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We consider a quantum system periodically driven with a strength which varies slowly on the scale of the driving period. The analysis is based on a general formulation of the Floquet theory relying on the extended Hilbert space. It is shown…

Floquet systems are governed by periodic, time-dependent, Hamiltonians. Prima facie they should absorb energy from the external drives involved in modulating their couplings and heat up to infinite temperature. However this unhappy state of…

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…

Floquet insulators are periodically driven quantum systems that can host novel topological phases as a function of the drive parameters. These new phases exhibit features reminiscent of fermion doubling in discrete-time lattice fermion…

Floquet engineering, modulating quantum systems in a time periodic way, lies at the central part for realizing novel topological dynamical states. Thanks to the Floquet engineering, various new realms on experimentally simulating…

We investigate the conditions under which periodically driven quantum systems subject to dissipation exhibit a stable subharmonic response. Noting that coupling to a bath introduces not only cooling but also noise, we point out that a…

Stimulated by the recent progress in engineering topological band structures in cold atomic gases, we study the dynamic topological phenomena for atoms loaded in a periodically driven optical lattice. When the frequency of the periodic…

We investigate the role of symmetries in determining the random matrix class describing quantum thermalization in a periodically driven many body quantum system. Using a combination of analytical arguments and numerical exact…

We demonstrate that the prethermal regime of periodically driven (Floquet), classical many-body systems can host nonequilibrium phases of matter. In particular, we show that there exists an effective Hamiltonian that captures the dynamics…

We provide an analytic solution to the problem of system-bath dynamics under the effect of high-frequency driving that has applications in a large class of settings, such as driven-dissipative many-body systems. Our method relies on…

Periodically driven many-body systems generally heat towards a featureless 'infinite-temperature' state. As an alternative to uniform heating in a clean system, here we establish a Floquet superheating regime, where fast heating nucleates…

Ultracold atomic gas provides a useful tool to explore many-body physics. One of the recent additions to this experimental toolbox is the Floquet engineering, where periodic modulation of the Hamiltonian allows the creation of effective…

We propose a general method of cooling -- periodic driving generated by spatially deformed Hamiltonians -- and study it in general one-dimensional quantum critical systems described by a conformal field theory. Our protocol is able to…

We construct a dynamical decoupling protocol for accurately generating local and global symmetries in general many-body systems. Multiple commuting and non-commuting symmetries can be created by means of a self-similar-in-time…

It is proved that the energy absorption in a periodically driven classical spin system is exponentially slow in frequency, which results in a two-step relaxation called the Floquet prethermalization. This result is shown by establishing the…

The classical Floquet theory allows to map a time-periodic system of linear differential equations into an autonomous one. By looking at it in a geometrical way, we extend the theory to a class of non-autonomous non-periodic equations. This…

The design of time-independent effective Hamiltonians that describe periodically modulated systems, provides a promising approach to realize new forms of matter. This, so-called, Floquet engineering approach is currently limited to the…

We study the dynamics and stability in a strongly interacting resonantly driven two-band model. Using exact numerical simulations, we find a stable regime at large driving frequencies where the time evolution is governed by a local Floquet…

The dynamics of qubits coupled to a harmonic oscillator with time-periodic coupling is investigated in the framework of Floquet theory. This system can be used to model nonadiabatic phenomena that require a periodic modulation of the…

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…