1,383 research outputs found
Resolved-sideband cooling and measurement of a micromechanical oscillator close to the quantum limit
The observation of quantum phenomena in macroscopic mechanical oscillators
has been a subject of interest since the inception of quantum mechanics.
Prerequisite to this regime are both preparation of the mechanical oscillator
at low phonon occupancy and a measurement sensitivity at the scale of the
spread of the oscillator's ground state wavefunction. It has been widely
perceived that the most promising approach to address these two challenges are
electro nanomechanical systems. Here we approach for the first time the quantum
regime with a mechanical oscillator of mesoscopic dimensions--discernible to
the bare eye--and 1000-times more massive than the heaviest nano-mechanical
oscillators used to date. Imperative to these advances are two key principles
of cavity optomechanics: Optical interferometric measurement of mechanical
displacement at the attometer level, and the ability to use measurement induced
dynamic back-action to achieve resolved sideband laser cooling of the
mechanical degree of freedom. Using only modest cryogenic pre-cooling to 1.65
K, preparation of a mechanical oscillator close to its quantum ground state
(63+-20 phonons) is demonstrated. Simultaneously, a readout sensitivity that is
within a factor of 5.5+-1.5 of the standard quantum limit is achieved. The
reported experiments mark a paradigm shift in the approach to the quantum limit
of mechanical oscillators using optical techniques and represent a first step
into a new era of experimental investigation which probes the quantum nature of
the most tangible harmonic oscillator: a mechanical vibration.Comment: 14 pages, 4 figure
Etude du milieu terrestre des atolls de la Polynésie française : caractéristiques et potentialités agricoles
Cet article présente les principales caractéristiques des sols des atolls et des récifs de la Polynésie française. Les auteurs discutent également les problèmes de la mise en valeur des sols sur ces îlots coralliens et illustrent les différentes techniques culturales utilisée
Numerical aspects of nonlinear Schrodinger equations in the presence of caustics
The aim of this text is to develop on the asymptotics of some 1-D nonlinear
Schrodinger equations from both the theoretical and the numerical perspectives,
when a caustic is formed. We review rigorous results in the field and give some
heuristics in cases where justification is still needed. The scattering
operator theory is recalled. Numerical experiments are carried out on the focus
point singularity for which several results have been proven rigorously.
Furthermore, the scattering operator is numerically studied. Finally,
experiments on the cusp caustic are displayed, and similarities with the focus
point are discussed.Comment: 20 pages. To appear in Math. Mod. Meth. Appl. Sc
Bipartite induced density in triangle-free graphs
We prove that any triangle-free graph on vertices with minimum degree at
least contains a bipartite induced subgraph of minimum degree at least
. This is sharp up to a logarithmic factor in . Relatedly, we show
that the fractional chromatic number of any such triangle-free graph is at most
the minimum of and as . This is
sharp up to constant factors. Similarly, we show that the list chromatic number
of any such triangle-free graph is at most as
.
Relatedly, we also make two conjectures. First, any triangle-free graph on
vertices has fractional chromatic number at most
as . Second, any triangle-free
graph on vertices has list chromatic number at most as
.Comment: 20 pages; in v2 added note of concurrent work and one reference; in
v3 added more notes of ensuing work and a result towards one of the
conjectures (for list colouring
Qubit-Programmable Operations on Quantum Light Fields
Engineering quantum operations is one of the main abilities we need for
developing quantum technologies and designing new fundamental tests. Here we
propose a scheme for realising a controlled operation acting on a travelling
quantum field, whose functioning is determined by an input qubit. This study
introduces new concepts and methods in the interface of continuous- and
discrete-variable quantum optical systems.Comment: Comments welcom
Apodized Pupil Lyot Coronagraphs for Arbitrary Telescope Apertures
In the context of high dynamic range imaging, this study presents a
breakthrough for the understanding of Apodized Pupil Lyot Coronagraphs, making
them available for arbitrary aperture shapes. These new solutions find
immediate application in current, ground-based coronagraphic studies (Gemini,
VLT) and in existing instruments (AEOS Lyot Project). They also offer the
possiblity of a search for an on-axis design for TPF. The unobstructed aperture
case has already been solved by Aime et al. (2002) and Soummer et al. (2003).
Analytical solutions with identical properties exist in the general case and,
in particular, for centrally obscured apertures. Chromatic effects can be
mitigated with a numerical optimization. The combination of analytical and
numerical solutions enables the study of the complete parameter space (central
obstruction, apodization throughput, mask size, bandwidth, and Lyot stop size).Comment: 7 pages 4 figures - ApJL, accepte
(Semi)classical limit of the Hartree equation with harmonic potential
Nonlinear Schrodinger Equations (NLS) of the Hartree type occur in the
modeling of quantum semiconductor devices. Their "semiclassical" limit of
vanishing (scaled) Planck constant is both a mathematical challenge and
practically relevant when coupling quantum models to classical models.
With the aim of describing the semi-classical limit of the 3D
Schrodinger--Poisson system with an additional harmonic potential, we study
some semi-classical limits of the Hartree equation with harmonic potential in
space dimension n>1. The harmonic potential is confining, and causes focusing
periodically in time. We prove asymptotics in several cases, showing different
possible nonlinear phenomena according to the interplay of the size of the
initial data and the power of the Hartree potential. In the case of the 3D
Schrodinger-Poisson system with harmonic potential, we can only give a formal
computation since the need of modified scattering operators for this long range
scattering case goes beyond current theory. We also deal with the case of an
additional "local" nonlinearity given by a power of the local density - a model
that is relevant when incorporating the Pauli principle in the simplest model
given by the "Schrodinger-Poisson-X equation". Further we discuss the
connection of our WKB based analysis to the Wigner function approach to
semiclassical limits.Comment: 26 page
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