47 research outputs found
Optical pulse propagation in fibers with random dispersion
The propagation of optical pulses in two types of fibers with randomly
varying dispersion is investigated. The first type refers to a uniform fiber
dispersion superimposed by random modulations with a zero mean. The second type
is the dispersion-managed fiber line with fluctuating parameters of the
dispersion map. Application of the mean field method leads to the nonlinear
Schr\"odinger equation (NLSE) with a dissipation term, expressed by a 4th order
derivative of the wave envelope. The prediction of the mean field approach
regarding the decay rate of a soliton is compared with that of the perturbation
theory based on the Inverse Scattering Transform (IST). A good agreement
between these two approaches is found. Possible ways of compensation of the
radiative decay of solitons using the linear and nonlinear amplification are
explored. Corresponding mean field equation coincides with the complex
Swift-Hohenberg equation. The condition for the autosolitonic regime in
propagation of optical pulses along a fiber line with fluctuating dispersion is
derived and the existence of autosoliton (dissipative soliton) is confirmed by
direct numerical simulation of the stochastic NLSE. The dynamics of solitons in
optical communication systems with random dispersion-management is further
studied applying the variational principle to the mean field NLSE, which
results in a system of ODE's for soliton parameters. Extensive numerical
simulations of the stochastic NLSE, mean field equation and corresponding set
of ODE's are performed to verify the predictions of the developed theory.Comment: 17 pages, 7 eps figure
Stable two-dimensional dispersion-managed soliton
The existence of a dispersion-managed soliton in two-dimensional nonlinear
Schr\"odinger equation with periodically varying dispersion has been explored.
The averaged equations for the soliton width and chirp are obtained which
successfully describe the long time evolution of the soliton. The slow dynamics
of the soliton around the fixed points for the width and chirp are investigated
and the corresponding frequencies are calculated. Analytical predictions are
confirmed by direct PDE and ODE simulations. Application to a Bose-Einstein
condensate in optical lattice is discussed. The existence of a
dispersion-managed matter-wave soliton in such system is shown.Comment: 4 pages, 3 figures, Submitted to Phys. Rev.
Formation of soliton trains in Bose-Einstein condensates as a nonlinear Fresnel diffraction of matter waves
The problem of generation of atomic soliton trains in elongated Bose-Einstein
condensates is considered in framework of Whitham theory of modulations of
nonlinear waves. Complete analytical solution is presented for the case when
the initial density distribution has sharp enough boundaries. In this case the
process of soliton train formation can be viewed as a nonlinear Fresnel
diffraction of matter waves. Theoretical predictions are compared with results
of numerical simulations of one- and three-dimensional Gross-Pitaevskii
equation and with experimental data on formation of Bose-Einstein bright
solitons in cigar-shaped traps.Comment: 8 pages, 3 figure
Modulational instability of matter waves under strong nonlinearity management
We study modulational instability of matter-waves in Bose-Einstein
condensates (BEC) under strong temporal nonlinearity-management. Both BEC in an
optical lattice and homogeneous BEC are considered in the framework of the
Gross-Pitaevskii equation, averaged over rapid time modulations. For a BEC in
an optical lattice, it is shown that the loop formed on a dispersion curve
undergoes transformation due to the nonlinearity-management. A critical
strength for the nonlinearity-management strength is obtained that changes the
character of instability of an attractive condensate. MI is shown to occur
below(above) the threshold for the positive (negative) effective mass. The
enhancement of number of atoms in the nonlinearity-managed gap soliton is
revealed
Quasi 1D Bose-Einstein condensate flow past a nonlinear barrier
The problem of a quasi 1D {\it repulsive} BEC flow past through a nonlinear
barrier is investigated. Two types of nonlinear barriers are considered, wide
and short range ones. Steady state solutions for the BEC moving through a wide
repulsive barrier and critical velocities have been found using hydrodynamical
approach to the 1D Gross-Pitaevskii equation. It is shown that in contrast to
the linear barrier case, for a wide {\it nonlinear} barrier an interval of
velocities {\it always} exists, where the flow is superfluid
regardless of the barrier potential strength. For the case of the
function-like barrier, below a critical velocity two steady solutions exist,
stable and unstable one. An unstable solution is shown to decay into a gray
soliton moving upstream and a stable solution. The decay is accompanied by a
dispersive shock wave propagating downstream in front of the barrier.Comment: 6 pages, 7 figures, extended abstract, revised arguments in Sects 2,3
results unchanged, added reference
Controlling collapse in Bose-Einstein condensates by temporal modulation of the scattering length
We consider, by means of the variational approximation (VA) and direct
numerical simulations of the Gross-Pitaevskii (GP) equation, the dynamics of 2D
and 3D condensates with a scattering length containing constant and
harmonically varying parts, which can be achieved with an ac magnetic field
tuned to the Feshbach resonance. For a rapid time modulation, we develop an
approach based on the direct averaging of the GP equation,without using the VA.
In the 2D case, both VA and direct simulations, as well as the averaging
method, reveal the existence of stable self-confined condensates without an
external trap, in agreement with qualitatively similar results recently
reported for spatial solitons in nonlinear optics. In the 3D case, the VA again
predicts the existence of a stable self-confined condensate without a trap. In
this case, direct simulations demonstrate that the stability is limited in
time, eventually switching into collapse, even though the constant part of the
scattering length is positive (but not too large). Thus a spatially uniform ac
magnetic field, resonantly tuned to control the scattering length, may play the
role of an effective trap confining the condensate, and sometimes causing its
collapse.Comment: 7 figure
Stability analysis of the D-dimensional nonlinear Schroedinger equation with trap and two- and three-body interactions
Considering the static solutions of the D-dimensional nonlinear Schroedinger
equation with trap and attractive two-body interactions, the existence of
stable solutions is limited to a maximum critical number of particles, when D
is greater or equal 2. In case D=2, we compare the variational approach with
the exact numerical calculations. We show that, the addition of a positive
three-body interaction allows stable solutions beyond the critical number. In
this case, we also introduce a dynamical analysis of the conditions for the
collapse.Comment: 6 pages, 7 figure
Interaction of pulses in nonlinear Schroedinger model
The interaction of two rectangular pulses in nonlinear Schroedinger model is
studied by solving the appropriate Zakharov-Shabat system. It is shown that two
real pulses may result in appearance of moving solitons. Different limiting
cases, such as a single pulse with a phase jump, a single chirped pulse,
in-phase and out-of-phase pulses, and pulses with frequency separation, are
analyzed. The thresholds of creation of new solitons and multi-soliton states
are found.Comment: 9 pages, 7 figures. Accepted to Phys. Rev. E, 200
A fundamental limit for integrated atom optics with Bose-Einstein condensates
The dynamical response of an atomic Bose-Einstein condensate manipulated by
an integrated atom optics device such as a microtrap or a microfabricated
waveguide is studied. We show that when the miniaturization of the device
enforces a sufficiently high condensate density, three-body interactions lead
to a spatial modulational instability that results in a fundamental limit on
the coherent manipulation of Bose-Einstein condensates.Comment: 6 pages, 3 figure