21 research outputs found
Solitons in tunnel-coupled repulsive and attractive condensates
We study solitons in the condensate trapped in a double-well potential with
far-separated wells, when the s-wave scattering length has different signs in
the two parts of the condensate. By employing the coupled-mode approximation it
is shown that there are unusual stable bright solitons in the condensate, with
the larger share of atoms being gathered in the repulsive part. Such unusual
solitons derive their stability from the quantum tunneling and correspond to
the strong coupling between the parts of the condensate. The ground state of
the system, however, corresponds to weak coupling between the condensate parts,
with the larger share of atoms being gathered in the attractive part of the
condensate.Comment: LaTex, 23 pages, 6 figures; revised version; to appear in Physical
Review
Interband resonant transitions in two-dimensional hexagonal lattices: Rabi oscillations, Zener tunnelling, and tunnelling of phase dislocations
We study, analytically and numerically, the dynamics of
interband transitions in two-dimensional hexagonal periodic photonic
lattices. We develop an analytical approach employing the Bragg resonances
of different types and derive the effective multi-level models of
the Landau-Zener-Majorana type. For two-dimensional periodic potentials
without a tilt, we demonstrate the possibility of the Rabi oscillations
between the resonant Fourier amplitudes. In a biased lattice, i.e., for a
two-dimensional periodic potential with an additional linear tilt, we identify
three basic types of the interband transitions or Zener tunnelling. First, this
is a quasi-one-dimensional tunnelling that involves only two Bloch bands
and occurs when the Bloch index crosses the Bragg planes away from one
of the high-symmetry points. In contrast, at the high-symmetry points (i.e.,
at the M and Ξ points), the Zener tunnelling is essentially two-dimensional,
and it involves either three or six Bloch bands being described by the
corresponding multi-level Landau-Zener-Majorana systems. We verify
our analytical results by numerical simulations and observe an excellent
agreement. Finally, we show that phase dislocations, or optical vortices, can
tunnel between the spectral bands preserving their topological charge. Our
theory describes the propagation of light beams in fabricated or opticallyinduced
two-dimensional photonic lattices, but it can also be applied to
the physics of cold atoms and Bose-Einstein condensates tunnelling in
tilted two-dimensional optical potentials and other types of resonant wave
propagation in periodic media
Mixed-isotope Bose-Einstein condensates in Rubidium
We consider the ground state properties of mixed Bose-Einstein condensates of
87Rb and 85Rb atoms in the isotropic pancake trap, for both signs of the
interspecies scattering length. In the case of repulsive interspecies
interaction, there are the axially-symmetric and symmetry-breaking ground
states. The threshold for the symmetry breaking transition, which is related to
appearance of a zero dipole-mode, is found numerically. For attractive
interspecies interactions, the two condensates assume symmetric ground states
for the numbers of atoms up to the collapse instability of the mixture.Comment: Revised; 21 pages, 5 figures, submitted to Physical Review
General soliton matrices in the Riemann-Hilbert problem for integrable nonlinear equations
We derive the soliton matrices corresponding to an arbitrary number of
higher-order normal zeros for the matrix Riemann-Hilbert problem of arbitrary
matrix dimension, thus giving the complete solution to the problem of
higher-order solitons. Our soliton matrices explicitly give all higher-order
multi-soliton solutions to the nonlinear partial differential equations
integrable through the matrix Riemann-Hilbert problem. We have applied these
general results to the three-wave interaction system, and derived new classes
of higher-order soliton and two-soliton solutions, in complement to those from
our previous publication [Stud. Appl. Math. \textbf{110}, 297 (2003)], where
only the elementary higher-order zeros were considered. The higher-order
solitons corresponding to non-elementary zeros generically describe the
simultaneous breakup of a pumping wave into the other two components
( and ) and merger of and waves into the pumping
wave. The two-soliton solutions corresponding to two simple zeros generically
describe the breakup of the pumping wave into the and
components, and the reverse process. In the non-generic cases, these
two-soliton solutions could describe the elastic interaction of the and
waves, thus reproducing previous results obtained by Zakharov and Manakov
[Zh. Eksp. Teor. Fiz. \textbf{69}, 1654 (1975)] and Kaup [Stud. Appl. Math.
\textbf{55}, 9 (1976)].Comment: To appear in J. Math. Phy