508 research outputs found
Theory of Multidimensional Solitons
We review a number of topics germane to higher-dimensional solitons in
Bose-Einstein condensates. For dark solitons, we discuss dark band and planar
solitons; ring dark solitons and spherical shell solitons; solitary waves in
restricted geometries; vortex rings and rarefaction pulses; and multi-component
Bose-Einstein condensates. For bright solitons, we discuss instability,
stability, and metastability; bright soliton engineering, including pulsed atom
lasers; solitons in a thermal bath; soliton-soliton interactions; and bright
ring solitons and quantum vortices. A thorough reference list is included.Comment: review paper, to appear as Chapter 5a in "Emergent Nonlinear
Phenomena in Bose-Einstein Condensates: Theory and Experiment," edited by P.
G. Kevrekidis, D. J. Frantzeskakis, and R. Carretero-Gonzalez
(Springer-Verlag
Functional co-monotony of processes with applications to peacocks and barrier options
We show that several general classes of stochastic processes satisfy a
functional co-monotony principle, including processes with independent
increments, Brownian diffusions, Liouville processes. As a first application,
we recover some recent results about peacock processes obtained by Hirsch et
al. which were themselves motivated by a former work of Carr et al. about the
sensitivity of Asian Call options with respect to their volatility and residual
maturity (seniority). We also derive semi-universal bounds for various barrier
options.Comment: 27 page
Experiments on Multidimensional Solitons
This article presents an overview of experimental efforts in recent years
related to multidimensional solitons in Bose-Einstein condensates. We discuss
the techniques used to generate and observe multidimensional nonlinear waves in
Bose-Einstein condensates with repulsive interactions. We further summarize
observations of planar soliton fronts undergoing the snake instability, the
formation of vortex rings, and the emergence of hybrid structures.Comment: review paper, to appear as Chapter 5b in "Emergent Nonlinear
Phenomena in Bose-Einstein Condensates: Theory and Experiment," edited by P.
G. Kevrekidis, D. J. Frantzeskakis, and R. Carretero-Gonzalez
(Springer-Verlag
Formation and Propagation of Matter Wave Soliton Trains
Attraction between atoms in a Bose-Einstein-Condensate renders the condensate
unstable to collapse. Confinement in an atom trap, however, can stabilize the
condensate for a limited number of atoms, as was observed with 7Li, but beyond
this number, the condensate collapses. Attractive condensates constrained to
one-dimensional motion are predicted to form stable solitons for which the
attractive interactions exactly compensate for the wave packet dispersion. Here
we report the formation or bright solitons of 7Li atoms created in a quasi-1D
optical trap. The solitons are created from a stable Bose-Einstein condensate
by magnetically tuning the interactions from repulsive to attractive. We
observe a soliton train, containing many solitons. The solitons are set in
motion by offsetting the optical potential and are observed to propagate in the
potential for many oscillatory cycles without spreading. Repulsive interactions
between neighboring solitons are inferred from their motion
Dipolar collisions of polar molecules in the quantum regime
Ultracold polar molecules offer the possibility of exploring quantum gases
with interparticle interactions that are strong, long-range, and spatially
anisotropic. This is in stark contrast to the dilute gases of ultracold atoms,
which have isotropic and extremely short-range, or "contact", interactions. The
large electric dipole moment of polar molecules can be tuned with an external
electric field; this provides unique opportunities such as control of ultracold
chemical reactions, quantum information processing, and the realization of
novel quantum many-body systems. In spite of intense experimental efforts aimed
at observing the influence of dipoles on ultracold molecules, only recently
have sufficiently high densities been achieved. Here, we report the observation
of dipolar collisions in an ultracold molecular gas prepared close to quantum
degeneracy. For modest values of an applied electric field, we observe a
dramatic increase in the loss rate of fermionic KRb molecules due to ultrcold
chemical reactions. We find that the loss rate has a steep power-law dependence
on the induced electric dipole moment, and we show that this dependence can be
understood with a relatively simple model based on quantum threshold laws for
scattering of fermionic polar molecules. We directly observe the spatial
anisotropy of the dipolar interaction as manifested in measurements of the
thermodynamics of the dipolar gas. These results demonstrate how the long-range
dipolar interaction can be used for electric-field control of chemical reaction
rates in an ultracold polar molecule gas. The large loss rates in an applied
electric field suggest that creating a long-lived ensemble of ultracold polar
molecules may require confinement in a two-dimensional trap geometry to
suppress the influence of the attractive dipolar interactions
Oscillations and interactions of dark and dark-bright solitons in Bose-Einstein condensates
Solitons are among the most distinguishing fundamental excitations in a wide
range of non-linear systems such as water in narrow channels, high speed
optical communication, molecular biology and astrophysics. Stabilized by a
balance between spreading and focusing, solitons are wavepackets, which share
