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We show that when a quantum many-body system is subjected to coherent periodic driving, the response may exhibit exotic freezing behavior in high driving frequency ($\omega$) regime. In a periodically driven classical thermodynamic system,…

We experimentally demonstrate the phenomenon of dynamical many-body freezing in a periodically driven Ising chain. Theoretically [Phys. Rev. B 82, 172402 (2010)], for certain values of the drive parameters all fundamental degrees of freedom…

The question of how systems respond to perturbations is ubiquitous in physics. Predicting this response for large classes of systems becomes particularly challenging if many degrees of freedom are involved and linear response theory cannot…

Understanding and controlling non-equilibrium dynamics in quantum many-body systems is a fundamental challenge in modern physics, with profound implications for advancing quantum technologies. Typically, periodically driven systems in the…

Quantum interference lies at the heart of several surprising equilibrium and non-equilibrium phenomena in many-body Physics. Here we discuss two recently explored non-equilibrium scenarios where external periodic drive applied to closed…

Time periodic forcing in the form of coherent radiation is a standard tool for the coherent manipulation of small quantum systems like single atoms. In the last years, periodic driving has more and more also been considered as a means for…

We consider a many-body generalization of the Kapitza pendulum: the periodically-driven sine-Gordon model. We show that this interacting system is dynamically stable to periodic drives with finite frequency and amplitude. This finding is in…

Quantum refrigerators pump heat from a cold to a hot reservoir. In the few-particle regime, counter-diabatic (CD) driving of, originally adiabatic, work-exchange strokes is a promising candidate to overcome the bottleneck of vanishing…

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…

The nature of the behaviour of an isolated many-body quantum system periodically driven in time has been an open question since the beginning of quantum mechanics. After an initial transient, such a system is known to synchronize with the…

We study feedback control of classical Hamiltonian systems with the controlling parameter varying slowly in time. The control aims to change system's energy. We show that the control problems can be solved with help of an adiabatic…

Periodic driving enables the engineering of complex quantum matter, yet in interacting systems it generically leads to energy absorption, which limits the lifetime of the engineered states. To address this challenge, dynamical freezing has…

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…

The assumption that quantum systems relax to a stationary state in the long-time limit underpins statistical physics and much of our intuitive understanding of scientific phenomena. For isolated systems this follows from the eigenstate…

Exploiting the rich phenomenology of periodically-driven many-body systems is notoriously hindered by persistent heating in both the classical and quantum realm. Here, we investigate to what extent coupling to a large thermal reservoir…

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…

The evolution of a driven quantum system is said to be adiabatic whenever the state of the system stays close to an instantaneous eigenstate of its time-dependent Hamiltonian. The celebrated quantum adiabatic theorem ensures that such pure…

High control in the preparation and manipulation of states is an experimental and theoretical important task in many quantum protocols. Shortcuts to adiabaticity methods allow to obtain desirable states of a adiabatic dynamics but in short…

Periodic driving can be used to coherently control the properties of a many-body state and to realize new phases which are not accessible in static systems. For example, exposing materials to intense laser pulses enables to provoke…

The long-time dynamics of quantum systems, typically, but not always, results in a thermal steady state. The microscopic processes that lead to or circumvent this fate are of interest, since everyday experience tells us that not all spatial…