17 research outputs found
Partially incoherent gap solitons in Bose-Einstein condensates
We construct families of incoherent matter-wave solitons in a repulsive
degenerate Bose gas trapped in an optical lattice (OL), i.e., gap solitons, and
investigate their stability at zero and finite temperature, using the
Hartree-Fock-Bogoliubov equations. The gap solitons are composed of a coherent
condensate, and normal and anomalous densities of incoherent vapor co-trapped
with the condensate. Both intragap and intergap solitons are constructed, with
chemical potentials of the components falling in one or different bandgaps in
the OL-induced spectrum. Solitons change gradually with temperature. Families
of intragap solitons are completely stable (both in direct simulations, and in
terms of eigenvalues of perturbation modes), while the intergap family may have
a very small unstable eigenvalue (nevertheless, they feature no instability in
direct simulations). Stable higher-order (multi-humped) solitons, and bound
complexes of fundamental solitons are found too.Comment: 8 pages, 9 figures. Physical Review A, in pres
Gap solitons in a model of a hollow optical fiber
We introduce a models for two coupled waves propagating in a hollow-core
fiber: a linear dispersionless core mode, and a dispersive nonlinear
quasi-surface one. The linear coupling between them may open a bandgap, through
the mechanism of the avoidance of crossing between dispersion curves. The
third-order dispersion of the quasi-surface mode is necessary for the existence
of the gap. Numerical investigation reveals that the entire bandgap is filled
with solitons, and they all are stable in direct simulations. The gap-soliton
(GS) family is extended to include pulses moving relative to the given
reference frame, up to limit values of the corresponding boost ,
beyond which the solitons do not exists. The limit values are nonsymmetric for
and . The extended gap is also entirely filled with the
GSs, all of which are stable in simulations. Recently observed solitons in
hollow-core photonic-crystal fibers may belong to this GS family.Comment: 5 pages, 5 figure
Gap solitons in Bragg gratings with a harmonic superlattice
Solitons are studied in a model of a fiber Bragg grating (BG) whose local
reflectivity is subjected to periodic modulation. The superlattice opens an
infinite number of new bandgaps in the model's spectrum. Averaging and
numerical continuation methods show that each gap gives rise to gap solitons
(GSs), including asymmetric and double-humped ones, which are not present
without the superlattice.Computation of stability eigenvalues and direct
simulation reveal the existence of completely stable families of fundamental
GSs filling the new gaps - also at negative frequencies, where the ordinary GSs
are unstable. Moving stable GSs with positive and negative effective mass are
found too.Comment: 7 pages, 3 figures, submitted to EP
Stability of Waves in Multi-component DNLS system
In this work, we systematically generalize the Evans function methodology to
address vector systems of discrete equations. We physically motivate and
mathematically use as our case example a vector form of the discrete nonlinear
Schrodinger equation with both nonlinear and linear couplings between the
components. The Evans function allows us to qualitatively predict the stability
of the nonlinear waves under the relevant perturbations and to quantitatively
examine the dependence of the corresponding point spectrum eigenvalues on the
system parameters. These analytical predictions are subsequently corroborated
by numerical computations.Comment: to appear Journal of Physics A: Mathematical and Theoretica
Causality and defect formation in the dynamics of an engineered quantum phase transition in a coupled binary Bose-Einstein condensate
Continuous phase transitions occur in a wide range of physical systems, and
provide a context for the study of non-equilibrium dynamics and the formation
of topological defects. The Kibble-Zurek (KZ) mechanism predicts the scaling of
the resulting density of defects as a function of the quench rate through a
critical point, and this can provide an estimate of the critical exponents of a
phase transition. In this work we extend our previous study of the
miscible-immiscible phase transition of a binary Bose-Einstein condensate (BEC)
composed of two hyperfine states in which the spin dynamics are confined to one
dimension [J. Sabbatini et al., Phys. Rev. Lett. 107, 230402 (2011)]. The
transition is engineered by controlling a Hamiltonian quench of the coupling
amplitude of the two hyperfine states, and results in the formation of a random
pattern of spatial domains. Using the numerical truncated Wigner phase space
method, we show that in a ring BEC the number of domains formed in the phase
transitions scales as predicted by the KZ theory. We also consider the same
experiment performed with a harmonically trapped BEC, and investigate how the
density inhomogeneity modifies the dynamics of the phase transition and the KZ
scaling law for the number of domains. We then make use of the symmetry between
