25,507 research outputs found
Robust Piecewise-Constant Smoothing: M-Smoother Revisited
A robust estimator, namely M-smoother, for piecewise-constant smoothing is
revisited in this paper. Starting from its generalized formulation, we propose
a numerical scheme/framework for solving it via a series of weighted-average
filtering (e.g., box filtering, Gaussian filtering, bilateral filtering, and
guided filtering). Because of the equivalence between M-smoother and
local-histogram-based filters (such as median filter and mode filter), the
proposed framework enables fast approximation of histogram filters via a number
of box filtering or Gaussian filtering. In addition, high-quality
piecewise-constant smoothing can be achieved via a number of bilateral
filtering or guided filtering integrated in the proposed framework. Experiments
on depth map denoising show the effectiveness of our framework.Comment: 11 pages, 9 figures, update url link
Carrier envelope phase dynamics of cavity solitons: soliton stability and scaling law
The relationship between carrier envelope phase (CEP) slip of cavity soliton
(CS) and pump phase detuning is derived analytically and numerically. To
preserve the stability of CS, CEP slip always equals to the pump phase
detuning. When CEP slip fails to follow the pump phase detuning, CS becomes
unstable. The locking between CEP slip and pump phase detuning results in a
scaling law for CS.Comment: 4 pages, 3 figure
Berry phases of quantum trajectories in semiconductors under strong terahertz fields
Quantum evolution of particles under strong fields can be essentially
captured by a small number of quantum trajectories that satisfy the stationary
phase condition in the Dirac-Feynmann path integrals. The quantum trajectories
are the key concept to understand extreme nonlinear optical phenomena, such as
high-order harmonic generation (HHG), above-threshold ionization (ATI), and
high-order terahertz sideband generation (HSG). While HHG and ATI have been
mostly studied in atoms and molecules, the HSG in semiconductors can have
interesting effects due to possible nontrivial "vacuum" states of band
materials. We find that in a semiconductor with non-vanishing Berry curvature
in its energy bands, the cyclic quantum trajectories of an electron-hole pair
under a strong terahertz field can accumulate Berry phases. Taking monolayer
MoS as a model system, we show that the Berry phases appear as the Faraday
rotation angles of the pulse emission from the material under short-pulse
excitation. This finding reveals an interesting transport effect in the extreme
nonlinear optics regime.Comment: 5 page
On Picard Type Theorems and Entire Solutions of Differential Equations
We give a connection between the Picard type theorem of Polya-Saxer-Milliox
and characterization of entire solutions of a differential equation and then
their higher dimensional extensions, which leads further results on both
(ordinary and partial) differential equations and Picard type theorems.Comment: 7 page
Black holes of dimensionally continued gravity coupled to Born-Infeld electromagnetic field
In this paper, for dimensionally continued gravity coupled to Born-Infeld
electromagnetic field, we construct topological black holes in diverse
dimensions and construct dyonic black holes in general even dimensions. We
study thermodynamics of the black holes and obtain first laws. We study thermal
phase transitions of the black holes in - plane and find van der
Waals-like phase transitions for even-dimensional spherical black holes, such
phase transitions are not found for other types of black holes constructed in
this paper.Comment: 18 pages, 5 figure
Nonlinear optical response induced by non-Abelian Berry curvature in time-reversal-invariant insulators
We propose a general framework of nonlinear optics induced by non-Abelian
Berry curvature in time-reversal-invariant (TRI) insulators. We find that the
third-order response of a TRI insulator under optical and terahertz light
fields is directly related to the integration of the non-Abelian Berry
curvature over the Brillouin zone. We apply the result to insulators with
rotational symmetry near the band edge. Under resonant excitations, the optical
susceptibility is proportional to the flux of the Berry curvature through the
iso-energy surface, which is equal to the Chern number of the surface times
. For the III-V compound semiconductors, microscopic calculations based
on the six-band model give a third-order susceptibility with the Chern number
of the iso-energy surface equal to three
Imaginary geometric phases of quantum trajectories
A quantum object can accumulate a geometric phase when it is driven along a
trajectory in a parameterized state space with non-trivial gauge structures.
Inherent to quantum evolutions, a system can not only accumulate a quantum
phase but may also experience dephasing, or quantum diffusion. Here we show
that the diffusion of quantum trajectories can also be of geometric nature as
characterized by the imaginary part of the geometric phase. Such an imaginary
geometric phase results from the interference of geometric phase dependent
fluctuations around the quantum trajectory. As a specific example, we study the
quantum trajectories of the optically excited electron-hole pairs, driven by an
elliptically polarized terahertz field, in a material with non-zero Berry
curvature near the energy band extremes. While the real part of the geometric
phase leads to the Faraday rotation of the linearly polarized light that
excites the electron-hole pair, the imaginary part manifests itself as the
polarization ellipticity of the terahertz sidebands. This discovery of
geometric quantum diffusion extends the concept of geometric phases.Comment: 5 pages with 3 figure
Finite-key analysis of a practical decoy-state high-dimensional quantum key distribution
Compared with two-level quantum key distribution (QKD), highdimensional QKD
enable two distant parties to share a secret key at a higher rate. We provide a
finite-key security analysis for the recently proposed practical
highdimensional decoy-state QKD protocol based on time-energy entanglement. We
employ two methods to estimate the statistical fluctuation of the postselection
probability and give a tighter bound on the secure-key capacity. By numerical
evaluation, we show the finite-key effect on the secure-key capacity in
different conditions. Moreover, our approach could be used to optimize
parameters in practical implementations of highdimensional QKD
Geometric phases for two-mode squeezed state
Although the geometric phase for one-mode squeezed state had been studied in
detail, the counterpart for two-mode squeezed state is vacant. It is be
evaluated explicitly in this paper. Furthermore, the total phase factor is in
an elegent form, which is just identical to one term of product of two squeezed
operators. In addition, when this system undergoes cyclic evolutions, the
corresponding geometric phase is obtained, which is just the sum of the
counterparts of two isolated one-mode squeezed state. Finally, the relationship
between the cyclic geomtric phase and entanglement of two-mode squeezed state
is established.Comment: 9 pages, 1 figur
Strongly polarizing weakly coupled C nuclear spins with optically pumped nitrogen-vacancy center
Enhancing the polarization of nuclear spins surrounding the nitrogen-vacancy
(NV) center in diamond has attracted widespread attention recently due to its
various applications. Here we present an analytical theory and comprehensive
understanding on how to optimize the dynamic nuclear polarization by an
optically pumped NV center near the ground state level anticrossing. Our
results not only provide a parameter-free explanation and a clearly physics
picture for the recently observed polarization dependence on the magnetic field
for strongly coupled C nuclei [H. J. Wang \textit{et al}., Nat. Commun.
4, 1 (2013)], but also demonstrate the possibility to strongly polarize weakly
coupled C nuclei under weak optical pumping and suitably chosen magnetic
field. This allows sensitive magnetic control of the C nuclear spin
polarization for NMR applications and significant suppression of the C
nuclear spin noise to prolong the NV spin coherence time
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