19,794 research outputs found
An Optimal Control Formulation for Inviscid Incompressible Ideal Fluid Flow
In this paper we consider the Hamiltonian formulation of the equations of
incompressible ideal fluid flow from the point of view of optimal control
theory. The equations are compared to the finite symmetric rigid body equations
analyzed earlier by the authors. We discuss various aspects of the Hamiltonian
structure of the Euler equations and show in particular that the optimal
control approach leads to a standard formulation of the Euler equations -- the
so-called impulse equations in their Lagrangian form. We discuss various other
aspects of the Euler equations from a pedagogical point of view. We show that
the Hamiltonian in the maximum principle is given by the pairing of the
Eulerian impulse density with the velocity. We provide a comparative discussion
of the flow equations in their Eulerian and Lagrangian form and describe how
these forms occur naturally in the context of optimal control. We demonstrate
that the extremal equations corresponding to the optimal control problem for
the flow have a natural canonical symplectic structure.Comment: 6 pages, no figures. To appear in Proceedings of the 39th IEEEE
Conference on Decision and Contro
Ordered and disordered dynamics in monolayers of rolling particles
We consider the ordered and disordered dynamics for monolayers of rolling
self-interacting particles with an offset center of mass and a non-isotropic
inertia tensor. The rolling constraint is considered as a simplified model of a
very strong, but rapidly decaying bond with the surface, preventing application
of the standard tools of statistical mechanics. We show the existence and
nonlinear stability of ordered lattice states, as well as disturbance
propagation through and chaotic vibrations of these states. We also investigate
the dynamics of disordered gas states and show that there is a surprising and
robust linear connection between distributions of angular and linear velocity
for both lattice and gas states, allowing to define the concept of temperature
Sub-Doppler resonances in the back-scattered light from random porous media infused with Rb vapor
We report on the observation of sub-Doppler resonances on the back-scattered
light from a random porous glass medium with rubidium vapor filling its
interstices. The sub-Doppler spectral lines are the consequence of saturated
absorption where the incident laser beam saturates the atomic medium and the
back-scattered light probes it. Some specificities of the observed spectra
reflect the transient atomic evolution under confinement inside the pores.
Simplicity, robustness and potential miniaturization are appealing features of
this system as a spectroscopic reference.Comment: 6 pages, 4 figure
Observation of long-lived polariton states in semiconductor microcavities across the parametric threshold
The excitation spectrum around the pump-only stationary state of a polariton
optical parametric oscillator (OPO) in semiconductor microcavities is
investigated by time-resolved photoluminescence. The response to a weak pulsed
perturbation in the vicinity of the idler mode is directly related to the
lifetime of the elementary excitations. A dramatic increase of the lifetime is
observed for a pump intensity approaching and exceeding the OPO threshold. The
observations can be explained in terms of a critical slowing down of the
dynamics upon approaching the threshold and the following onset of the soft
Goldstone mode
Signal of Bose condensation in an optical lattice at finite temperature
We discuss the experimental signal for the Bose condensation of cold atoms in
an optical lattice at finite temperature. Instead of using the visibility of
the interference pattern via the time-of-flight imaging, we show that the
momentum space density profile in the first Brillouin zone, in particular its
bimodal distribution, provides an unambiguous signal for the Bose condensation.
We confirm this point with detailed calculation of the change in the atomic
momentum distribution across the condensation phase transition, taking into
account both the global trapping potential and the atomic interaction effects.Comment: 4 pages, 2 figures, replaced with the published versio
An acoustic black hole in a stationary hydrodynamic flow of microcavity polaritons
We report an experimental study of superfluid hydrodynamic effects in a
one-dimensional polariton fluid flowing along a laterally patterned
semiconductor microcavity and hitting a micron-sized engineered defect. At high
excitation power, superfluid propagation effects are observed in the polariton
dynamics, in particular, a sharp acoustic horizon is formed at the defect
position, separating regions of sub- and super-sonic flow. Our experimental
findings are quantitatively reproduced by theoretical calculations based on a
generalized Gross-Pitaevskii equation. Promising perspectives to observe
Hawking radiation via photon correlation measurements are illustrated.Comment: 5 pages Main + 5 pages Supplementary, 8 figure
A variational problem on Stiefel manifolds
In their paper on discrete analogues of some classical systems such as the
rigid body and the geodesic flow on an ellipsoid, Moser and Veselov introduced
their analysis in the general context of flows on Stiefel manifolds. We
consider here a general class of continuous time, quadratic cost, optimal
control problems on Stiefel manifolds, which in the extreme dimensions again
yield these classical physical geodesic flows. We have already shown that this
optimal control setting gives a new symmetric representation of the rigid body
flow and in this paper we extend this representation to the geodesic flow on
the ellipsoid and the more general Stiefel manifold case. The metric we choose
on the Stiefel manifolds is the same as that used in the symmetric
representation of the rigid body flow and that used by Moser and Veselov. In
the extreme cases of the ellipsoid and the rigid body, the geodesic flows are
known to be integrable. We obtain the extremal flows using both variational and
optimal control approaches and elucidate the structure of the flows on general
Stiefel manifolds.Comment: 30 page
A subradiant optical mirror formed by a single structured atomic layer
Efficient and versatile interfaces for the interaction of light with matter
are an essential cornerstone for quantum science. A fundamentally new avenue of
controlling light-matter interactions has been recently proposed based on the
rich interplay of photon-mediated dipole-dipole interactions in structured
subwavelength arrays of quantum emitters. Here we report on the direct
observation of the cooperative subradiant response of a two-dimensional (2d)
square array of atoms in an optical lattice. We observe a spectral narrowing of
the collective atomic response well below the quantum-limited decay of
individual atoms into free space. Through spatially resolved spectroscopic
measurements, we show that the array acts as an efficient mirror formed by only
a single monolayer of a few hundred atoms. By tuning the atom density in the
array and by changing the ordering of the particles, we are able to control the
cooperative response of the array and elucidate the interplay of spatial order
and dipolar interactions for the collective properties of the ensemble. Bloch
oscillations of the atoms out of the array enable us to dynamically control the
reflectivity of the atomic mirror. Our work demonstrates efficient optical
metamaterial engineering based on structured ensembles of atoms and paves the
way towards the controlled many-body physics with light and novel light-matter
interfaces at the single quantum level.Comment: 8 pages, 5 figures + 12 pages Supplementary Infomatio
Geometrically constrained magnetic wall
The structure and properties of a geometrically constrained magnetic wall in
a constriction separating two wider regions are investigated theoretically.
They are shown to differconsiderably from those of an unconstrained wall, so
that the geometrically constrained magnetic wall truly constitutes a new kind
of magnetic wall, besides the well known Bloch and Neel walls. In particular,
the width of a constrained wall cann become very small if the characteristic
length of the constriction is small, as is actually the case in an atomic point
contact. This provides a simple, natural explanation for the large
magnetoresistance observed in ferromagnetic atomic point contacts.Comment: RevTeX, 4 pages, 4 eps figures; v2: revised version; v3: ref. adde
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