We study a quantum system that consists of two fermionic chains coupled by a driven quantum point contact (QPC). The QPC contains a bond with a periodically varying tunneling amplitude. Initially, the left chain is packed with fermions, while the right one is empty. We numerically track the evolution of the system and demonstrate that, at frequencies above a certain threshold, the current through the QPC halts, and the particle imbalance between the chains remains forever. This implies a spectacular breakdown of the Floquet version of the eigenstate thermalization hypothesis that predicts a homogeneous particle density profile at large times. We confirm the effect for various driving protocols and interparticle interactions.
We study a quantum system that consists of two fermionic chains coupled by a driven quantum point contact (QPC). The QPC contains a bond with a periodically varying tunneling amplitude. Initially, the left chain is packed with fermions, while the right one is empty. We numerically track the evolution of the system and demonstrate that, at frequencies above a certain threshold, the current through the QPC halts, and the particle imbalance between the chains remains forever. This implies a spectacular breakdown of the Floquet version of the eigenstate thermalization hypothesis that predicts a homogeneous particle density profile at large times. We confirm the effect for various driving protocols and interparticle interactions.
We study the transport of noninteracting fermions through a periodically driven quantum point contact (QPC) connecting two tight-binding chains. Initially, each chain is prepared in its own equilibrium state, generally with a bias in chemical potentials and temperatures. We examine the heating rate (or, alternatively, energy increase per cycle) in the nonequilibrium time-periodic steady state established after initial transient dynamics. We find that the heating rate vanishes identically when the driving frequency exceeds the bandwidth of the chain. We first establish this fact for a particular type of QPCs where the heating rate can be calculated analytically. Then we verify numerically that this nonequilibrium phase transition is present for a generic QPC. Finally, we derive this effect perturbatively in leading order for cases when the QPC Hamiltonian can be considered a small perturbation. Strikingly, we discover that for certain QPCs the current averaged over the driving cycle also vanishes above the critical frequency, despite a persistent bias. This shows that a driven QPC can act as a frequency-controlled quantum switch.
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.
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.
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.
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 compute the Floquet Hamiltonian HF for weakly interacting fermions subjected to a continuous periodic drive using a Floquet perturbation theory (FPT) with the interaction amplitude being the perturbation parameter. This allows us to address the dynamics of the system at intermediate drive frequencies $\ensuremath{\hbar}{\ensuremath{\omega}}_{D}\ensuremath{\ge}{V}_{0}\ensuremath{\ll}{\mathcal{J}}_{0}$, where J0 is the amplitude of the kinetic term, ${\ensuremath{\omega}}_{D}$ is the drive frequency, and V0 is the typical interaction strength between the fermions. We compute, for random initial states, the fidelity F between wave functions after a drive cycle obtained using HF and that obtained using exact diagonalization (ED). We find that FPT yields a substantially larger value of F compared to its Magnus counterpart for ${V}_{0}\ensuremath{\le}\ensuremath{\hbar}{\ensuremath{\omega}}_{D}$ and ${V}_{0}\ensuremath{\ll}{\mathcal{J}}_{0}$. We use the HF obtained to study the nature of the steady state of an weakly interacting fermion chain; we find a wide range of ${\ensuremath{\omega}}_{D}$ which leads to subthermal or superthermal steady states for finite chains. The driven fermionic chain displays perfect dynamical localization for V0=0; we address the fate of this dynamical localization in the steady state of a finite interacting chain and show that there is a crossover between localized and delocalized steady states. We discuss the implication of our results for thermodynamically large chains and chart out experiments which can test our theory.