304 research outputs found
Bound States in the Continuum and Fano Resonances in the Dirac Cone Spectrum
We consider light scattering by two dimensional arrays of high-index
dielectric spheres arranged into the triangular lattice. It is demonstrated
that in the case a triple degeneracy of resonant leaky modes in the Gamma-point
the scattering spectra exhibit a complicated picture of Fano resonances with
extremely narrow line-width. The Fan features are explained through coupled
mode theory for a Dirac cone spectrum as a signature of optical bound states in
the continuum (BIC). It is found that the standing wave in-Gamma BIC induces a
ring of off-Gamma BICs due to different scaling laws for real and imaginary
parts of the resonant eigenfrequencies in the Dirac cone spectrum. A
quantitative theory of the spectra is proposed
Correlated behavior of conductance and phase rigidity in the transition from the weak-coupling to the strong-coupling regime
We study the transmission through different small systems as a function of
the coupling strength to the two attached leads. The leads are identical
with only one propagating mode in each of them. Besides the
conductance , we calculate the phase rigidity of the scattering wave
function in the interior of the system. Most interesting results are
obtained in the regime of strongly overlapping resonance states where the
crossover from staying to traveling modes takes place. The crossover is
characterized by collective effects. Here, the conductance is plateau-like
enhanced in some energy regions of finite length while corridors with zero
transmission (total reflection) appear in other energy regions. This
transmission picture depends only weakly on the spectrum of the closed system.
It is caused by the alignment of some resonance states of the system with the
propagating modes in the leads. The alignment of resonance states
takes place stepwise by resonance trapping, i.e. it is accompanied by the
decoupling of other resonance states from the continuum of propagating modes.
This process is quantitatively described by the phase rigidity of the
scattering wave function. Averaged over energy in the considered energy window,
is correlated with . In the regime of strong coupling, only two
short-lived resonance states survive each aligned with one of the channel wave
functions . They may be identified with traveling modes through the
system. The remaining trapped narrow resonance states are well separated
from one another.Comment: Resonance trapping mechanism explained in the captions of Figs. 7 to
11. Recent papers added in the list of reference
Complex Energy Spectrum and Time Evolution of QBIC States in a Two-Channel Quantum wire with an Adatom Impurity
We provide detailed analysis of the complex energy eigenvalue spectrum for a
two-channel quantum wire with an attached adatom impurity. The study is based
on our previous work [Phys. Rev. Lett. 99, 210404 (2007)], in which we
presented the quasi-bound states in continuum (or QBIC states). These are
resonant states with very long lifetimes that form as a result of two
overlapping continuous energy bands one of which, at least, has a divergent van
Hove singularity at the band edge. We provide analysis of the full energy
spectrum for all solutions, including the QBIC states, and obtain an expansion
for the complex eigenvalue of the QBIC state. We show that it has a small decay
rate of the order , where is the coupling constant. As a result of
this expansion, we find that this state is a non-analytic effect resulting from
the van Hove singularity; it cannot be predicted from the ordinary perturbation
analysis that relies on Fermi's golden rule. We will also numerically
demonstrate the time evolution of the QBIC state using the effective potential
method in order to show the stability of the QBIC wave function in comparison
with that of the other eigenstates.Comment: Around 20 pages, 50 total figure
Phase rigidity and avoided level crossings in the complex energy plane
We consider the effective Hamiltonian of an open quantum system, its
biorthogonal eigenfunctions and define the value that characterizes the
phase rigidity of the eigenfunctions . In the scenario with
avoided level crossings, varies between 1 and 0 due to the mutual
influence of neighboring resonances. The variation of may be
considered as an internal property of an {\it open} quantum system. In the
literature, the phase rigidity of the scattering wave function
is considered. Since can be represented in the interior
of the system by the , the phase rigidity of the
is related to the and therefore also to the mutual
influence of neighboring resonances. As a consequence, the reduction of the
phase rigidity to values smaller than 1 should be considered, at least
partly, as an internal property of an open quantum system in the overlapping
regime. The relation to measurable values such as the transmission through a
quantum dot, follows from the fact that the transmission is, in any case,
resonant with respect to the effective Hamiltonian. We illustrate the relation
between phase rigidity and transmission numerically for small open
cavities.Comment: 6 pages, 3 figure
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