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1.
Using a three-dimensional mean-field model we study one-dimensional dipolar Bose–Einstein condensate (BEC) solitons on a weak two-dimensional (2D) square and triangular optical lattice (OL) potentials placed perpendicular to the polarization direction. The stabilization against collapse and expansion of these solitons for a fixed dipolar interaction and a fixed number of atoms is possible for short-range atomic interaction lying between two critical limits. The solitons collapse below the lower limit and escapes to infinity above the upper limit. One can also stabilize identical tiny BEC solitons arranged on the 2D square OL sites forming a stable 2D array of interacting droplets when the OL sites are filled with a filling factor of 1/2 or less. Such an array is unstable when the filling factor is made more than 1/2 by occupying two adjacent sites of OL. These stable 2D arrays of dipolar superfluid BEC solitons are quite similar to the recently studied dipolar Mott insulator states on 2D lattice in the Bose–Hubbard model by Capogrosso-Sansone et al. [B. Capogrosso-Sansone, C. Trefzger, M. Lewenstein, P. Zoller, G. Pupillo, Phys. Rev. Lett. 104 (2010) 125301]. 相似文献
2.
We consider the effects of anisotropy on two types of localized states with topological charges equal to 1 in two-dimensional nonlinear lattices, using the discrete nonlinear Schr?dinger equation as a paradigm model. We find that on-site-centered vortices with different propagation constants are not globally stable, and that upper and lower boundaries of the propagation constant exist. The region between these two boundaries is the domain outside of which the on-site-centered vortices are unstable. This region decreases in size as the anisotropy parameter is gradually increased. We also consider off-site-centered vortices on anisotropic lattices, which are unstable on this lattice type and either transform into stable quadrupoles or collapse. We find that the transformation of off-sitecentered vortices into quadrupoles, which occurs on anisotropic lattices, cannot occur on isotropic lattices. In the quadrupole case, a propagation-constant region also exists, outside of which the localized states cannot stably exist. The influence of anisotropy on this region is almost identical to its effects on the on-site-centered vortex case. 相似文献
3.
R. Driben B. A. Malomed 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2008,50(3):317-323
It is known that optical-lattice (OL) potentials can stabilize solitons and
solitary vortices against the critical collapse, generated by cubic
attractive nonlinearity in the 2D geometry. We demonstrate that OLs can also
stabilize various species of fundamental and vortical solitons against the
supercritical collapse, driven by the double-attractive cubic-quintic
nonlinearity (however, solitons remain unstable in the case of the pure
quintic nonlinearity). Two types of OLs are considered, producing similar
results: the 2D Kronig-Penney “checkerboard”, and the sinusoidal potential.
Soliton families are obtained by means of a variational approximation, and
as numerical solutions. The stability of all families, which include
fundamental and multi-humped solitons, vortices of oblique and straight
types, vortices built of quadrupoles, and supervortices, strictly
obeys the Vakhitov-Kolokolov criterion. The model applies to optical media
and BEC in “pancake” traps. 相似文献
4.
We analyze the rhombic to square vortex lattice phase transition in anisotropic superconductors using a variant of Ginzburg-Landau theory. The mean-field phase diagram is determined to second order in the anisotropy parameter, and shows a reorientation transition of the square vortex lattice with respect to the crystal lattice. We then derive the long-wavelength elastic moduli of the lattices, and use them to show that thermal fluctuations produce a reentrant rhombic to square lattice transition line, similar to recent studies which used a nonlocal London model. 相似文献
5.
We consider a dynamical model for a Fermi gas in the Bardeen-Cooper-Schrieffer (BCS) superfluid state, trapped in a combination of a 1D or 2D optical lattice (OL) and a tight parabolic potential, acting in the transverse direction(s). The model is based on an equation for the order parameter (wave function), which is derived from the energy density for the weakly coupled BCS superfluid. The equation includes a nonlinear self-repulsive term of power 7/3, which accounts for the Fermi pressure. Reducing the equation to the 1D or 2D form, we construct families of stable 1D and 2D gap solitons (GSs) by means of numerical simulations, which are guided by the variational approximation (VA). The GSs are, chiefly, compact objects trapped in a single cell of the OL potential. In the linear limit, the VA predicts almost exact positions of narrow Bloch bands that separate the semi-infinite and first finite gaps, as well as the first and second finite ones. Families of stable even and odd bound states of 1D GSs are constructed, too. We also demonstrate that the GS can be dragged without much distortion by an OL moving at a moderate velocity (, in physical units). The predicted GSs contain ∼103-104 and ∼103 atoms per 1D and 2D settings, respectively. 相似文献
6.
