eigenstate thermalization hypothesis in a large class of closed quantum many-body systems in the presence of a two-rate drive characterized by frequencies Ω1 and Ω2=νΩ1. We provide the exact analytic condition for this phenomenon to occur for a generic protocol; in particular, ν=(2p+1), where p is an integer, leads to such flat bands for both square-pulse and cosine drive protocols for arbitrary Ω1. In the vicinity of these points, heating is suppressed up to very long timescales in such driven systems, leading to a prethermal regime; we demonstrate this by exact numerical studies of distribution and bandwidth of the Floquet eigenstates, spectral form factor, entanglement entropy, and correlation functions of an experimentally realizable finite driven Rydberg chain. The corresponding micromotion exhibits coherent reversal of excitations reminiscent of echoes. Our analysis constitutes a yet unexplored mechanism for heating suppression in driven closed quantum 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.
This work provides a convenient and powerful means towards the engineering of Floquet bands via Bloch oscillations, by adding a tilted linear potential to periodically driven lattice systems. The added linear field not only restricts the spreading of a time-evolving wave packet but also, depending on the ratio between the Bloch oscillation frequency and the modulation frequency of the periodic driving, dramatically modifies the band profile and topology. Specifically, we consider a driven Aubry-Andr\'e-Harper model as a working example, in the presence of a linear field. Almost flat Floquet bands or Floquet bands with large Chern numbers due to the interplay between the periodic driving and Bloch oscillations can be obtained, with the band structure and topology extensively tunable by adjusting the ratio of two competing frequencies. To confirm our finding, we further execute the Thouless pumping of one and two interacting bosons in such a lattice system and establish its connection with the topological properties of single- and two-particle Floquet bands.