Floquet engineering is a powerful method that can be used to modify the properties of interacting many-body Hamiltonians via the application of periodic time-dependent drives. Here, we consider the physics of an inductively shunted superconducting Josephson junction in the presence of Floquet drives in the fluxonium regime and beyond, which we dub the frozonium artificial atom. We find that in the vicinity of special ratios of the drive amplitude and frequency, the many-body dynamics can be tuned to that of an effectively linear bosonic oscillator, with additional nonlinear corrections that are suppressed in higher powers of the drive frequency. By analyzing the inverse participation ratios between the time-evolved frozonium wavefunctions and the eigenbasis of a linear oscillator, we demonstrate the ability to achieve a novel dynamical control using a combination of numerical exact diagonalization and Floquet-Magnus expansion. We discuss the physics of resonances between quasi-energy states induced by the drive and ways to mitigate their effects. We also highlight the enhanced protection of frozonium against external sources of noise present in experimental setups. This work lays the foundation for future applications in quantum memory and bosonic quantum control using superconducting circuits.
Floquet engineering is a powerful method that can be used to modify the properties of interacting many-body Hamiltonians via the application of periodic time-dependent drives. Here, we consider the physics of an inductively shunted superconducting Josephson junction in the presence of Floquet drives in the fluxonium regime and beyond, which we dub the frozonium artificial atom. We find that in the vicinity of special ratios of the drive amplitude and frequency, the many-body dynamics can be tuned to that of an effectively linear bosonic oscillator, with additional nonlinear corrections that are suppressed in higher powers of the drive frequency. By analyzing the inverse participation ratios between the time-evolved frozonium wavefunctions and the eigenbasis of a linear oscillator, we demonstrate the ability to achieve a novel dynamical control using a combination of numerical exact diagonalization and Floquet-Magnus expansion. We discuss the physics of resonances between quasi-energy states induced by the drive and ways to mitigate their effects. We also highlight the enhanced protection of frozonium against external sources of noise present in experimental setups. This work lays the foundation for future applications in quantum memory and bosonic quantum control using superconducting circuits.
Periodic driving can suppress the Josephson nonlinearity of a fluxonium superconducting circuit, producing a nearly harmonic Floquet spectrum at isolated freezing points [K. Lewellen et al., Newton 2, 100434 (2026)]. Here we show that this dynamically frozen behavior does not generically suppress quasiparticle-induced dissipation in the resulting frozonium circuit. We formulate quasiparticle processes in the frozonium using a Floquet framework and analyze both drive-assisted Cooper-pair breaking and tunneling of pre-existing quasiparticles. Pair generation is controlled by gap-breaking thresholds at high drive frequencies, while multiphoton resonances produce pronounced rate enhancements at lower frequencies. Quasiparticle tunneling exhibits connected resonance structures organized by the harmonic Floquet-Magnus spectrum near the freezing point, with resonant hybridization generating characteristic avoided crossings. Our results show that suitable operating regimes must balance dynamical freezing against quasiparticle loss and provide a framework for identifying experimental drive parameters away from harmful resonances.
Considering the example of superconducting circuits, we show how Floquet engineering can be combined with reservoir engineering for the controlled preparation of target states. Floquet engineering refers to the control of a quantum system by means of time-periodic forcing, typically in the high-frequency regime, so that the system is governed effectively by a time-independent Floquet Hamiltonian with novel interesting properties. Reservoir engineering, on the other hand, can be achieved in superconducting circuits by coupling a system of artificial atoms (or qubits) dispersively to pumped leaky cavities, so that the induced dissipation guides the system into a desired target state. It is not obvious that the two approaches can be combined, since reaching the dispersive regime, in which system and cavities exchange excitations only virtually, can be spoiled by driving-induced resonant transitions. However, working in the extended Floquet space and treating both system-cavity coupling as well as driving-induced excitation processes on the same footing perturbatively, we identify regimes, where reservoir engineering of targeted Floquet states is possible and accurately described by an effective time-independent master equation. We successfully benchmark our approach for the preparation of the ground state in a system of interacting bosons subjected to Floquet-engineered magnetic fields in different lattice geometries.
