Periodically driven quantum systems provide a powerful route to engineer novel states of matter by controlling their effective Hamiltonians through external fields. However, most treatments are usually simplified by considering the high-frequency limit, and do not account for the processes taking place in the transient regime during the onset of the drive. In this work, we introduce a time and momentum resolved tunneling spectroscopy protocol to probe the instantaneous energy spectrum of Floquet-driven systems beyond the high-frequency regime, capturing both emergent effects and non-adiabatic phenomena without requiring explicit reconstruction of the full time-dependent Green's function. We benchmark the method on driven non-interacting fermionic models, and then generalize the approach to strongly correlated systems with the aid of time-dependent density matrix renormalization group techniques. We also provide a microscopic description to the emergence of in-gap states under resonant driving, and briefly explore its finite temperature analog.
Periodically driven quantum systems provide a powerful route to engineer novel states of matter by controlling their effective Hamiltonians through external fields. However, most treatments are usually simplified by considering the high-frequency limit, and do not account for the processes taking place in the transient regime during the onset of the drive. In this work, we introduce a time and momentum resolved tunneling spectroscopy protocol to probe the instantaneous energy spectrum of Floquet-driven systems beyond the high-frequency regime, capturing both emergent effects and non-adiabatic phenomena without requiring explicit reconstruction of the full time-dependent Green's function. We benchmark the method on driven non-interacting fermionic models, and then generalize the approach to strongly correlated systems with the aid of time-dependent density matrix renormalization group techniques. We also provide a microscopic description to the emergence of in-gap states under resonant driving, and briefly explore its finite temperature analog.
Driving a quantum system periodically in time can profoundly alter its long-time correlations and give rise to exotic quantum states of matter. The complexity of the combination of many-body correlations and dynamic manipulations has the potential to uncover a whole field of new phenomena, but the theoretical and numerical understanding becomes extremely difficult. We now propose a promising numerical method by generalizing the density matrix renormalization group to a superposition of Fourier components of periodically driven many-body systems using Floquet theory. With this method we can study the full time-dependent quantum solution in a large parameter range for all evolution times, beyond the commonly used high-frequency approximations. Numerical results are presented for the isotropic Heisenberg antiferromagnetic spin-1/2 chain under both local(edge) and global driving for spin-spin correlations and temporal fluctuations. As the frequency is lowered, we demonstrate that more and more Fourier components become relevant and determine strong length- and frequency-dependent changes of the quantum correlations that cannot be described by effective static models.
Periodically driven systems have emerged as a useful technique to engineer the properties of quantum systems, and are in the process of being developed into a standard toolbox for quantum simulation. An outstanding challenge that leaves this toolbox incomplete is the manipulation of the states dressed by strong periodic drives. The state-of-the-art in Floquet control is the adiabatic change of parameters. Yet, this requires long protocols conflicting with the limited coherence times in experiments. To achieve fast control of nonequilibrium quantum matter, we generalize the notion of variational counterdiabatic driving away from equilibrium focusing on Floquet systems. We derive a nonperturbative variational principle to find local approximations to the adiabatic gauge potential for the effective Floquet Hamiltonian. It enables transitionless driving of Floquet eigenstates far away from the adiabatic regime. We discuss applications to two-level, Floquet band, and interacting periodically driven models. The developed technique allows us to capture nonperturbative photon resonances and obtain high-fidelity protocols that respect experimental limitations like the locality of the accessible control terms.
Time-periodically driven systems are a versatile toolbox for realizing interesting effective Hamiltonians. Heating, caused by excitations to high-energy states, is a challenge for experiments. While most setups so far address the relatively weakly interacting regime, it is of general interest to study heating in strongly correlated systems. Using Floquet dynamical mean-field theory, we study nonequilibrium steady states (NESS) in the Falicov-Kimball model, with time-periodically driven kinetic energy or interaction. We systematically investigate the nonequilibrium properties of the NESS. For a driven kinetic energy, we show that resonant tunneling, where the interaction is an integer multiple of the driving frequency, plays an important role in the heating. In the strongly correlated regime, we show that this can be well understood using Fermi's golden rule and the Schrieffer-Wolff transformation for a time-periodically driven system. We furthermore demonstrate that resonant tunneling can be used to control the population of Floquet states to achieve ``photodoping.'' For driven interactions introduced by an oscillating magnetic field near a widely adopted Feshbach resonance, we find that the double occupancy is strongly modulated. Our calculations apply to shaken ultracold-atom systems and to solid-state systems in a spatially uniform but time-dependent electric field. They are also closely related to lattice modulation spectroscopy. Our calculations are helpful to understand the latest experiments on strongly correlated Floquet systems.
