Abstract We report on the control of spin pair fluctuations using two-tone Floquet engineering. We consider a one-dimensional spin-1/2 lattice with periodically modulated spin exchanges using parametric resonances. The stroboscopic dynamics generated from distributed spin exchange modulations lead to spin pair fluctuations reaching quasi-maximally correlated states and a subharmonic response in local observables, breaking the discrete-time translational symmetry. We present a protocol to control the interacting many-body dynamics, producing spatial and temporal localization of correlated spin pairs via dynamically breaking correlated spin pairs from the edges towards the center of the lattice. Our result reveals how spin fluctuations distribute in a heterogeneous lattice depending on parametric resonances. This may open new routes for exploring distinct nonequilibrium states of matter and the conduction of quasiparticles in quantum materials.
Abstract We report on the control of spin pair fluctuations using two-tone Floquet engineering. We consider a one-dimensional spin-1/2 lattice with periodically modulated spin exchanges using parametric resonances. The stroboscopic dynamics generated from distributed spin exchange modulations lead to spin pair fluctuations reaching quasi-maximally correlated states and a subharmonic response in local observables, breaking the discrete-time translational symmetry. We present a protocol to control the interacting many-body dynamics, producing spatial and temporal localization of correlated spin pairs via dynamically breaking correlated spin pairs from the edges towards the center of the lattice. Our result reveals how spin fluctuations distribute in a heterogeneous lattice depending on parametric resonances. This may open new routes for exploring distinct nonequilibrium states of matter and the conduction of quasiparticles in quantum materials.
In quantum gases, two-body interactions are responsible for a variety of instabilities that depend on the characteristics of both trapping and interactions. These instabilities can lead to the appearance of new structures or patterns. We report on the Floquet engineering of such a parametric instability, on a Bose-Einstein condensate held in a time-modulated optical lattice. The modulation triggers a destabilization of the condensate into a state exhibiting a density modulation with a new spatial periodicity. This new crystal-like order, which shares characteristic correlation properties with a supersolid, directly depends on the modulation parameters: The interplay between the Floquet spectrum and interactions generates narrow and adjustable instability regions, leading to the growth, from quantum or thermal fluctuations, of modes with a density modulation noncommensurate with the lattice spacing. This study demonstrates the production of metastable exotic states of matter through Floquet engineering and paves the way for further studies of dissipation in the resulting phase and of similar phenomena in other geometries.
We propose a novel protocol to realize discrete time-crystal (DTC) order in clean, periodically driven spin-1/2 chains. In each drive cycle, a global spin flip is followed by a two-tone flat-band segment. This flat-band segment engineers a fully degenerate Floquet quasienergy spectrum, suppresses thermalization, and stabilizes a robust period-doubled subharmonic response. Using exact time evolution, we identify a pronounced subharmonic peak at half the drive frequency in the Fourier spectrum of the order parameter, thereby providing clear evidence for the emergence of stable DTC. The resulting phase is insensitive to system size, interaction strength, and interaction range; however, it remains sensitive to spin-rotation errors (εr), which can destabilize the subharmonic response. Compared with disorder-induced many-body localized (MBL) and disorder-free dynamically many-body localized (DMBL) DTCs, we find that the exact flat-band protocol offers a broader tunability of drive parameters, whereas MBL and DMBL based DTCs are more resistant to εr. In particular, the εr sensitivity can be suppressed by incorporating additional spin-spin interactions that have modest deviations from the ideal flat-band protocol. This manifests itself in a robust DTC response over a finite window of spin-coupling strengths and drive frequencies. Our results establish flat-band driving as a versatile and experimentally relevant route to DTC order in disorder-free spin systems and motivate further exploration of nonequilibrium phases.
Neutral atom arrays driven into Rydberg states constitute a promising approach for realizing programmable quantum systems. Enabled by strong interactions associated with Rydberg blockade, they allow for simulation of complex spin models and quantum dynamics. We introduce a new Floquet engineering technique for systems in the blockade regime that provides control over novel forms of interactions and entanglement dynamics in such systems. Our approach is based on time-dependent control of Rydberg laser detuning and leverages perturbations around periodic many-body trajectories as resources for operator spreading. These time-evolved operators are utilized as a basis for engineering interactions in the effective Hamiltonian describing the stroboscopic evolution. As an example, we show how our method can be used to engineer strong spin exchange, consistent with the blockade, in a one-dimensional chain, enabling the exploration of gapless Luttinger liquid phases. In addition, we demonstrate that combining gapless excitations with Rydberg blockade can lead to dynamic generation of large-scale multipartite entanglement. Experimental feasibility and possible generalizations are discussed.
