1,879 research outputs found
Ensemble versus individual system in quantum optics
Modern techniques allow experiments on a single atom or system, with new
phenomena and new challenges for the theoretician. We discuss what quantum
mechanics has to say about a single system. The quantum jump approach as well
as the role of quantum trajectories are outlined and a rather sophisticated
example is given.Comment: Fundamental problems in quantum theory workshop, invited lecture. 11
pages Latex + 7 figures. To appear in Fortschr. d. Physi
An experiment on the shifts of reflected C-lines
An experiment is described that tests theoretical predictions on how C-lines
incident obliquely on a surface behave on reflection. C-lines in a polarised
wave are the analogues of the optical vortices carried by a complex scalar
wave, which is the usual model for describing light and other electromagnetic
waves. The centre of a laser beam that carries a (degenerate) C-line is shifted
on reflection by the well-known Goos-H\"anchen and Imbert-Fedorov effects, but
the C-line itself splits into two, both of which are shifted longitudinally and
laterally; their shifts are different from that of the beam centre. To maximise
the effect to be measured, internal reflection in a glass prism close to the
critical angle was used. In a simple situation like this two recently published
independent theories of C-line reflection overlap and it is shown that their
predictions are identical. The measured differences in the lateral shifts of
the two reflected C-lines are compared with theoretical expectations over a
range of incidence angles.Comment: 9 pages, 2 figure
Optimality of Spectral Clustering in the Gaussian Mixture Model
Spectral clustering is one of the most popular algorithms to group high
dimensional data. It is easy to implement and computationally efficient.
Despite its popularity and successful applications, its theoretical properties
have not been fully understood. In this paper, we show that spectral clustering
is minimax optimal in the Gaussian Mixture Model with isotropic covariance
matrix, when the number of clusters is fixed and the signal-to-noise ratio is
large enough. Spectral gap conditions are widely assumed in the literature to
analyze spectral clustering. On the contrary, these conditions are not needed
to establish optimality of spectral clustering in this paper
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
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
Co-induced nano-structures on Si(111) surface
The interaction of cobalt atoms with silicon (111) surface has been
investigated by means of scanning tunneling microscopy (STM) and low-energy
electron diffraction (LEED). Besides the Co silicide islands, we have
successfully distinguished two inequivalent Co-induced
reconstructions on Si (111) surface. Our
high-resolution STM images provide some structural properties of the two
different derived phases. Both of the two phases
seem to form islands with single domain. The new findings will help us to
understand the early stage of Co silicide formations.Comment: 4pages 4figure
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
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