Spectral and transport properties of time-periodic PT-symmetric tight-binding lattices

We investigate the spectral properties and dynamical features of a time-periodic PT-symmetric Hamiltonian on a one-dimensional tight-binding lattice. It is shown that a high-frequency modulation can drive the system under a transition between the broken-PT and the unbroken-PT phases. The time-periodic modulation in the unbroken-PT regime results in a significant broadening of the quasi-energy spectrum, leading to a hyper-ballistic transport regime. Also, near the PT-symmetry breaking the dispersion curve of the lattice band becomes linear, with a strong reduction of quantum wave packet spreading.Comment: 7 pages, 5 figure

Non-Hermitian transparency and one-way transport in low-dimensional lattices by an imaginary gauge field

Unidirectional and robust transport is generally observed at the edge of two- or three-dimensional quantum Hall and topological insulator systems. A hallmark of these systems is topological protection, i.e. the existence of propagative edge states that cannot be scattered by imperfections or disorder in the system. A different and less explored form of robust transport arises in non-Hermitian systems in the presence of an {\it imaginary} gauge field. As compared to topologically-protected transport in quantum Hall and topological insulator systems, robust non-Hermitian transport can be observed in {\it lower} dimensional (i.e. one dimensional) systems. In this work the transport properties of one-dimensional tight-binding lattices with an imaginary gauge field are theoretically investigated, and the physical mechanism underlying robust one-way transport is highlighted. Back scattering is here forbidden because reflected waves are evanescent rather than propagative. Remarkably, the spectral transmission of the non-Hermitian lattice is shown to be mapped into the one of the corresponding Hermitian lattice, i.e. without the gauge field, {\it but} computed in the complex plane. In particular, at large values of the gauge field the spectral transmittance becomes equal to one, even in the presence of disorder or lattice imperfections. This phenomenon can be referred to as {\it one-way non-Hermitian transparency}. Robust one-way transport can be also realized in a more realistic setting, namely in heterostructure systems, in which a non-Hermitian disordered lattice is embedded between two homogeneous Hermitian lattices. Such a double heterostructure realizes asymmetric (non-reciprocal) wave transmission. A physical implementation of non-Hermtian transparency, based on light transport in a chain of optical microring resonators, is suggested.Comment: final version, to appear in Physical Review

Robust light transport in non-Hermitian photonic lattices

Combating the effects of disorder on light transport in micro- and nano-integrated photonic devices is of major importance from both fundamental and applied viewpoints. In ordinary waveguides, imperfections and disorder cause unwanted back-reflections, which hinder large-scale optical integration. Topological photonic structures, a new class of optical systems inspired by quantum Hall effect and topological insulators, can realize robust transport via topologically-protected unidirectional edge modes. Such waveguides are realized by the introduction of synthetic gauge fields for photons in a two-dimensional structure, which break time reversal symmetry and enable one-way guiding at the edge of the medium. Here we suggest a different route toward robust transport of light in lower-dimensional (1D) photonic lattices, in which time reversal symmetry is broken because of the {\it non-Hermitian} nature of transport. While a forward propagating mode in the lattice is amplified, the corresponding backward propagating mode is damped, thus resulting in an asymmetric transport that is rather insensitive to disorder or imperfections in the structure. Non-Hermitian transport in two lattice models is considered: a tight-binding lattice with an imaginary gauge field (Hatano-Nelson model), and a non-Hermitian driven binary lattice. In the former case transport in spite of disorder is ensured by a mobility edge that arises because of a non-Hermitian delocalization transition. The possibility to observe non-Hermitian delocalization induced by a synthetic 'imaginary' gauge field is suggested using an engineered coupled-resonator optical waveguide (CROW) structure.Comment: revised and extended version, to appear in Sci. Re

