Floquet theory is a widely used framework to describe the dynamics of periodically driven quantum systems. The usual scenario to describe such systems is to consider the effect of an external control with a definite period in time that can act either locally or globally on the system of interest. However, apart from periodicity, such drives typically lack classical correlations or additional structure. In this work, we consider drives with intrinsic dynamics that undergo self-organization, leading to periodic steady states with emergent symmetries. To substantiate our results, we consider two examples of one-dimensional quantum spin chains coupled to a classical Kuramoto model. First, we investigate a Kuramoto model with all-to-all coupling driving a one-dimensional quantum Ising chain into a time-periodic steady state with an emergent translational symmetry. Next, we consider a Kuramoto model in a zigzag lattice driving an XX spin chain. The dynamics of traveling waves in the Kuramoto model trimerizes the lattice, effectively inducing topological behavior that can be exploited to perform topological pumping. Our results can be experimentally implemented in digital and analog near-term quantum devices.
Floquet theory is a widely used framework to describe the dynamics of periodically driven quantum systems. The usual scenario to describe such systems is to consider the effect of an external control with a definite period in time that can act either locally or globally on the system of interest. However, apart from periodicity, such drives typically lack classical correlations or additional structure. In this work, we consider drives with intrinsic dynamics that undergo self-organization, leading to periodic steady states with emergent symmetries. To substantiate our results, we consider two examples of one-dimensional quantum spin chains coupled to a classical Kuramoto model. First, we investigate a Kuramoto model with all-to-all coupling driving a one-dimensional quantum Ising chain into a time-periodic steady state with an emergent translational symmetry. Next, we consider a Kuramoto model in a zigzag lattice driving an XX spin chain. The dynamics of traveling waves in the Kuramoto model trimerizes the lattice, effectively inducing topological behavior that can be exploited to perform topological pumping. Our results can be experimentally implemented in digital and analog near-term quantum devices.
Controlling and manipulating complex many-body quantum systems will be a key ingredient \nfor the development of next-generation technologies. While the realisation of a \nuniversal quantum machine is still out of reach, in recent years experimental systems of \nultracold atoms have already evolved into a vivid field of research for quantum simulation. \nCrucially, such systems even allow for the successful quantum engineering of targeted \nmany-body systems by means of coherent periodic driving. The essential properties of \nthese Floquet systems encompass two main aspects: fast driving facilitates the simulation \nof effective static systems, and interactions lead to unique heating effects as energy is only \nconserved modulo the driving frequency. Within this thesis we theoretically study both \nof these aspects in respective model systems. \nIn part I of this thesis, we investigate the dynamics of excitations of a bosonic Mott \ninsulator in a designed one-dimensional Floquet system. Here, periodic driving in combination \nwith breaking all mirror symmetries of the system can induce directed motion of \nparticles. In the limit of small excitation densities, the effectively non-interacting quantum \nratchet determines the motion of holes and doublons in the Mott insulator and can in fact \nbe used to manipulate the dynamics of such. This little quantum machine can also be \nused to drive particles against an external force, where transport is possible but requires \nthe fulfilment of a commensurability condition for long times. \nIn part II, we discuss the role of interactions for periodically driven systems by means \nof a Floquet version of the Boltzmann equation. Starting from the Keldysh approach, \nwe develop this semiclassical formalism based on a clear separation of time scales. The \nresult is a description of the dynamics and the scattering of Floquet quasiparticles in \nsuch systems. Here, the property of discrete energy violation is naturally encoded in our \nformalism predicting the heating of interacting Floquet systems to infinite temperatures in \nthe long-time limit. As a first application of this approach, we investigate a cold atom setup \nrealising the Haldane model by means of periodic shaking. While homogeneous systems \nheat up globally, a confining potential evokes thermoelectric transport effects resulting \nfrom spatially dependent heating characteristics. Moreover, we show that the interplay \nof intrinsic heating, macroscopic diffusion and non-trivial topological properties of the \nHaldane model lead to an anomalous Floquet-Nernst effect, which describes anomalous \nparticle transport as the result of developing temperature gradients. \nIn part III, we elaborate on the quantum simulator aspect of ultracold atoms by providing \na theoretical framework for a possible simulation of a topological edge state in a \none-dimensional optical lattice. In this case, the one-dimensional Dirac equation with \nspatially varying mass is important, which captures the topological properties of a corresponding \nsystem of the BDI symmetry class. We analytically discuss such system and \ninvestigate the role of mean-field interaction effects. We also identify the emergence of \ndynamical instabilities in a realisation with bosonic atoms.
