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Time-periodic (Floquet) driving is a powerful way to control the dynamics of complex systems, which can be used to induce a plethora of new physical phenomena. However, when applied to many-body systems, Floquet driving can also cause…

Floquet engineering, the control of a quantum system by means of time-periodic driving, allows to modify the properties of the system so that it becomes described by an approximate effective time-independent Hamiltonian. However, in the…

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 consider the dynamics of a two-level system (qubit) driven by strong and short resonant pulses in the framework of Floquet theory. First we derive analytical expressions for the quasienergies and Floquet states of the driven system. If…

We investigate a class of periodically driven many-body systems that allows us to extend the phenomenon of prethermalization to the vicinity of isolated intermediate-to-low drive frequencies away from the high-frequency limit. We provide…

Periodically driven Floquet quantum systems provide a promising platform to investigate novel physics out of equilibrium. Unfortunately, the drive generically heats up the system to a featureless infinite temperature state. For large…

Periodically driven systems have emerged as a useful technique to engineer the properties of quantum systems, and are in the process of being developed into a standard toolbox for quantum simulation. An outstanding challenge that leaves…

In Floquet engineering, periodic driving is used to realize novel phases of matter which are inaccessible in thermal equilibrium. For this purpose, the Floquet theory provides us a recipe of obtaining a static effective Hamiltonian.…

A periodically driven quantum system, when coupled to a heat bath, relaxes to a non-equilibrium asymptotic state. In the general situation, the retrieval of this asymptotic state presents a rather non-trivial task. It was recently shown…

It is well understood that many-body systems driven at high frequency heat up only exponentially slowly and exhibit a long prethermalization regime. We prove rigorously that a certain relevant class of systems heat very slowly under weak…

Floquet (periodic) driving has recently emerged as a powerful technique for engineering quantum systems and realizing non-equilibrium phases of matter. A central challenge to stabilizing quantum phenomena in such systems is the need to…

Experiments on periodically driven quantum systems have effectively realized quasi-Hamiltonians, in the sense of Floquet theory, that are otherwise inaccessible in static condensed matter systems. Although the Floquet quasi-Hamiltonians are…

We discuss the universal nature of relaxation in isolated many-body quantum systems subjected to global and strong periodic driving. Our rigorous Floquet analysis shows that the energy of the system remains almost constant up to an…

An external periodic (Floquet) drive is believed to bring any initial state to the featureless infinite temperature state in generic nonintegrable isolated quantum many-body systems in the thermodynamic limit, irrespective of the driving…

The nonequilibrium quantum dynamics of closed many-body systems is a rich yet challenging field. While recent progress for periodically driven (Floquet) systems has yielded a number of rigorous results, our understanding on quantum…

We investigate both pure and mixed states Floquet dynamical quantum phase transition (DQPT) in the periodically time-dependent extended XY model. We exactly show that the proposed Floquet Hamiltonian of interacting spins can be expressed as…

We give a systematic review of the adiabatic theorem and the leading non-adiabatic corrections in periodically-driven (Floquet) systems. These corrections have a two-fold origin: (i) conventional ones originating from the gradually changing…

Controlling interactions is the key element for quantum engineering of many-body systems. Using time-periodic driving, a naturally given many-body Hamiltonian of a closed quantum system can be transformed into an effective target…

Periodic driving of a quantum (or classical) many-body system can alter the systems properties significantly and therefore has emerged as a promising way to engineer exotic quantum phases, such as topological insulators and discrete time…

We study the dynamics and timescales of a periodically driven Fermi-Hubbard model in a three-dimensional hexagonal lattice. The evolution of the Floquet many-body state is analyzed by comparing it to an equivalent implementation in undriven…