Ergodic quantum many-body systems evolving under unitary time dynamics typically lose memory of their initial state via information scrambling. Here, we consider a paradigmatic translationally invariant many-body Hamiltonian of interacting bosons—a Josephson junction array in the transmon regime—in the presence of a strong Floquet drive. Generically, such a time-dependent drive is expected to heat the system to an effectively infinite-temperature, featureless state in the late-time limit. However, using numerical exact diagonalization, we find evidence of special ratios of the drive amplitude and frequency where the system develops emergent conservation laws and approximate integrability. Remarkably, at these same set of points, the Lyapunov exponent associated with the semi-classical dynamics for the coupled many-body equations of motion drops by at least an order of magnitude, arresting the growth of chaos. We supplement our numerical results with an analytical Floquet-Magnus expansion that includes higher-order corrections and capture the slow dynamics that control decay away from exact freezing.
Quantum control and noise protection of a Floquet 0−π qubit
Time-periodic systems allow engineering new effective Hamiltonians from limited physical interactions. For example, the inverted position of the Kapitza pendulum emerges as a stable equilibrium with rapid drive of its pivot point. In this work, we propose the Kapitzonium: a Floquet qubit that is the superconducting circuit analog of a mechanical Kapitza pendulum. Under periodic driving, the emerging qubit states are exponentially protected against bit and phase flips caused by dissipation, which is the primary source of decoherence of current qubits. However, we find that dissipation causes leakage out of the Floquet qubit subspace. We engineer a passive cooling scheme to stabilize the qubit subspace, which is crucial for high fidelity quantum control under dissipation. Furthermore, we introduce a hardware-efficient fluorescence-based method for qubit measurement and discuss the experimental implementation of the Floquet qubit. The proposed Kapitzonium is one of the simplest Floquet qubits that can be realized with current technology -- and it already has many intriguing features and capabilities. Our work provides the first steps to develop more complex Floquet quantum systems from the ground up to realize large-scale protected engineered dynamics.
This dissertation presents a self-contained study of periodically-driven quantum systems. Following a brief introduction to Floquet theory, we introduce the inverse-frequency expansion, variants of which include the Floquet-Magnus, van Vleck, and Brillouin-Wigner expansions. We reveal that the convergence properties of these expansions depend strongly on the rotating frame chosen, and relate the former to the existence of Floquet resonances in the quasienergy spectrum. The theoretical design and experimental realisation (`engineering') of novel Floquet Hamiltonians is discussed introducing three universal high-frequency limits for systems comprising single-particle and many-body linear and nonlinear models. The celebrated Schrieffer-Wolff transformation for strongly-correlated quantum systems is generalised to periodically-driven systems, and a systematic approach to calculate higher-order corrections to the Rotating Wave Approximation is presented. Next, we develop Floquet adiabatic perturbation theory from first principles, and discuss extensively the adiabatic state preparation and the corresponding leading-order non-adiabatic corrections. Special emphasis is thereby put on geometrical and topological objects, such as the Floquet Berry curvature and the Floquet Chern number obtained within linear response in the presence of the drive. Last, pre-thermalisation and thermalisation in closed, clean periodically-driven quantum systems are studied in detail, with the focus put on the crucial role of Floquet many-body resonances for energy absorption.
Periodically driven quantum systems host exotic phenomena that often do not have any analog in undriven systems. Floquet prethermalization and dynamical freezing of certain observables, via the emergence of conservation laws, are realized by controlling the drive frequency. Recent experimental developments in synthetic quantum matter, such as superconducting qubits and cold atoms, have opened avenues for implementing local Floquet engineering which can achieve spatially modulated quantum control of states. Here, we uncover the novel memory effects of local periodic driving in a nonintegrable spin-half staggered Heisenberg chain. For a boundary-driven protocol at the dynamical freezing frequency, we show the formation of an approximate strong zero mode, a prethermal quasilocal operator, due to the emergence of a discrete global Z2 symmetry. This is captured by constructing an accurate effective Floquet Hamiltonian using a higher-order partially resummed Floquet-Magnus expansion. The lifetime of the boundary spin can be exponentially enhanced by enlarging the set of suitably chosen driven sites. We demonstrate that in the asymptotic limit, achieved by increasing the number of driven sites, a strong zero mode emerges, where the lifetime of the boundary spin grows exponentially with system size. The nonlocal processes in the Floquet Hamiltonian play a pivotal role in the total freezing of the boundary spin in the thermodynamic limit. The novel dynamics of the boundary spin is accompanied by a rich structure of entanglement in the Floquet eigenstates where specific bipartitions yield an area-law scaling while the entanglement for random bipartitions scales as a volume-law. Our work addresses the long-standing question of the existence of a strong zero mode in a nonintegrable model and elucidates the complex nature of thermalization in locally driven systems. Published by the American Physical Society 2024