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Chaotic dynamics have emerged as a versatile resource for neuromorphic and probabilistic computing, enabling high-dimensional nonlinear processing and classical analogues of quantum randomness. Exploiting chaos for computation requires…
We consider the evolution of the unstable periodic orbit structure of coupled chaotic systems. This involves the creation of a complicated set outside of the synchronization manifold (the emergent set). We quantitatively identify a critical…
Floquet systems are periodically driven systems. In this framework, the system Hamiltonian and associated spectra of interest are modified, giving rise to new quantum phases of matter and nonequilibrium dynamics without static counterparts.…
A key goal of quantum chaos is to establish a relationship between widely observed universal spectral fluctuations of clean quantum systems and random matrix theory (RMT). For single particle systems with fully chaotic classical…
Parametric instabilities in interacting systems can lead to the appearance of new structures or patterns. In quantum gases, two-body interactions are responsible for a variety of instabilities that depend on the characteristics of both…
Employing the external degrees of freedom of atoms as synthetic dimensions renders easy and new accesses to quantum engineering and quantum simulation. As a recent development, ultracold atoms suffering from two-photon Bragg transitions can…
We discuss recent results obtained for the Hamiltonian Mean Field model. The model describes a system of N fully-coupled particles in one dimension and shows a second-order phase transition from a clustered phase to a homogeneous one when…
Floquet modulations often yield effective Hamiltonians not easily accessible in traditional time-dependent systems, which brings opportunities for exploring novel physics of quantum dynamics. We investigate a Floquet system exhibiting…
We show that in systems with highly degenerate energy spectra, such as the 2D transverse-field Ising model (2DTFIM) in the strong-field limit, quantum chaos can emerge in finite systems for arbitrary small perturbations. In this regime, the…
We consider the chaotic dynamics of the interaction between an ensemble of two-level atoms in a high-Q Fabry-Perot cavity with a single mode of self-consistent field and with an external amplitude-modulated field. It is shown that in the…
Floquet driven systems represent an extremely interesting arena to study out-of-equilibrium phenomena. For instance, they provide realizations of discrete time crystals, where the discrete time translation symmetry of the periodic…
We investigate the chaotic phase of the Bose-Hubbard model [L. Pausch et al, Phys. Rev. Lett. 126, 150601 (2021)] in relation to the bosonic embedded random matrix ensemble, which mirrors the dominant few-body nature of many-particle…
Bichromatic control, in terms of the amplitude and relative phase of the second field as control knobs, is an useful approach for controlling a variety of quantum processes. In this context, understanding the features of the control…
Progress in the creation of large scale, artificial quantum coherent structures demands the investigation of their nonequilibrium dynamics when strong interactions, even between remote parts, are non-perturbative. Analysis of multiparticle…
Equilibration plays a fundamental role in our understanding of statistical mechanics and the long-time dynamics of many-body systems. In quantum systems, the route to equilibration is intimately related to level repulsion and quantum…
Periodically driven quantum systems, known as Floquet systems, have been a focus of non-equilibrium physics in recent years, thanks to their rich dynamics. Not only time-periodic systems exhibit symmetries similar to those in spatially…
Periodically kicked Floquet systems such as the kicked rotor are a paradigmatic and illustrative simple model of chaos. For non-integrable quantum dynamics there are several diagnostic measures of the presence of (or the transition to)…
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…
Recent work has shown that a variety of novel phases of matter arise in periodically driven Floquet systems. Among these are many-body localized phases which spontaneously break global symmetries and exhibit novel multiplets of Floquet…
We uncover a dynamical entanglement transition in a monitored quantum system that is heralded by a local order parameter. Classically, chaotic systems can be stochastically controlled onto unstable periodic orbits and exhibit controlled and…