1,243 research outputs found
Halving Balls in Deterministic Linear Time
Let \D be a set of pairwise disjoint unit balls in and the
set of their center points. A hyperplane \Hy is an \emph{-separator} for
\D if each closed halfspace bounded by \Hy contains at least points
from . This generalizes the notion of halving hyperplanes, which correspond
to -separators. The analogous notion for point sets has been well studied.
Separators have various applications, for instance, in divide-and-conquer
schemes. In such a scheme any ball that is intersected by the separating
hyperplane may still interact with both sides of the partition. Therefore it is
desirable that the separating hyperplane intersects a small number of balls
only. We present three deterministic algorithms to bisect or approximately
bisect a given set of disjoint unit balls by a hyperplane: Firstly, we present
a simple linear-time algorithm to construct an -separator for balls
in , for any , that intersects at most
balls, for some constant that depends on and . The number of
intersected balls is best possible up to the constant . Secondly, we present
a near-linear time algorithm to construct an -separator in
that intersects balls. Finally, we give a linear-time algorithm to
construct a halving line in that intersects
disks.
Our results improve the runtime of a disk sliding algorithm by Bereg,
Dumitrescu and Pach. In addition, our results improve and derandomize an
algorithm to construct a space decomposition used by L{\"o}ffler and Mulzer to
construct an onion (convex layer) decomposition for imprecise points (any point
resides at an unknown location within a given disk)
Fiber transport of spatially entangled photons
Entanglement in the spatial degrees of freedom of photons is an interesting
resource for quantum information. For practical distribution of such entangled
photons it is desireable to use an optical fiber, which in this case has to
support multiple transverse modes. Here we report the use of a hollow-core
photonic crystal fiber to transport spatially entangled qubits.Comment: 4 pages, 4 figure
Extended polarized semiclassical model for quantum-dot cavity QED and its application to single-photon sources
We present a simple extension of the semi-classical model for a two-level
system in a cavity, in order to incorporate multiple polarized transitions,
such as those appearing in neutral and charged quantum dots (QDs), and two
nondegenerate linearly polarized cavity modes. We verify the model by exact
quantum master equation calculations, and experimentally using a neutral QD in
a polarization non-degenerate micro-cavity, in both cases we observe excellent
agreement. Finally, the usefulness of this approach is demonstrated by
optimizing a single-photon source based on polarization postselection, where we
find an increase in the brightness for optimal polarization conditions as
predicted by the model.Comment: 8 pages, for simple code see https://doi.org/10.5281/zenodo.347666
Determination of the Carrier-Envelope Phase of Few-Cycle Laser Pulses with Terahertz-Emission Spectroscopy
The availability of few-cycle optical pulses opens a window to physical
phenomena occurring on the attosecond time scale. In order to take full
advantage of such pulses, it is crucial to measure and stabilise their
carrier-envelope (CE) phase, i.e., the phase difference between the carrier
wave and the envelope function. We introduce a novel approach to determine the
CE phase by down-conversion of the laser light to the terahertz (THz) frequency
range via plasma generation in ambient air, an isotropic medium where optical
rectification (down-conversion) in the forward direction is only possible if
the inversion symmetry is broken by electrical or optical means. We show that
few-cycle pulses directly produce a spatial charge asymmetry in the plasma. The
asymmetry, associated with THz emission, depends on the CE phase, which allows
for a determination of the phase by measurement of the amplitude and polarity
of the THz pulse
A Complexity View of Rainfall
We show that rain events are analogous to a variety of nonequilibrium
relaxation processes in Nature such as earthquakes and avalanches. Analysis of
high-resolution rain data reveals that power laws describe the number of rain
events versus size and number of droughts versus duration. In addition, the
accumulated water column displays scale-less fluctuations. These statistical
properties are the fingerprints of a self-organized critical process and may
serve as a benchmark for models of precipitation and atmospheric processes.Comment: 4 pages, 5 figure
Quantum fluctuations in the mazer
Quantum fluctuations in the mazer are considered, arising either from the
atomic motion or from the quantized intracavity field. Analytical results, for
both the meza and the hyperbolic secant mode profile, predict for example an
attenuation of tunneling resonances due to such fluctuations. The case of a
Gaussian mode profile is studied numerically using a wave packet propagation
approach. The method automatically takes into account fluctuations in the
atomic motion and the dynamics is especially considered at or adjacent to a
tunnel resonance. We find that the system evolution is greatly sensitive to the
atom-field detuning, bringing about a discussion about the concept of
adiabaticity in this model. Further, a novel collapse-revival phenomena is
demonstrated, originating from the quantum fluctuations in the atomic motion
rather from field fluctuations as is normally the case.Comment: 15 pages, 8 figures. Replaced with final versio
Single photons and unconventional photon blockade in quantum dot cavity-QED
We observe the unconventional photon blockade effect in quantum dot cavity
QED, which, in contrast to conventional photon blockade, operates in the weak
coupling regime. A single quantum dot transition is simultaneously coupled to
two orthogonally polarized optical cavity modes, and by careful tuning of the
input and output state of polarization, the unconventional photon blockade
effect is observed. We find a minimum second-order correlation
which corresponds to when
corrected for detector jitter, and observe the expected polarization dependency
and photon bunching and anti-bunching very close-by in parameter space, which
indicates the abrupt change from phase to amplitude squeezing.Comment: 5 page
Dark States and Interferences in Cascade Transitions of Ultra-Cold Atoms in a Cavity
We examine the competition among one- and two-photon processes in an
ultra-cold, three-level atom undergoing cascade transitions as a result of its
interaction with a bimodal cavity. We show parameter domains where two-photon
transitions are dominant and also study the effect of two-photon emission on
the mazer action in the cavity. The two-photon emission leads to the loss of
detailed balance and therefore we obtain the photon statistics of the cavity
field by the numerical integration of the master equation. The photon
distribution in each cavity mode exhibits sub- and super- Poissonian behaviors
depending on the strength of atom-field coupling. The photon distribution
becomes identical to a Poisson distribution when the atom-field coupling
strengths of the modes are equal.Comment: 15 pages including 7 figures in Revtex, submitted to PR
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