12,278 research outputs found
Localized modes of binary mixtures of Bose-Einstein condensates in nonlinear optical lattices
The properties of the localized states of a two component Bose-Einstein
condensate confined in a nonlinear periodic potential [nonlinear optical
lattice] are investigated. We reveal the existence of new types of solitons and
study their stability by means of analytical and numerical approaches. The
symmetry properties of the localized states with respect to the NOL are also
investigated. We show that nonlinear optical lattices allow the existence of
bright soliton modes with equal symmetry in both components, bright localized
modes of mixed symmetry type, as well as, dark-bright bound states and bright
modes on periodic backgrounds. In spite of the quasi 1D nature of the problem,
the fundamental symmetric localized modes undergo a delocalizing transition
when the strength of the nonlinear optical lattice is varied. This transition
is associated with the existence of an unstable solution, which exhibits a
shrinking (decaying) behavior for slightly overcritical (undercritical)
variations in the number of atoms.Comment: 13 pages, 14 figure
Dark soliton oscillations in Bose-Einstein condensates with multi-body interactions
We consider the dynamics of dark matter solitons moving through non-uniform
cigar-shaped Bose-Einstein condensates described by the mean field
Gross-Pitaevskii equation with generalized nonlinearities, in the case when the
condition for the modulation stability of the Bose-Einstein condensate is
fulfilled. The analytical expression for the frequency of the oscillations of a
deep dark soliton is derived for nonlinearities which are arbitrary functions
of the density, while specific results are discussed for the physically
relevant case of a cubic-quintic nonlinearity modeling two- and three-body
interactions, respectively. In contrast to the cubic Gross-Pitaevskii equation
for which the frequencies of the oscillations are known to be independent of
background density and interaction strengths, we find that in the presence of a
cubic-quintic nonlinearity an explicit dependence of the oscillations frequency
on the above quantities appears. This dependence gives rise to the possibility
of measuring these quantities directly from the dark soliton dynamics, or to
manage the oscillation via the changes of the scattering lengths by means of
Feshbach resonance. A comparison between analytical results and direct
numerical simulations of the cubic-quintic Gross-Pitaevskii equation shows good
agreement which confirms the validity of our approach.Comment: submitted in J. Phys.
Matter wave quantum dots (anti-dots) in ultracold atomic Bose-Fermi mixtures
The properties of ultracold atomic Bose-Fermi mixtures in external potentials
are investigated and the existence of gap solitons of Bose-Fermi mixtures in
optical lattices demonstrated. Using a self-consistent approach we compute the
energy spectrum and show that gap solitons can be viewed as matter wave
realizations of quantum dots (anti-dots) with the bosonic density playing the
role of trapping (expulsive) potential for the fermions. The fermionic states
trapped in the condensate are shown to be at the bottom of the Fermi sea and
therefore well protected from thermal decoherence. Energy levels, filling
factors and parameters dependence of gap soliton quantum dots are also
calculated both numerically and analytically.Comment: Extended version of talk given at the SOLIBEC conference, Almagro,
Spain, 8-12 February 2005. To be published on Phys.Rev.
The Hubbard model on a complete graph: Exact Analytical results
We derive the analytical expression of the ground state of the Hubbard model
with unconstrained hopping at half filling and for arbitrary lattice sites.Comment: Email:[email protected]
Delocalizing transition of multidimensional solitons in Bose-Einstein condensates
Critical behavior of solitonic waveforms of Bose-Einstein condensates in
optical lattices (OL) has been studied in the framework of continuous
mean-field equation. In 2D and 3D OLs bright matter-wave solitons undergo
abrupt delocalization as the strength of the OL is decreased below some
critical value. Similar delocalizing transition happens when the coefficient of
nonlinearity crosses the critical value. Contrarily, bright solitons in 1D OLs
retain their integrity over the whole range of parameter variations. The
interpretation of the phenomenon in terms of quantum bound states in the
effective potential is proposed.Comment: 12 pages, 19 figures, submitted to Phys. Rev.