Dipole and quadrupole solitons in a two-dimensional optically induced defocusing photonic lattice are theoretically predicted and experimentally observed. It is shown that in-phase nearest-neighbor and out-of-phase next-nearest-neighbor dipoles exist and can be stable in the intermediate intensity regime. There are also different types of dipoles that are always unstable. In-phase nearest-neighbor quadrupoles are also numerically obtained, and may also be linearly stable. Out-of-phase, nearest-neighbor quadrupoles are found to be typically unstable. These numerical results are found to be aligned with the main predictions obtained analytically in the discrete nonlinear Schrödinger model. Finally, experimental results are presented for both dipole and quadrupole structures, indicating that self-trapping of such structures in the defocusing lattice can be realized for the length of the nonlinear crystal (10 mm). 相似文献
7.
Z. Z. Chen Y. L. Ma 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2007,41(1):163-170
The minimal energy configurations of finite Nv-body vortices in a
rotating trapped Bose-Einstein condensate is studied analytically by
extending the previous work [Y. Castin, R. Dum, Eur. Phys. J.
D 7, 399 (1999)], and taking into account the finite
size effects on z-direction and the bending of finite vortex lines. The
calculation of the energy of the vortices as a function of the rotation
frequency of the trap gives number, curvature, configuration of vortices and
width of vortex cores self-consistently. The numerical results show that (1)
the simplest regular polynomial of the several vortex configurations is
energetically favored; while the hexagonal vortex lattice is more stable
than square lattice; (2) bending is more stable then straight vortex line
along the z-axis for λ<1; (3) the boundary effect is obvious:
compared with the estimation made under infinite boundary, the finite size
effect leads to a lower vortex density, while the adding vortex bending
results in a less higher density because of the expansion. The results are
in well agreement with the other authors' ones. 相似文献
8.
Jia-Sheng Huang Xun-Da Jiang Huai-Yu Chen Zhi-Wei Fan Wei Pang Yong-Yao Li 《Frontiers of Physics》2015,10(4):100507
We study two-dimensional (2D) matter-wave solitons in the mean-field models formed by electric quadrupole particles with long-range quadrupole–quadrupole interaction (QQI) in 2D free space. The existence of 2D matter-wave solitons in the free space was predicted using the 2D Gross–Pitaevskii Equation (GPE). We find that the QQI solitons have a higher mass (smaller size and higher intensity) and stronger anisotropy than the dipole–dipole interaction (DDI) solitons under the same environmental parameters. Anisotropic soliton–soliton interaction between two identical QQI solitons in 2D free space is studied. Moreover, stable anisotropic dipole solitons are observed, to our knowledge, for the first time in 2D free space under anisotropic nonlocal cubic nonlinearity. 相似文献
9.
J.P. Zagorodny Y. Gaididei F.G. Mertens A.R. Bishop 《The European Physical Journal B - Condensed Matter and Complex Systems》2003,31(4):471-487
We investigate the dynamics of out-of-plane (OP) vortices, in a 2-dimensional (2D) classical Heisenberg magnet with a weak
anisotropy in the coupling of z-components of spins (easy plane anisotropy), on square lattices, under the influence of a rotating in-plane (IP) magnetic
field. Switching of the z-component of magnetization of the vortex is studied in computer simulations as a function of the magnetic field's amplitude
and frequency. The effects of the size and the anisotropy of the system on the switching process are shown. An approximate
dynamical equivalence of the system, in the bulk limit, to another system with both IP and OP static fields in the rotating reference frame is demonstrated, and qualitatively the same switching and critical behavior is obtained
in computer simulations for both systems. We briefly discuss the interplay between finite size effects (image vortices) and
the applied field in the dynamics of OP vortices. In the framework of a discrete reduced model of the vortex core we propose a mechanism for switching the vortex polarization, which can account qualitatively
for all our results. A coupling between the IP movement (trajectories) of the vortex center and the OP core structure oscillations,
due to the discreteness of the underlying lattice, is shown. A connection between this coupling and our reduced model is made
clear, through an analogy with a generalized Thiele equation.
