Dynamic localization and transport in complex crystals

The behavior of a Bloch particle in a complex crystal with PT symmetry subjected to a sinusoidal ac force is theoretically investigated. For unbroken PT symmetry and in the single-band approximation, it is shown that time reversal symmetry of the ac force preserves the reality of the quasienergy spectrum. Like in ordinary crystals, exact band collapse, corresponding to dynamic localization, is attained for a sinusoidal band shape. The wave packet dynamics turns out to be deeply modified at the PT symmetry breaking point, where band merging occurs and Bragg scattering in the crystal becomes highly non-reciprocal.Comment: 6 pages, 3 figure

Bloch oscillations in complex crystals with PT symmetry

Bloch oscillations (BO) in complex lattices with PT symmetry are theoretically investigated with specific reference to optical BO in photonic lattices with gain/loss regions. Novel dynamical phenomena with no counterpart in ordinary lattices, such as non-reciprocal BO related to violation of the Friedel's law of Bragg scattering in complex potentials, are highlighted.Comment: 4 pages, 3 figure

Optical Realization of Coherent Vibrational Dynamics in Molecules

Optical analogues of coherent vibrational phenomena in molecules, such as light-induced molecular stabilization and wave packet dynamics at a potential crossing, are proposed for light beams in coupled slab waveguides.Comment: 11 pages, 3 figure

Dynamic localization in Glauber-Fock lattices

Glauber-Fock lattices refer to a special class of semi-infinite tight-binding lattices with inhomogeneous hopping rates which are found in certain simple solid-state, quantum optics and quantum field theoretical models. Here it is shown that dynamic localization, i.e. suppression of quantum diffusion and periodic quantum self-imaging by an external sinusoidal force [D.H. Dunlap and V.M. Kenkre, Phys. Rev. B {\bf 34}, 3625 (1986)], can be exactly realized in Glauber-Fock lattices, in spite of inhomogeneity of hopping rates and lattice truncation.Comment: 3 figure

Mitigation of dynamical instabilities in laser arrays via non-Hermitian coupling

Arrays of coupled semiconductor lasers are systems possessing complex dynamical behavior that are of major interest in photonics and laser science. Dynamical instabilities, arising from supermode competition and slow carrier dynamics, are known to prevent stable phase locking in a wide range of parameter space, requiring special methods to realize stable laser operation. Inspired by recent concepts of parity-time ($\mathcal{PT}$) and non-Hermitian photonics, in this work we consider non-Hermitian coupling engineering in laser arrays in a ring geometry and show, both analytically and numerically, that non-Hermitian coupling can help to mitigate the onset of dynamical laser instabilities. In particular, we consider in details two kinds of nearest-neighbor non-Hermitian couplings: symmetric but complex mode coupling (type-I non-Hermitian coupling) and asymmetric mode coupling (type-II non-Hermitian coupling). Suppression of dynamical instabilities can be realized in both coupling schemes, resulting in stable phase-locking laser emission with the lasers emitting in phase (for type-I coupling) or with $\pi/2$ phase gradient (for type-II coupling), resulting in a vortex far-field beam. In type-II non-Hermitian coupling, chirality induced by asymmetric mode coupling enables laser phase locking even in presence of moderate disorder in the resonance frequencies of the lasers.Comment: revised version, changed title, added one figure and some reference

Coherent perfect absorbers for transient, periodic or chaotic optical fields: time-reversed lasers beyond threshold

Recent works [Y.D. Chong {\it et al.}, Phys. Rev. Lett. {\bf 105}, 053901 (2010); W. Wan {\it et al.}, Science {\bf 331}, 889 (2011)] have shown that the time-reversed process of lasing at threshold realizes a coherent perfect absorber (CPA). In a CPA, a lossy medium in an optical cavity with a specific degree of dissipation, equal in modulus to the gain of the lasing medium, can perfectly absorb coherent optical waves at discrete frequencies that are the time-reversed counterpart of the lasing modes. Here the concepts of time-reversal of lasing and CPA are extended for optical radiation emitted by a laser operated in an arbitrary (and generally highly-nonlinear) regime, i.e. for transient, chaotic or periodic coherent optical fields. We prove that any electromagnetic signal $E(t)$ generated by a laser system \textbf{S} operated in an arbitrary regime can be perfectly absorbed by a CPA device $\bf{S'}$ which is simply realized by placing inside \textbf{S} a broadband linear absorber (attenuator) of appropriate transmittance. As examples, we discuss CPA devices that perfectly absorb a chaotic laser signal and a frequency-modulated optical wave.Comment: 9 pages, 3 figure; to appear in Phys. Rev.

Absence of Floquet scattering in oscillating non-Hermitian potential wells

Scattering of a quantum particle from an oscillating barrier or well does not generally conserve the particle energy owing to energy exchange with the photon field, and an incoming particle-free state is scattered into a set of outgoing (transmitted and reflected) free states according to Floquet scattering theory. Here we introduce two families of oscillating non-Hermitian potential wells in which Floquet scattering is fully suppressed for any energy of the incident particle. The scattering-free oscillating potentials are synthesized by application of the Darboux transformation to the time-dependent Schr\"{o}dinger equation. For one of the two families of scattering-free potentials, the oscillating potential turns out to be fully invisible.Comment: 5 figure

Low-energy doublons in the ac-driven two-species Hubbard model

The hopping dynamics of two fermionic species with different effective masses in the one-dimensional Hubbard model driven by an external field is theoretically investigated. A multiple-time-scale asymptotic analysis of the driven asymmetric Hubbard model shows that a high-frequency bichromatic external field can sustain a new kind of low-energy particle bound state (doublon), in which two fermions of different species occupy nearest neighbor sites and co-tunnel along the lattice. The predictions of the asymptotic analysis are confirmed by direct numerical simulations of the two-particle Hubbard Hamiltonian.Comment: 4 figure

Invisible defects in complex crystals

We show that invisible localized defects, i.e. defects that can not be detected by an outside observer, can be realized in a crystal with an engineered imaginary potential at the defect site. The invisible defects are synthesized by means of supersymmetric (Darboux) transformations of an ordinary crystal using band-edge wave functions to construct the superpotential. The complex crystal has an entire real-valued energy spectrum and Bragg scattering is not influenced by the defects. An example of complex crystal synthesis is presented for the Mathieu potential

Optical lattices with exceptional points in the continuum

The spectral, dynamical and topological properties of physical systems described by non-Hermitian (including $\mathcal{PT}$-symmetric) Hamiltonians are deeply modified by the appearance of exceptional points and spectral singularities. Here we show that exceptional points in the continuum can arise in non-Hermitian (yet admitting and entirely real-valued energy spectrum) optical lattices with engineered defects. At an exceptional point, the lattice sustains a bound state with an energy embedded in the spectrum of scattered states, similar to the von-Neumann Wigner bound states in the continuum of Hermitian lattices. However, the dynamical and scattering properties of the bound state at an exceptional point are deeply different from those of ordinary von-Neumann Wigner bound states in an Hermitian system. In particular, the bound state in the continuum at an exceptional point is an unstable state that can secularly grow by an infinitesimal perturbation. Such properties are discussed in details for transport of discretized light in a $\mathcal{PT}$-symmetric array of coupled optical waveguides, which could provide an experimentally accessible system to observe exceptional points in the continuum.Comment: 11 pages, 4 figures, slightly revised revision (corrected misprints in caption of Figs.2 and 4 from published version