16,468 research outputs found
Macroscopic quantum tunnelling of Bose-Einstein condensates in a finite potential well
Bose-Einstein condensates are studied in a potential of finite depth which
supports both bound and quasi-bound states. This potential, which is harmonic
for small radii and decays as a Gaussian for large radii, models experimentally
relevant optical traps. The nonlinearity, which is proportional to both the
number of atoms and the interaction strength, can transform bound states into
quasi-bound ones. The latter have a finite lifetime due to tunnelling through
the barriers at the borders of the well. We predict the lifetime and stability
properties for repulsive and attractive condensates in one, two, and three
dimensions, for both the ground state and excited soliton and vortex states. We
show, via a combination of the variational and WKB approximations, that
macroscopic quantum tunnelling in such systems can be observed on time scales
of 10 milliseconds to 10 seconds.Comment: J. Phys. B: At. Mol. Opt. Phys. in pres
Tunable tunneling: An application of stationary states of Bose-Einstein condensates in traps of finite depth
The fundamental question of how Bose-Einstein condensates tunnel into a
barrier is addressed. The cubic nonlinear Schrodinger equation with a finite
square well potential, which models a Bose-Einstein condensate in a
quasi-one-dimensional trap of finite depth, is solved for the complete set of
localized and partially localized stationary states, which the former evolve
into when the nonlinearity is increased. An immediate application of these
different solution types is tunable tunneling. Magnetically tunable Feshbach
resonances can change the scattering length of certain Bose-condensed atoms,
such as Rb, by several orders of magnitude, including the sign, and
thereby also change the mean field nonlinearity term of the equation and the
tunneling of the wavefunction. We find both linear-type localized solutions and
uniquely nonlinear partially localized solutions where the tails of the
wavefunction become nonzero at infinity when the nonlinearity increases. The
tunneling of the wavefunction into the non-classical regime and thus its
localization therefore becomes an external experimentally controllable
parameter.Comment: 11 pages, 5 figure
Limits of sympathetic cooling of fermions by zero temperature bosons due to particle losses
It has been suggested by Timmermans [Phys. Rev. Lett. {\bf 87}, 240403
(2001)] that loss of fermions in a degenerate system causes strong heating. We
address the fundamental limit imposed by this loss on the temperature that may
be obtained by sympathetic cooling of fermions by bosons. Both a quantum
Boltzmann equation and a quantum Boltzmann \emph{master} equation are used to
study the evolution of the occupation number distribution. It is shown that, in
the thermodynamic limit, the Fermi gas cools to a minimal temperature , where
is a constant loss rate, is the
bare fermion--boson collision rate not including the reduction due to Fermi
statistics, and is the chemical potential. It
is demonstrated that, beyond the thermodynamic limit, the discrete nature of
the momentum spectrum of the system can block cooling. The unusual non-thermal
nature of the number distribution is illustrated from several points of view:
the Fermi surface is distorted, and in the region of zero momentum the number
distribution can descend to values significantly less than unity. Our model
explicitly depends on a constant evaporation rate, the value of which can
strongly affect the minimum temperature.Comment: 14 pages, 7 figures. Phys. Rev. A in pres
Dynamic behavior of an unsteady trubulent boundary layer
Experiments on an unsteady turbulent boundary layer are reported in which the upstream portion of the flow is steady (in the mean) and in the downstream region, the boundary layer sees a linearly decreasing free stream velocity. This velocity gradient oscillates in time, at frequencies ranging from zero to approximately the bursting frequency. For the small amplitude, the mean velocity and mean turbulence intensity profiles are unaffected by the oscillations. The amplitude of the periodic velocity component, although as much as 70% greater than that in the free stream for very low frequencies, becomes equal to that in the free stream at higher frequencies. At high frequencies, both the boundary layer thickness and the Reynolds stress distribution across the boundary layer become frozen. The behavior at higher amplitude is quite similar. At sufficiently high frequencies, the boundary layer thickness remains frozen at the mean value over the oscillation cycle, even though flow reverses near the wall during a part of the cycle
Relativistic linear stability equations for the nonlinear Dirac equation in Bose-Einstein condensates
We present relativistic linear stability equations (RLSE) for
quasi-relativistic cold atoms in a honeycomb optical lattice. These equations
are derived from first principles and provide a method for computing
stabilities of arbitrary localized solutions of the nonlinear Dirac equation
(NLDE), a relativistic generalization of the nonlinear Schr\"odinger equation.
We present a variety of such localized solutions: skyrmions, solitons,
vortices, and half-quantum vortices, and study their stabilities via the RLSE.
When applied to a uniform background, our calculations reveal an experimentally
observable effect in the form of Cherenkov radiation. Remarkably, the Berry
phase from the bipartite structure of the honeycomb lattice induces a
boson-fermion transmutation in the quasi-particle operator statistics.Comment: 6 pages, 3 figure
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Formation of a Matter-Wave Bright Soliton
We report the production of matter-wave solitons in an ultracold lithium 7
gas. The effective interaction between atoms in a Bose-Einstein condensate is
tuned with a Feshbach resonance from repulsive to attractive before release in
a one-dimensional optical waveguide. Propagation of the soliton without
dispersion over a macroscopic distance of 1.1 mm is observed. A simple
theoretical model explains the stability region of the soliton. These
matter-wave solitons open fascinating possibilities for future applications in
coherent atom optics, atom interferometry and atom transport.Comment: 11 pages, 5 figure
Semi-Static Hedging Based on a Generalized Reflection Principle on a Multi Dimensional Brownian Motion
On a multi-assets Black-Scholes economy, we introduce a class of barrier
options. In this model we apply a generalized reflection principle in a context
of the finite reflection group acting on a Euclidean space to give a valuation
formula and the semi-static hedge.Comment: Asia-Pacific Financial Markets, online firs
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