Domain walls and bubble-droplets in immiscible binary Bose gases
The existence and stability of domain walls (DWs) and bubble-droplet (BD)
states in binary mixtures of quasi-one-dimensional ultracold Bose gases with
inter- and intra-species repulsive interactions is considered. Previously, DWs
were studied by means of coupled systems of Gross-Pitaevskii equations (GPEs)
with cubic terms, which model immiscible binary Bose-Einstein condensates
(BECs). We address immiscible BECs with two- and three-body repulsive
interactions, as well as binary Tonks--Girardeau (TG) gases, using systems of
GPEs with cubic and quintic nonlinearities for the binary BEC, and coupled
nonlinear Schr\"{o}dinger equations with quintic terms for the TG gases. Exact
DW\ solutions are found for the symmetric BEC mixture, with equal intra-species
scattering lengths. Stable asymmetric DWs in the BEC mixtures with dissimilar
interactions in the two components, as well as of symmetric and asymmetric DWs
in the binary TG gas, are found by means of numerical and approximate
analytical methods. In the BEC system, DWs can be easily put in motion by phase
imprinting. Combining a DW and anti-DW on a ring, we construct BD states for
both the BEC and TG models. These consist of a dark soliton in one component
(the "bubble"), and a bright soliton (the "droplet") in the other. In the BEC
system, these composite states are mobile too.Comment: Phys. Rev. A, in pres
Landau-Zener Tunneling of Bose-Einstein Condensates in an Optical Lattice
A theory of the non-symmetric Landau-Zener tunneling of Bose-Einstein
condensates in deep optical lattices is presented. It is shown that periodic
exchange of matter between the bands is described by a set of linearly coupled
nonlinear Schr\"{o}dinger equations. The key role of the modulational
instability in rendering the inter-band transitions irreversible is
highlighted.Comment: 4 pages, 3 figure
Quantum-tunneling dynamics of a spin-polarized Fermi gas in a double-well potential
We study the exact dynamics of a one-dimensional spin-polarized gas of
fermions in a double-well potential at zero and finite temperature. Despite the
system is made of non-interacting fermions, its dynamics can be quite complex,
showing strongly aperiodic spatio-temporal patterns during the tunneling. The
extension of these results to the case of mixtures of spin-polarized fermions
in interaction with self-trapped Bose-Einstein condensates (BECs) at zero
temperature is considered as well. In this case we show that the fermionic
dynamics remains qualitatively similar to the one observed in absence of BEC
but with the Rabi frequencies of fermionic excited states explicitly depending
on the number of bosons and on the boson-fermion interaction strength. From
this, the possibility to control quantum fermionic dynamics by means of
Feshbach resonances is suggested.Comment: Accepted for publication in Phys. Rev.
Mixed symmetry localized modes and breathers in binary mixtures of Bose-Einstein condensates in optical lattices
We study localized modes in binary mixtures of Bose-Einstein condensates
embedded in one-dimensional optical lattices. We report a diversity of
asymmetric modes and investigate their dynamics. We concentrate on the cases
where one of the components is dominant, i.e. has much larger number of atoms
than the other one, and where both components have the numbers of atoms of the
same order but different symmetries. In the first case we propose a method of
systematic obtaining the modes, considering the "small" component as
bifurcating from the continuum spectrum. A generalization of this approach
combined with the use of the symmetry of the coupled Gross-Pitaevskii equations
allows obtaining breather modes, which are also presented.Comment: 11 pages, 16 figure
Dynamical localization of gap-solitons by time periodic forces
The phenomenon of dynamical localization of matter wave solitons in optical
lattices is first demonstrated and the conditions for its existence are
discussed. In addition to the trapping linear periodic potential we use a
periodic modulation of the nonlinearity in space to eliminate nonexistence
regions of gap-solitons in reciprocal space. We show that when this condition
is achieved, the observation of dynamical localization in true nonlinear regime
becomes possible. The results apply to all systems described by the periodic
nonlinear Schr\"odinger equation, including Bose-Einstein condensates of
ultracold atoms trapped in optical lattices and arrays of waveguides or
photonic crystals in nonlinear optics.Comment: accepted for Europhysics Letter
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