191 research outputs found
Pitfalls in the theory of carrier dynamics in semiconductor quantum dots: the single-particle basis vs. the many-particle configuration basis
We analyze quantum dot models used in current research for misconceptions
that arise from the choice of basis states for the carriers. The examined
models originate from semiconductor quantum optics, but the illustrated
conceptional problems are not limited to this field. We demonstrate how the
choice of basis states can imply a factorization scheme that leads to an
artificial dependency between two, actually independent, quantities.
Furthermore, we consider an open quantum dot-cavity system and show how the
dephasing, generated by the dissipator in the von Neumann Lindblad equation,
depends on the choice of basis states that are used to construct the collapse
operators. We find that the Rabi oscillations of the s-shell exciton are either
dephased by the dissipative decay of the p-shell exciton or remain unaffected,
depending on the choice of basis states. In a last step we resolve this
discrepancy by taking the full system-reservoir interaction Hamiltonian into
account
Unidirectional light emission from high-Q modes in optical microcavities
We introduce a new scheme to design optical microcavities supporting high-Q
modes with unidirectional light emission. This is achieved by coupling a low-Q
mode with unidirectional emission to a high-Q mode. The coupling is due to
enhanced dynamical tunneling near an avoided resonance crossing. Numerical
results for a microdisk with a suitably positioned air hole demonstrate the
feasibility and the potential of this concept.Comment: 4 pages, 6 figures (in reduced resolution
Hexagonal dielectric resonators and microcrystal lasers
We study long-lived resonances (lowest-loss modes) in hexagonally shaped
dielectric resonators in order to gain insight into the physics of a class of
microcrystal lasers. Numerical results on resonance positions and lifetimes,
near-field intensity patterns, far-field emission patterns, and effects of
rounding of corners are presented. Most features are explained by a
semiclassical approximation based on pseudointegrable ray dynamics and boundary
waves. The semiclassical model is also relevant for other microlasers of
polygonal geometry.Comment: 12 pages, 17 figures (3 with reduced quality
Asymmetric scattering and non-orthogonal mode patterns in optical micro-spirals
Quasi-bound states in an open system do in general not form an orthogonal and
complete basis. It is, however, expected that the non-orthogonality is weak in
the case of well-confined states except close to a so-called exceptional point
in parameter space. We present numerical evidence showing that for passive
optical microspiral cavities the parameter regime where the non-orthogonality
is significant is rather broad. Here we observe almost-degenerate pairs of
well-confined modes which are highly non-orthogonal. Using a non-Hermitian
model Hamiltonian we demonstrate that this interesting phenomenon is related to
the asymmetric scattering between clockwise and counterclockwise propagating
waves in the spiral geometry. Numerical simulations of ray dynamics reveal a
clear ray-wave correspondence.Comment: 8 pages, 10 figure
Formation of long-lived, scarlike modes near avoided resonance crossings in optical microcavities
We study the formation of long-lived states near avoided resonance crossings
in open systems. For three different optical microcavities (rectangle, ellipse,
and semi-stadium) we provide numerical evidence that these states are localized
along periodic rays, resembling scarred states in closed systems. Our results
shed light on the morphology of long-lived states in open mesoscopic systems.Comment: 4 pages, 5 figures (in reduced quality), to appear in Phys. Rev. Let
A pseudointegrable Andreev billiard
A circular Andreev billiard in a uniform magnetic field is studied. It is
demonstrated that the classical dynamics is pseudointegrable in the same sense
as for rational polygonal billiards. The relation to a specific polygon, the
asymmetric barrier billiard, is discussed. Numerical evidence is presented
indicating that the Poincare map is typically weak mixing on the invariant
sets. This link between these different classes of dynamical systems throws
some light on the proximity effect in chaotic Andreev billiards.Comment: 5 pages, 5 figures, to appear in PR
Spectral properties of quantized barrier billiards
The properties of energy levels in a family of classically pseudointegrable
systems, the barrier billiards, are investigated. An extensive numerical study
of nearest-neighbor spacing distributions, next-to-nearest spacing
distributions, number variances, spectral form factors, and the level dynamics
is carried out. For a special member of the billiard family, the form factor is
calculated analytically for small arguments in the diagonal approximation. All
results together are consistent with the so-called semi-Poisson statistics.Comment: 8 pages, 9 figure
Evanescent wave approach to diffractive phenomena in convex billiards with corners
What we are going to call in this paper "diffractive phenomena" in billiards
is far from being deeply understood. These are sorts of singularities that, for
example, some kind of corners introduce in the energy eigenfunctions. In this
paper we use the well-known scaling quantization procedure to study them. We
show how the scaling method can be applied to convex billiards with corners,
taking into account the strong diffraction at them and the techniques needed to
solve their Helmholtz equation. As an example we study a classically
pseudointegrable billiard, the truncated triangle. Then we focus our attention
on the spectral behavior. A numerical study of the statistical properties of
high-lying energy levels is carried out. It is found that all computed
statistical quantities are roughly described by the so-called semi-Poisson
statistics, but it is not clear whether the semi-Poisson statistics is the
correct one in the semiclassical limit.Comment: 7 pages, 8 figure
Superthermal photon bunching in terms of simple probability distributions
We analyze the second-order photon autocorrelation function with
respect to the photon probability distribution and discuss the generic features
of a distribution that result in superthermal photon bunching ().
Superthermal photon bunching has been reported for a number of optical
microcavity systems that exhibit processes like superradiance or mode
competition. We show that a superthermal photon number distribution cannot be
constructed from the principle of maximum entropy, if only the intensity and
the second-order autocorrelation are given. However, for bimodal systems an
unbiased superthermal distribution can be constructed from second-order
correlations and the intensities alone. Our findings suggest modeling
superthermal single-mode distributions by a mixture of a thermal and a lasing
like state and thus reveal a generic mechanism in the photon probability
distribution responsible for creating superthermal photon bunching. We relate
our general considerations to a physical system, a (single-emitter) bimodal
laser, and show that its statistics can be approximated and understood within
our proposed model. Furthermore the excellent agreement of the statistics of
the bimodal laser and our model reveal that the bimodal laser is an ideal
source of bunched photons, in the sense that it can generate statistics that
contain no other features but the superthermal bunching
Fractal Weyl law for chaotic microcavities: Fresnel's laws imply multifractal scattering
We demonstrate that the harmonic inversion technique is a powerful tool to
analyze the spectral properties of optical microcavities. As an interesting
example we study the statistical properties of complex frequencies of the fully
chaotic microstadium. We show that the conjectured fractal Weyl law for open
chaotic systems [W. T. Lu, S. Sridhar, and M. Zworski, Phys. Rev. Lett. 91,
154101 (2003)] is valid for dielectric microcavities only if the concept of the
chaotic repeller is extended to a multifractal by incorporating Fresnel's laws.Comment: 8 pages, 12 figure
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