Periodically driven quantum systems can host nonequilibrium phenomena without static analogs, including in their entanglement dynamics. Here, we discover temporal entanglement transitions (TETs) in a Floquet spin chain, which correspond to a quantum phase transition in the spectrum of the entanglement Hamiltonian and are signaled by dynamical spontaneous symmetry breaking. We identify the symmetry principles underlying these transitions: they appear when the driven Hamiltonian preserves global symmetry (here, Z_{2}), the initial state respects this symmetry, and the reduced density matrix carries weight in both subsystem-parity sectors, with TETs occurring precisely when the sector weights become equal (given the previous two conditions are also satisfied). Intriguingly, we find these transitions across a broad range of driving frequencies (from adiabatic to high-frequency regime) and independent of drive details, where they manifest as periodic, sharp entanglement spectrum reorganizations marked by the Schmidt-gap closure, a vanishing entanglement echo, and symmetry-quantum-number flips, while remaining invisible to conventional local observables. At high frequencies, the entanglement Hamiltonian acquires an intrinsic timescale decoupled from the drive period, rendering the transitions genuine steady-state features. Finite-size scaling reveals universal critical behavior with correlation-length exponent ν=1, matching equilibrium Ising universality despite its emergence from purely dynamical mechanisms decoupled from static criticality. Our Letter establishes TETs as novel features in Floquet quantum matter.
We consider topological phases in periodically driven (Floquet) systems exhibiting many-body localization, protected by a symmetry G. We argue for a general correspondence between such phases and topological phases of undriven systems protected by symmetry $\mathbb{Z}\ensuremath{\rtimes}G$ where the additional Z accounts for the discrete time-translation symmetry. Thus, for example, the bosonic phases in d spatial dimensions without intrinsic topological order [symmetry-protected topological (SPT) phases] are classified by the cohomology group ${H}^{d+1}[\mathbb{Z}\ensuremath{\rtimes}G,\mathrm{U}(1)]$. For unitary symmetries, we interpret the additional resulting Floquet phases in terms of the lower-dimensional SPT phases that are pumped to the boundary during one time step. These results also imply the existence of novel symmetry-enriched topological (SET) orders protected solely by the periodicity of the drive.
Dynamical quantum phase transitions (DQPTs) are manifested by time-domain nonanalytic behaviors of many-body systems. Introducing a quench is so far understood as a typical scenario to induce DQPTs. In this work, we discover a type of DQPTs, termed Floquet DQPTs, as intrinsic features of time-periodic systems. Floquet DQPTs occur within each period of continuous driving, without the need for any quenches. In particular, in a harmonically driven spin chain model, we find analytically the existence of Floquet DQPTs in and only in a parameter regime hosting a certain nontrivial Floquet topological phase. The Floquet DQPTs are further characterized by a dynamical topological invariant defined as the winding number of the Pancharatnam geometric phase versus quasimomentum. These findings are experimentally demonstrated with a single spin in diamond. This work thus opens a door for future studies of DQPTs in connection with topological matter.
We study the dynamics of a class of integrable non-Hermitian free-fermionic models driven periodically using a continuous drive protocol characterized by an amplitude g1 and frequency ${\ensuremath{\omega}}_{D}$. We derive an analytic, albeit perturbative, Floquet Hamiltonian for describing such systems using Floquet perturbation theory with ${g}_{1}^{\ensuremath{-}1}$ being the perturbation parameter. Our analysis indicates the existence of special drive frequencies at which an approximately conserved quantity emerges. The presence of such an almost conserved quantity is reflected in the dynamics of the fidelity, the correlation functions, and the half-chain entanglement entropy of the driven system. In addition, it also controls the nature of the steady state of the system. We show that one-dimensional transverse field Ising model, with an imaginary component of the transverse field, serves as an experimentally relevant example of this phenomenon. In this case, the transverse magnetization is approximately conserved; this conservation leads to complete suppression of oscillatory features in the transient dynamics of fidelity, magnetization, and entanglement of the driven chain at special drive frequencies. We discuss the nature of the steady state of the Ising chain near and away from these special frequencies, demonstrate the protocol independence of this phenomenon by showing its existence for discrete drive protocols, and suggest experiments which can test our theory.
The periodically driven quantum Ising chain has recently attracted a large attention in the context of Floquet engineering. In addition to the common paramagnet and ferromagnet, this driven model can give rise to new topological phases. In this work, we systematically explore its quantum phase diagram by examining the properties of its Floquet ground state. We specifically focus on driving protocols with time-reversal invariant points, and demonstrate the existence of an infinite number of distinct phases. These phases are separated by second-order quantum phase transitions, accompanied by continuous changes of local and string order parameters, as well as sudden changes of a topological winding number and of the number of protected edge states. When one of these phase transitions is adiabatically crossed, the correlator associated to the order parameter is nonvanishing over a length scale which shows a Kibble-Zurek scaling. In some phases, the Floquet ground state spontaneously breaks the discrete time-translation symmetry of the Hamiltonian. Our findings provide a better understanding of topological phases in periodically driven clean integrable models.