Non-Hermitian shortcut to stimulated Raman adiabatic passage

We propose a non-Hermitian generalization of stimulated Raman adiabatic passage (STIRAP), which allows one to increase speed and fidelity of the adiabatic passage. This is done by adding balanced imaginary (gain/loss) terms in the diagonal (bare energy) terms of the Hamiltonian and choosing them such that they cancel exactly the nonadiabatic couplings, providing in this way an effective shortcut to adiabaticity. Remarkably, for a STIRAP using delayed Gaussian-shaped pulses in the counter-intuitive scheme the imaginary terms of the Hamiltonian turn out to be time independent. A possible physical realization of non-Hermitian STIRAP, based on light transfer in three evanescently-coupled optical waveguides, is proposed.Comment: 7 pages, 4 figure

Quantum simulation of the Riemann-Hurwitz zeta function

We propose a simple realization of a quantum simulator of the Riemann-Hurwitz (RH) \zeta\ function based on a truncation of its Dirichlet representation. We synthesize a nearest-neighbour-interaction Hamiltonian, satisfying the property that the temporal evolution of the autocorrelation function of an initial bare state of the Hamiltonian reproduces the RH function along the line \sigma+i \omega t of the complex plane, with \sigma>1. The tight-binding Hamiltonian with engineered hopping rates and site energies can be implemented in a variety of physical systems, including trapped ion systems and optical waveguide arrays. The proposed method is scalable, which means that the simulation can be in principle arbitrarily accurate. Practical limitations of the suggested scheme, arising from a finite number of lattice sites N and from decoherence, are briefly discussed.Comment: 6 pages, 3 figure

Dynamics of high-energy excitations in few-particle Hubbard models

The coherent motion of few correlated particles in Hubbard models shows rather distinctive dynamical features that go beyond the predictions of mean-field (NLSE) models. In this contribution we will discuss the dynamical properties of strongly correlated particles forming a bound particle state (doublons) driven by external forces, including the existence of fractional Bloch oscillations, the coherent destruction of particle correlation, super-Bloch and anyonic Bloch oscillations, Klein tunneling of correlated particles and low-excitation bound states  in ac-driven two-species Hubbard models. Photonic simulations of fractional Bloch oscillations in a waveguide-based optical setting will be also presented

Fractional Bloch oscillations in photonic lattices

Bloch oscillations, the oscillatory motion of a quantum particle in a periodic potential, are one of the most fascinating effects of coherent quantum transport. Originally studied in the context of electrons in crystals, Bloch oscillations manifest the wave nature of matter and are found in a wide variety of different physical systems. Here we report on the first experimental observation of fractional Bloch oscillations, using a photonic lattice as a model system of a two-particle extended Bose-Hubbard Hamiltonian. In our photonic simulator, the dynamics of two correlated particles hopping on a one-dimensional lattice is mapped into the motion of a single particle in a two-dimensional lattice with engineered defects and mimicked by light transport in a square waveguide lattice with a bent axis

Ultrafast hot electron dynamics in plasmonic nanostructures: experiments, modelling, design

Abstract Metallic nanostructures exhibit localized surface plasmons (LSPs), which offer unprecedented opportunities for advanced photonic materials and devices. Following resonant photoexcitation, LSPs quickly dephase, giving rise to a distribution of energetic 'hot' electrons in the metal. These out-of-equilibrium carriers undergo ultrafast internal relaxation processes, nowadays pivotal in a variety of applications, from photodetection and sensing to the driving of photochemical reactions and ultrafast all-optical modulation of light. Despite the intense research activity, exploitation of hot carriers for real-world nanophotonic devices remains extremely challenging. This is due to the complexity inherent to hot carrier relaxation phenomena at the nanoscale, involving short-lived out-of-equilibrium electronic states over a very broad range of energies, in interaction with thermal electronic and phononic baths. These issues call for a comprehensive understanding of ultrafast hot electron dynamics in plasmonic nanostructures. This paper aims to review our contribution to the field: starting from the fundamental physics of plasmonic nanostructures, we first describe the experimental techniques used to probe hot electrons; we then introduce a numerical model of ultrafast nanoscale relaxation processes, and present examples in which experiments and modelling are combined, with the aim of designing novel optical functionalities enabled by ultrafast hot-electron dynamics