3,393 research outputs found
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 () 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 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 generated by a laser system \textbf{S} operated
in an arbitrary regime can be perfectly absorbed by a CPA device
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 -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
-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
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