inhomogeneous phase transitions in anisotropic systems, and an inhomogeneous
quench in a homogeneous system, to engineer coupling quenches that allow us to
quantify several aspects of inhomogeneous phase transitions. In particular, we
quantify the effect of causality in the propagation of the phase transition
front on the resulting formation of domain walls, and find indications that the
density of defects is determined during the impulse to adiabatic transition
after the crossing of the critical point.Comment: 23 pages, 10 figures. Minor corrections, typos, additional referenc
Discrete embedded solitons
We address the existence and properties of discrete embedded solitons (ESs),
i.e., localized waves existing inside the phonon band in a nonlinear
dynamical-lattice model. The model describes a one-dimensional array of optical
waveguides with both the quadratic (second-harmonic generation) and cubic
nonlinearities. A rich family of ESs was previously known in the continuum
limit of the model. First, a simple motivating problem is considered, in which
the cubic nonlinearity acts in a single waveguide. An explicit solution is
constructed asymptotically in the large-wavenumber limit. The general problem
is then shown to be equivalent to the existence of a homoclinic orbit in a
four-dimensional reversible map. From properties of such maps, it is shown that
(unlike ordinary gap solitons), discrete ESs have the same codimension as their
continuum counterparts. A specific numerical method is developed to compute
homoclinic solutions of the map, that are symmetric under a specific reversing
transformation. Existence is then studied in the full parameter space of the
problem. Numerical results agree with the asymptotic results in the appropriate
limit and suggest that the discrete ESs may be semi-stable as in the continuous
case.Comment: A revtex4 text file and 51 eps figure files. To appear in
Nonlinearit
Rabi switch of condensate wavefunctions in a multicomponent Bose gas
Using a time-dependent linear (Rabi) coupling between the components of a
weakly interacting multicomponent Bose-Einstein condensate (BEC), we propose a
protocol for transferring the wavefunction of one component to the other. This
"Rabi switch" can be generated in a binary BEC mixture by an electromagnetic
field between the two components, typically two hyperfine states. When the
wavefunction to be transfered is - at a given time - a stationary state of the
multicomponent Hamiltonian, then, after a time delay (depending on the Rabi
frequency), it is possible to have the same wavefunction on the other
condensate. The Rabi switch can be used to transfer also moving bright
matter-wave solitons, as well as vortices and vortex lattices in
two-dimensional condensates. The efficiency of the proposed switch is shown to
be 100% when inter-species and intra-species interaction strengths are equal.
The deviations from equal interaction strengths are analyzed within a two-mode
model and the dependence of the efficiency on the interaction strengths and on
the presence of external potentials is examined in both 1D and 2D settings
Nonlinear Waves in Bose-Einstein Condensates: Physical Relevance and Mathematical Techniques
The aim of the present review is to introduce the reader to some of the
physical notions and of the mathematical methods that are relevant to the study
of nonlinear waves in Bose-Einstein Condensates (BECs). Upon introducing the
general framework, we discuss the prototypical models that are relevant to this
setting for different dimensions and different potentials confining the atoms.
We analyze some of the model properties and explore their typical wave
solutions (plane wave solutions, bright, dark, gap solitons, as well as
vortices). We then offer a collection of mathematical methods that can be used
to understand the existence, stability and dynamics of nonlinear waves in such
BECs, either directly or starting from different types of limits (e.g., the
linear or the nonlinear limit, or the discrete limit of the corresponding
equation). Finally, we consider some special topics involving more recent
developments, and experimental setups in which there is still considerable need
for developing mathematical as well as computational tools.Comment: 69 pages, 10 figures, to appear in Nonlinearity, 2008. V2: new
references added, fixed typo
Dark solitons in atomic Bose-Einstein condensates: from theory to experiments
This review paper presents an overview of the theoretical and experimental
progress on the study of matter-wave dark solitons in atomic Bose-Einstein
condensates. Upon introducing the general framework, we discuss the statics and
dynamics of single and multiple matter-wave dark solitons in the quasi
one-dimensional setting, in higher-dimensional settings, as well as in the
dimensionality crossover regime. Special attention is paid to the connection
between theoretical results, obtained by various analytical approaches, and
relevant experimental observations.Comment: 82 pages, 13 figures. To appear in J. Phys. A: Math. Theor