some exceptional generic features like form-stability and particle-like
properties. Ultra-cold quantum gases represent very pure and well-controlled
non-linear systems, therefore offering unique possibilities to study soliton
dynamics. Here we report on the first observation of long-lived dark and
dark-bright solitons with lifetimes of up to several seconds as well as their
dynamics in highly stable optically trapped Rb Bose-Einstein
condensates. In particular, our detailed studies of dark and dark-bright
soliton oscillations reveal the particle-like nature of these collective
excitations for the first time. In addition, we discuss the collision between
these two types of solitary excitations in Bose-Einstein condensates.Comment: 9 pages, 4 figure
Spontaneous creation of Kibble-Zurek solitons in a Bose-Einstein condensate
When a system crosses a second-order phase transition on a finite timescale,
spontaneous symmetry breaking can cause the development of domains with
independent order parameters, which then grow and approach each other creating
boundary defects. This is known as Kibble-Zurek mechanism. Originally
introduced in cosmology, it applies both to classical and quantum phase
transitions, in a wide variety of physical systems. Here we report on the
spontaneous creation of solitons in Bose-Einstein condensates via the
Kibble-Zurek mechanism. We measure the power-law dependence of defects number
with the quench time, and provide a check of the Kibble-Zurek scaling with the
sonic horizon. These results provide a promising test bed for the determination
of critical exponents in Bose-Einstein condensates.Comment: 7 pages, 4 figure
Controlling the quantum stereodynamics of ultracold bimolecular reactions
Chemical reaction rates often depend strongly on stereodynamics, namely the
orientation and movement of molecules in three-dimensional space. An ultracold
molecular gas, with a temperature below 1 uK, provides a highly unusual regime
for chemistry, where polar molecules can easily be oriented using an external
electric field and where, moreover, the motion of two colliding molecules is
strictly quantized. Recently, atom-exchange reactions were observed in a
trapped ultracold gas of KRb molecules. In an external electric field, these
exothermic and barrierless bimolecular reactions, KRb+KRb -> K2+Rb2, occur at a
rate that rises steeply with increasing dipole moment. Here we show that the
quantum stereodynamics of the ultracold collisions can be exploited to suppress
the bimolecular chemical reaction rate by nearly two orders of magnitude. We
use an optical lattice trap to confine the fermionic polar molecules in a
quasi-two-dimensional, pancake-like geometry, with the dipoles oriented along
the tight confinement direction. With the combination of sufficiently tight
confinement and Fermi statistics of the molecules, two polar molecules can
approach each other only in a "side-by-side" collision, where the chemical
reaction rate is suppressed by the repulsive dipole-dipole interaction. We show
that the suppression of the bimolecular reaction rate requires quantum-state
control of both the internal and external degrees of freedom of the molecules.
The suppression of chemical reactions for polar molecules in a
quasi-two-dimensional trap opens the way for investigation of a dipolar
molecular quantum gas. Because of the strong, long-range character of the
dipole-dipole interactions, such a gas brings fundamentally new abilities to
quantum-gas-based studies of strongly correlated many-body physics, where
quantum phase transitions and new states of matter can emerge.Comment: 19 pages, 4 figure
Laser Cooling of Optically Trapped Molecules
Calcium monofluoride (CaF) molecules are loaded into an optical dipole trap
(ODT) and subsequently laser cooled within the trap. Starting with
magneto-optical trapping, we sub-Doppler cool CaF and then load CaF
molecules into an ODT. Enhanced loading by a factor of five is obtained when
sub-Doppler cooling light and trapping light are on simultaneously. For trapped
molecules, we directly observe efficient sub-Doppler cooling to a temperature
of . The trapped molecular density of
cm is an order of magnitude greater than in the initial sub-Doppler
cooled sample. The trap lifetime of 750(40) ms is dominated by background gas
collisions.Comment: 5 pages, 5 figure
Aharonov-Bohm interferences from local deformations in graphene
One of the most interesting aspects of graphene is the tied relation between
structural and electronic properties. The observation of ripples in the
graphene samples both free standing and on a substrate has given rise to a very
active investigation around the membrane-like properties of graphene and the
origin of the ripples remains as one of the most interesting open problems in
the system. The interplay of structural and electronic properties is
successfully described by the modelling of curvature and elastic deformations
by fictitious gauge fields that have become an ex- perimental reality after the
suggestion that Landau levels can form associated to strain in graphene and the
subsequent experimental confirmation. Here we propose a device to detect
microstresses in graphene based on a scanning-tunneling-microscopy setup able
to measure Aharonov-Bohm inter- ferences at the nanometer scale. The
interferences to be observed in the local density of states are created by the
fictitious magnetic field associated to elastic deformations of the sample.Comment: Some bugs fixe
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