I introduce a modular framework for constructing long-range, high-fidelity quantum channels via Floquet-engineered quasienergy structures in driven atomic arrays embedded in structured electromagnetic backgrounds. Periodic driving sculpts the local density of states (LDOS) to produce emergent transport channels whose properties can be precisely tailored by the drive pattern. Using large-scale mean-field Floquet simulations, I demonstrate coherent bridging of four physically disconnected sub-arrays into a single collective mode: a probe wavepacket launched in one region spreads symmetrically and reaches perfect amplitude locking across all four regions, maintaining exact balance for over 20,000 drive periods with only negligible numerical jitter. Remarkably, this transport occurs while deliberately violating standard Floquet-theoretical invariants, including local linearity, isotropy, time-reversal symmetry, and naive correlation-front shape conservation, confirming that these assumptions are not required for stable, controllable causal connectivity. Local synthetic curvature emerges along the channels, producing measurable geodesic-like deviations in wavepacket trajectories without inducing instability or decoherence. These results establish a concrete, modular platform for scalable, concatenable quantum transport and provide the first explicit demonstration that emergent quasi-spacetime causal structure can arise in driven quantum systems independent of physical adjacency or previously assumed invariants.
I introduce a modular framework for constructing long-range, high-fidelity quantum channels via Floquet-engineered quasienergy structures in driven atomic arrays embedded in structured electromagnetic backgrounds. Periodic driving sculpts the local density of states (LDOS) to produce emergent transport channels whose properties can be precisely tailored by the drive pattern. Using large-scale mean-field Floquet simulations, I demonstrate coherent bridging of four physically disconnected sub-arrays into a single collective mode: a probe wavepacket launched in one region spreads symmetrically and reaches perfect amplitude locking across all four regions, maintaining exact balance for over 20,000 drive periods with only negligible numerical jitter. Remarkably, this transport occurs while deliberately violating standard Floquet-theoretical invariants, including local linearity, isotropy, time-reversal symmetry, and naive correlation-front shape conservation, confirming that these assumptions are not required for stable, controllable causal connectivity. Local synthetic curvature emerges along the channels, producing measurable geodesic-like deviations in wavepacket trajectories without inducing instability or decoherence. These results establish a concrete, modular platform for scalable, concatenable quantum transport and provide the first explicit demonstration that emergent quasi-spacetime causal structure can arise in driven quantum systems independent of physical adjacency or previously assumed invariants.
We simulate periodically driven Rydberg arrays with purely imaginary-phase driving, showing that it reshapes both internal dynamics and the structure of coupled vacuum fluctuations. In a driven Rydberg array, this interplay produces\emph{hybrid vacuum--photonic quasienergy channels}---coherent,directional modes arising from Floquet-induced modulation of theelectromagnetic local density of states (LDOS). These channels enable a coherent mapping of correlation structure far beyond the nominal dipolar range andexhibit stability characteristic of attractor-like Floquet fixed points. Using a microscopic Hamiltonian with spatiotemporally structureddipole--vacuum coupling, we derive a Floquet--Magnus expression for theeffective LDOS:ρeff(ω)=∑mJm2(A)ρ0(ω+mΩ),revealing how the drive imprints anisotropic vacuum structure.Large-scale open-system simulations confirm that this LDOS reshapingproduces long-lived, quasienergy-resolved photonic corridors, alongwhich correlation fronts propagate with direction-dependent velocities. We further show that the system's long-time behavior is well describedby an \emph{effective geometric picture}: anisotropic correlationfronts define a synthetic light cone, LDOS-induced anisotropies definean emergent spatial metric, and wavepacket bundle separation obeys ageodesic-deviation-like equation whose curvature is determined directlyfrom simulated trajectories over thousands of drive periods. We conclude with a speculative perspective: if driven matter can imprintstable geometric structure onto the vacuum LDOS, then controlled analogspacetime engineering---without material waveguides or externalphotonic scaffolds---may be achievable.
Abstract The discovery of time crystals and topological phases has fundamentally altered our understanding of quantum matter, yet a unified framework that combines temporal quasi-order, topological protection, and engineered dissipation remains a central challenge. Here we introduce Floquet-engineered dissipative time quasicrystals (FDTCs) —a class of nonequilibrium topological phases that emerge from the synergy of quasi-periodic driving, non-local dissipation, and non-Hermitian topology. Using a combination of Floquet-Lindblad theory and frequency-space topology, we demonstrate that FDTCs exhibit three defining hallmarks: (i) fractal temporal correlations with multiple incommensurate frequencies, (ii) a quantized topological invariant robust against disorder, and (iii) algebraically decaying memory of phase perturbations—a signature of intrinsic protection. We establish a general theoretical framework mapping quasi-periodically driven dissipative systems to non-Hermitian tight-binding models on synthetic frequency lattices, revealing topological edge modes in the frequency domain that manifest as persistent temporal order. We provide explicit experimental blueprints for two leading quantum platforms: parametrically driven superconducting qubit arrays and Rydberg atom chains with structured dissipation. Numerical simulations validate the phase diagram, showing that FDTCs occupy a distinct region bounded by trivial dissipative dynamics, conventional time crystals, and thermal phases. Our work establishes FDTCs as a bridge between topological matter, non-equilibrium physics, and quantum simulation, opening pathways to dissipationprotected quantum memory, topologically robust frequency combs, and novel non-Hermitian quantum technologies.
