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Workhorse theories throughout all of physics derive effective Hamiltonians to describe slow time evolution, even though low-frequency modes are actually coupled to high-frequency modes. Such effective Hamiltonians are accurate because of…
Periodically driven quantum systems host exotic phenomena which often do not have any analog in undriven systems. Floquet prethermalization and dynamical freezing of certain observables, via the emergence of conservation laws, are realized…
Many physically interesting models show a quantum phase transition when a single parameter is varied through a critical point, where the ground state and the first excited state become degenerate. When this parameter appears as a coupling…
Time-periodic (Floquet) drive is a powerful method to engineer quantum phases of matter, including fundamentally non-equilibrium states that are impossible in static Hamiltonian systems. One characteristic example is the anomalous Floquet…
We present details and expand on the framework leading to the recently introduced degenerate adiabatic perturbation theory [Phys. Rev. Lett. 104, 170406 (2010)], and on the formulation of the degenerate adiabatic theorem, along with its…
In adiabatic quantum computing the aim is to track an eigenstate as the Hamiltonian changes. In the usual setup this is achieved using the natural time-dependent Hamiltonian evolution of the system and the main technical tool is the…
Validity conditions for the adiabatic approximation are useful tools to understand and predict the quantum dynamics. Remarkably, the resonance phenomenon in oscillating quantum systems has challenged the adiabatic theorem. In this scenario,…
Non-Abelian topological insulators are characterized by matrix-valued, non-commuting topological charges with regard to more than one energy gap. Their descriptions go beyond the conventional topological band theory, in which an additive…
The strategy of shortcuts to adiabaticity enables us to realize adiabatic dynamics in finite time. In the counter-diabatic driving approach, an auxiliary Hamiltonian which is called the counter-diabatic Hamiltonian is appended to an…
We show how second-order Floquet engineering can be employed to realize systems in which many-body localization coexists with topological properties in a driven system. This allows one to implement and dynamically control a…
Adiabaticity is a cornerstone of many promising approaches to quantum control, computing, and simulation. In practice, however, there is always a trade-off. Although the deleterious effects of noise can be diminished by running a control…
Quantum adiabatic algorithms are commonly analyzed through local spectral properties of an interpolating Hamiltonian, most notably the minimum energy gap. While this perspective captures an important constraint on adiabatic runtimes, it…
Floquet engineering offers a path to optically-controlled materials, but experimental implementations have frequently relied on femtosecond pulses to achieve the high peak fields required to maximise interactions and obtain a measurable…
The present qubit technology, in particular in Josephson qubits, allows an unprecedented control of discrete energy levels. This motivates a new study of the old pump-probe problem, where a discrete quantum system is driven by a strong…
We discuss the application of the adiabatic perturbation theory to analyze the dynamics in various systems in the limit of slow parametric changes of the Hamiltonian. We first consider a two-level system and give an elementary derivation of…
We derive a systematic high-frequency expansion for the effective Hamiltonian and the micromotion operator of periodically driven quantum systems. Our approach is based on the block diagonalization of the quasienergy operator in the…
Results are presented for an open Floquet topological system represented by Dirac fermions coupled to a circularly polarized laser and an external reservoir. It is shown that when the separation between quasi-energy bands becomes small, and…
The adiabatic theorem is an important concept in quantum mechanics, it tells that a quantum system subjected to gradually changing external conditions remains to the same instantaneous eigenstate of its Hamiltonian as it initially in. In…
We reveal universal dynamical scaling behavior across adiabatic quantum phase transitions (QPTs) in networks ranging from traditional spatial systems (Ising model) to fully connected ones (Dicke and Lipkin-Meshkov-Glick models). Our…
The finite-time operation of a quantum heat engine that uses a single particle as a working medium generally increases the output power at the expense of inducing friction that lowers the cycle efficiency. We propose to scale up a quantum…