In this review we focus on electronic transport through semiconductor nanostructures which are driven by ac fields. Along the review we describe the available experimental information on different nanostructures, like resonant tunneling diodes, superlattices or quantum dots, together with the theoretical tools needed to describe the observed features. These theoretical tools such as, for instance, the Floquet formalism, the non-equilibrium Green's function technique or the density matrix technique, are suitable for tackling with photon-assisted transport problems where the interplay of different aspects like nonequilibrium, nonlinearity, quantum confinement or electron-electron interactions gives rise to many intriguing new phenomena. Along the review we give many examples which demonstrate the possibility of using appropriate ac fields to control/manipulate coherent quantum states in semiconductor nanostructures.

We propose a general framework to solve tight binding models in D dimensional lattices driven by ac electric fields. Our method is valid for arbitrary driving regimes and allows to obtain effective Hamiltonians for different external fields configurations. We establish an equivalence with time independent lattices in D+1 dimensions, and analyze their topological properties. Further, we demonstrate that non-adiabaticity drives a transition from topological invariants defined in D+1 to D dimensions. Our approach provides a theoretical framework to analyze ac driven systems, with potential applications in topological states of matter, and non-adiabatic topological quantum computation, predicting novel outcomes for future experiments.Introduction: Periodically driven quantum systems has been a fastly growing research field in the last years. The development of effective Hamiltonians describing ac driven systems at certain regimes, has allowed to predict novel properties such as topological phases [1][2][3], and quantum phase transitions [4,5] that otherwise, would be impossible to achieve in the undriven case. Therefore, the application of ac fields has become a very promising tool to engineer quantum systems. On the other hand, the obtention of effective Hamiltonians can be a difficult task, depending on the driving regime to be considered.In this work, we provide a general framework to study periodically driven quantum lattices. By means of our approach, it is possible to solve with arbitrary accuracy their time evolution, and obtain effective Hamiltonians for the different driving regimes. We consider solutions of Floquet-Bloch form, based on the symmetries of the system, and characterize the states in terms of the quasienergies, which are well defined for all driving regimes. The states belong to a composed Hilbert space, in which time is treated as a parameter. As we will see below, it allows to formally describe the ac driven D dimensional lattice, as analog to a time independent D+1 dimensional lattice. This description enlightens the underlaying structure of periodically driven systems, in which the initial Bloch band splits into several copies (FloquetBloch bands), where the coupling between them directly depends on the driving regime. Interestingly, the isolated Floquet-Bloch bands possess the same topological properties as the Bloch bands of the undriven system, now tuned by the external field parameters. Thus, the topological invariants for the isolated Floquet-Bloch bands can be obtained following the general classification of time independent systems (AZ classes [6][7][8]). However, we also demonstrate that lowering the frequency, the bands couple to each other. In that case, the topological structures are classified according to a base manifold of dimension D+1. In consequence, one can simulate higher dimensional tight binding (TB) models with exotic tunable hoppings by just coupling the system to ac electric fields.Our approach is valid for arbitrary dimension, and it

We investigate the effect of an in-plane ac electric field coupled to electrons in the honeycomb lattice and show that it can be used to manipulate the Dirac points of the electronic structure. We find that the position of the Dirac points can be controlled by the amplitude and the polarization of the field for high-frequency drivings, providing a new platform to achieve their merging, a topological transition which has not been observed yet in electronic systems. Importantly, for lower frequencies we find that the multiphoton absorptions and emissions processes yield the creation of additional pairs of Dirac points. This provides an additional method to achieve the merging transition by just tuning the frequency of the driving. Our approach, based on Floquet formalism, is neither restricted to specific choice of amplitude or polarization of the field, nor to a low-energy approximation for the Hamiltonian.

We analyze the current-biased Shapiro experiment in a Josephson junction formed by two one-dimensional nanowires featuring Majorana fermions. Ideally, these junctions are predicted to have an unconventional $4\pi$-periodic Josephson effect and thus only Shapiro steps at even multiples of the driving frequency. Taking additionally into account overlap between the Majorana fermions, due to the finite length of the wire, renders the Josephson junction conventional for any dc-experiments. We show that probing the current-phase relation in a current biased setup dynamically decouples the Majorana fermions. We find that besides the even integer Shapiro steps there are additional steps at odd and fractional values. However, different from the voltage biased case, the even steps dominate for a wide range of parameters even in the case of multiple modes thus giving a clear experimental signature of the presence of Majorana fermions.Comment: 5+10pages, 5+8 Figures, published in PRB (rapid

The discovery of topological materials has motivated recent developments to export topological concepts into photonics to make light behave in exotic ways. Here, we predict several unconventional quantum optical phenomena that occur when quantum emitters interact with a topological waveguide quantum electrodynamics bath, namely, the photonic analog of the Su-Schrieffer-Heeger model. When the emitters’ frequency lies within the topological bandgap, a chiral bound state emerges, which is located on just one side (right or left) of the emitter. In the presence of several emitters, this bound state mediates topological, tunable interactions between them, which can give rise to exotic many-body phases such as double Néel ordered states. Furthermore, when the emitters’ optical transition is resonant with the bands, we find unconventional scattering properties and different super/subradiant states depending on the band topology. Last, we propose several implementations where these phenomena can be observed with state-of-the-art technology.