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.
This thesis reports on the realization of Floquet topological systems with ultracold atoms in an optical honeycomb lattice. Using periodically driven quantum systems, topological phases of matter can be simulated by an effective, static Hamiltonian related to the time-evolution at integer multiples of the driving period, which is known as Floquet engineering. However, periodic driving can also give rise to genuinely time-dependent settings without static counterparts. One example is the anomalous Floquet phase in two dimensions, in which all bulk bands have a Chern number of zero but nevertheless robust chiral edge modes appear, which would be precluded by the bulk-edge correspondence in a static system. In an optical honeycomb lattice, anomalous Floquet systems can be created by continuous, periodic modulation of the laser intensities. This driving scheme results in different topological regimes, three of which are investigated, including the anomalous Floquet phase and a Haldane-like phase. Periodically driven systems feature periodic quasienergies and can be characterized in terms of winding numbers, which count the number of chiral edge modes in each quasienergy gap. By interferometric measurements of the quasienergy gaps between the first two Floquet bands, the topological phase transitions, emerging as gap closings, are located. For periodically driven systems, a modified bulk-edge correspondence can be formulated. In particular, the change of the winding number at a phase transition is related to the sign change of the local Berry curvature. The Berry curvature at the gap closing points is probed by Hall deflection measurements to obtain the winding numbers in each of the topological regimes, revealing the existence of chiral edge modes also in a setting with smooth boundaries as used in the experiments. The measured quasienergy gaps and transverse deflections are quantitatively well described by a numerical calculation of the Floquet bandstructure that includes coupling to higher bands during the driving period. To derive the spectrum of the modulated lattice in a geometry with edges, a tight-binding description of the system is discussed. Circular phase modulation of the honeycomb lattice can also give rise to an anomalous Floquet system when inversion symmetry is broken. The topological phase diagrams and the experimental feasibility are compared for both modulation schemes. Due to the vanishing Chern numbers, the bulk states in the anomalous Floquet regime can be fully localized by a disorder potential. This could prevent heating in interacting, periodically driven systems, resulting in a many-body localized bulk coexisting with thermalizing edge states. The experimental realization of disorder and strong interactions, as well as independent probes of the edge states are investigated. Bloch band geometry can be extended to multiband systems, using Wilson lines. The possible symmetry protection of their eigenvalues is discussed, along with measurements in the optical honeycomb lattice. Moreover, the onset of heating in weakly-interacting, periodically driven systems, triggered by parametric instabilities, is studied experimentally in a one-dimensional lattice.
Strong periodic driving of cavity-quantum electrodynamics (QED) in the ultrastrong-coupling regime creates nonequilibrium states whose dissipation is governed by Floquet quasienergies rather than undriven dressed resonances. However, modeling such a regime is a significant theoretical challenge, including a number of subtle problems such as the need to ensure gauge invariance for truncated matter-cavity systems with time-dependent driving. To fill this theoretical gap, we introduce a nonsecular Floquet generalized master equation framework for strongly driven open cavity-QED systems, formulated in the dressed basis of the quantum Rabi model and applicable to structured reservoirs without rotating-wave approximations. Our theory can thus model Floquet-driven dynamics in open ultrastrong-coupling cavity-QED, and demonstrates a wide range of quantum state control. Using strong optical pumping and parametric mechanical modulation, we compute long-time populations, fluorescence spectra, and the Floquet-Liouville eigenspectra, resolving observable resonances into hybridized quasienergy channels and decay rates. By systematically comparing with conventional time-independent dressed-basis generalized master equations, we show that static approaches only reproduce steady-state populations in restricted excitation regimes, and fail for frequency-resolved observables and break down under appropriate Floquet engineering, surprisingly, even for spectrally flat baths. Structured environments, such as Lorentzian-Ohmic reservoirs, further amplify these discrepancies through sideband-selective decay. Our results demonstrate that dissipation in driven ultrastrong cavity-QED is intrinsically quasienergy resolved and we establish Floquet-dissipative theory as an accurate and powerful framework for predicting spectra, controlling decay pathways, and engineering nonequilibrium quantum states and reservoirs.
Coherent control via periodic modulation, also known as Floquet engineering, has emerged as a powerful experimental method for the realization of novel quantum systems with exotic properties. In particular, it has been employed to study topological phenomena in a variety of different platforms. In driven systems, the topological properties of the quasienergy bands can often be determined by standard topological invariants, such as Chern numbers, which are commonly used in static systems. However, due to the periodic nature of the quasienergy spectrum, this topological description is incomplete and new invariants are required to fully capture the topological properties. Most prominently, there exist two-dimensional anomalous Floquet systems that exhibit robust chiral edge modes, despite all Chern numbers are equal to zero. Here, we realize such a system with bosonic atoms in a periodically-driven hexagonal lattice and infer the complete set of topological invariants from energy gap measurements and local Hall deflections.