Coherent control of interacting spin systems under time-periodic driving is a central challenge in spin-based quantum technologies. Here we demonstrate the applicability of a full Floquet-space formalism, adapted from Nuclear Magnetic Resonance (NMR) methodologies, to model the dynamics of driven coupled electron spins in the presence of a static magnetic field B0 and a transverse oscillating field B1. The framework explicitly includes isotropic exchange coupling J and the chiral Dzyaloshinskii-Moriya antisymmetric exchange interaction (DMI), and its numerical convergence is systematically validated with respect to Fourier-space truncation. In the non-interacting limit, the expected driven-spin dynamics is recovered, with the oscillation periodicity governed by B1. Exchange coupling alone does not modify the collective spin expectation values under the chosen initial condition, consistent with symmetry considerations. In contrast, increasing DMI generates a finite Sy component, suppresses Sz, and produces tilted, elliptical Bloch-sphere trajectories, reflecting the emergence of chiral spin-spin correlations. These effects are pronounced for open boundary conditions, while remaining nearly negligible in the periodic boundary case. When exchange coupling and DMI coexist, the dynamics becomes strongly perturbed and multi-frequency in nature. Together, these results demonstrate that full Floquet-space modeling provides a robust and predictive framework for analyzing and engineering coherent dynamics in driven interacting spin systems beyond simple coherent-rotation regimes.
We theoretically investigate a one-dimensional quantum droplet with spin-orbit (SO) coupling and periodically modulated Raman coupling. Using a Floquet approach, we derive an effective time-independent model that reveals a controlled phase diagram. Crucially, the interplay of quantum fluctuations encoded in the Lee-Huang-Yang correction and SO coupling suppresses the plane-wave phase that is typical of mean-field SO-coupled condensates. The ground state is instead restricted to two distinct phases: a stripe phase, with periodic density modulations, and a zero-momentum phase, with a flat-top density profile. The plane-wave droplet is a metastable state of the system. We demonstrate that the boundary between these phases can be dynamically manipulated by tuning the driving parameters. Furthermore, we explore the system's response to quantum quenches, uncovering a wealth of nonequilibrium phenomena, including the dynamical formation of stable, solitonlike structures. Our work establishes periodic driving as a powerful tool for the dynamical control of self-bound quantum matter and elucidates the fundamental role of quantum fluctuations in shaping the phase diagram of SO-coupled droplets.
This work explores the possibility of creating and controlling unconventional nonlinearities by periodic driving, in a broad class of systems described by the nonlinear Schrödinger equation (NLSE).By means of a parent quantum many-body description, we demonstrate that such driven systems are well captured by an effective NLSE with emergent nonlinearities, which can be finely controlled by tuning the driving sequence.We first consider a general class of two-mode nonlinear systems-relevant to optical Kerr cavities, waveguides, and Bose-Einstein condensates-where we find an emergent four-wave mixing nonlinearity, which originates from pair-hopping processes in the parent quantum picture.Tuning this drive-induced nonlinearity is shown to modify the phase-space topology, which can be detected through relative population and phase measurements, and also leads to enhanced quantum properties such as spin squeezing.We then couple individual (two-mode) dimers in view of designing extended lattice models with unconventional nonlinearities and controllable pair-hopping processes.Following this general dimerization construction, we obtain an effective lattice model with drive-induced interactions, whose ground state exhibits orbital order, chiral currents, and emergent magnetic fluxes through the spontaneous breaking of time-reversal symmetry.We analyze these intriguing properties both in the weakly interacting (mean-field) regime, captured by the effective NLSE, and in the strongly correlated quantum regime.Our general approach opens a route for the engineering of unconventional optical nonlinearities in photonic devices and controllable drive-induced interactions in ultracold quantum matter.