Periodically driven quantum systems provide a versatile platform for engineering and exploring non-equilibrium states of matter that have no equilibrium counterparts– a field commonly re- ferred to as Floquet engineering. The research presented in this thesis addresses the microscopic interpretation of experimental spectroscopic signatures, the stability of these driven states in the presence of strong many-body interactions, and the emergence of novel forms of non-equilibrium criticality encoded in quantum entanglement. The first part of the thesis focuses on the interpretation of time- and angle-resolved photo- emission spectroscopy (tr-ARPES), the primary experimental tool for detecting Floquet–Bloch sidebands (FBs). The measured signal reflects interference between processes occurring both inside the material and in the vacuum. In particular, Floquet-dressed initial states coexist and interfere with Volkov-dressed final states arising from the laser-assisted photoelectric effect (LAPE). Their experimental identification requires careful comparison with theoretical predic- tions. Using graphene as a model Dirac material, we perform a systematic comparison between two theoretical frameworks: the first-order perturbative Born approximation (PB1) and time- dependent nonequilibrium Green’s functions (tdNEGF), and compare them with experimental results. We disentangle intrinsic Floquet states, LAPE, and their interference, and quantify how polarization, incidence angle, and near-surface screening shape the observed spectra. Our findings show that, once matrix elements are included, both methods capture qualitative trends, but tdNEGF is necessary to describe the full energy–momentum-resolved features, including hybridization gaps. While non-interacting systems exhibit well-defined FBs, interacting systems absorb energy and can evolve toward an infinite-temperature state. To study this competition between coherent driving and many-body heating, in the second part we consider a one-dimensional chain of interacting spinless fermions using exact diagonalization (ED) and matrix product state (MPS) methods. We compute time-dependent spectral functions and correlation measures, and compare the spectral width of the many-body excitation continuum with the driving frequency to define low- and high-frequency regimes. In our parameter regime, low-frequency driving leads to strong overlap between Floquet sectors, resulting in rapid heating and loss of coherence. For weakly populated continua, we find a transient timescale for the suppression of FBs. When the driving frequency exceeds the continuum width, FBs are well separated and long-lived. Thefinalpartofthethesisinvestigatesnon-equilibriumphenomenafromaninformation-theoretic perspective. Wereportanewclassofdynamicalphasetransitions,termedtemporalentanglement transitions (TET) characterized by non-analytic reorganizations of the entanglement spectrum, in a periodically driven transverse-field Ising chain. These transitions occur in the spectrum of the entanglement Hamiltonian and are signaled by dynamical spontaneous symmetry breaking, marked by the closure of the Schmidt gap and parity flips. These transitions remain invisible to conventional local observables. Finite-size scaling reveals that TET belong to a universality class with a correlation-length exponent ν = 1, mirroring equilibrium Ising universality despite their purely dynamical origin.
We present a computational technique to calculate time- and momentum-resolved nonequilibrium spectral density of correlated systems using a tunneling approach akin to scanning tunneling spectroscopy. The important difference is that our probe is extended, basically a copy of the sample, allowing one to extract the momentum information of the excitations. We illustrate the method by measuring the spectrum of a Mott-insulating extended Hubbard chain after a sudden quench with the aid of time-dependent density-matrix renormalization-group calculations. We demonstrate that the system realizes a nonthermal state that is an admixture of spin and charge density wave states, with corresponding signatures that are recognizable as in-gap subbands. In particular, we identify a band of excitons and one of stable antibound states at high energies that gains enhanced visibility after the pump. We do not appreciate noticeable relaxation within the time scales considered, which is attributed to the lack of decay channels due to spin-charge separation. These ideas can be readily applied to study transient dynamics and spectral signatures of correlation-driven nonequilibrium processes.
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.