Received 6 June 2002 / Received in final form 4 November 2002 Published online 6 March 2003
RID="a"
ID="a"e-mail: juan.zagorodny@uni-bayreuth.de 相似文献
10.
The nonlinear lattice — a new and nonlinear class of periodic potentials — was recently introduced to generate various nonlinear localized modes. Several attempts failed to stabilize two-dimensional (2D) solitons against their intrinsic critical collapse in Kerr media. Here, we provide a possibility for supporting 2D matter-wave solitons and vortices in an extended setting — the cubic and quintic model — by introducing another nonlinear lattice whose period is controllable and can be different from its cubic counterpart, to its quintic nonlinearity, therefore making a fully “nonlinear quasi-crystal”.A variational approximation based on Gaussian ansatz is developed for the fundamental solitons and in particular, their stability exactly follows the inverted Vakhitov–Kolokolov stability criterion, whereas the vortex solitons are only studied by means of numerical methods. Stability regions for two types of localized mode — the fundamental and vortex solitons — are provided. A noteworthy feature of the localized solutions is that the vortex solitons are stable only when the period of the quintic nonlinear lattice is the same as the cubic one or when the quintic nonlinearity is constant, while the stable fundamental solitons can be created under looser conditions. Our physical setting (cubic-quintic model) is in the framework of the Gross–Pitaevskii equation or nonlinear Schrödinger equation, the predicted localized modes thus may be implemented in Bose–Einstein condensates and nonlinear optical media with tunable cubic and quintic nonlinearities. 相似文献
11.
P. Rose T. Richter B. Terhalle J. Imbrock F. Kaiser C. Denz 《Applied physics. B, Lasers and optics》2007,89(4):521-526
We investigate the formation of fundamental discrete solitons and dipole-mode gap solitons in triangular photonic lattices
imprinted in photorefractive nonlinear media. These lattices are strongly affected by the photorefractive anisotropy, resulting
in orientation-dependent refractive index structures with reduced symmetry. It is demonstrated that two different orientations
of the lattice wave enable the formation of fundamental discrete solitons in the total internal reflection gap. Furthermore,
it is shown that one lattice orientation additionally supports dipole-mode solitons in the Bragg reflection gap. The experimental
results are corroborated by numerical simulations using the full anisotropic model.
PACS 42.65.Tg; 42.65.Wi; 42.70.Qs 相似文献
12.
T. Kamppeter S.A. Leonel F.G. Mertens M.E. Gouvêa A.S.T. Pires A.S. Kovalev 《The European Physical Journal B - Condensed Matter and Complex Systems》2001,21(1):93-102
The properties of dynamical solitons (magnon droplets) in the classical, two-dimensional anisotropic Heisenberg model with
easy-axis exchange anisotropy are studied. The solution of the Landau-Lifshitz equation in the continuum limit for the soliton
with topological charge q = 1 is obtained numerically using a shooting method. We analized a wide range of the anisotropy parameter and our results
are in good agreement with results obtained from spin dynamics simulations. The dependence of an internal precession frequency
of the soliton on both the anisotropy parameter and the radius of the soliton is also investigated. Finally, the limits of
applicability of the continuum approach are discussed.
Received 22 August 2000 相似文献
13.
The effective interaction between gauge vortices on a square lattice is revealed to be attractive at short distance and oscillate
between repulsion and attraction at long distance. It is analyzed that the strong attraction at short distance makes the gauge
vortices cluster at a given flux concentration; while the oscillatory nature in the interaction potential is the consequence
of the existence of the electron Fermi surface in the nonuniform flux phases states. 相似文献
14.
We present a scenario for the peculiar coexistence of charge fluctuations observed in quasi-2D 1/4-filled organic conductors theta-(BEDT-TTF)2X in the quantum critical regime where the charge ordering is suppressed down to zero temperature. The scenario is explored in the extended Hubbard model including electron-phonon couplings on an anisotropic triangular lattice. We find that the coexisting fluctuations emerge from two different instabilities, the "Wigner crystallization on a lattice" driven by the off-site Coulomb repulsion and the charge-density-wave formation due to the nesting of the Fermi surface, not from phase competition or real-space inhomogeneity. This mechanism explains the contrastive temperature dependence of two fluctuations in experiments. 相似文献
15.
Zangi R Rice SA 《Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics》2000,61(1):671-681
We report the results of extensive molecular dynamics simulations of the reconstructive hexagonal to square lattice conversion in bilayer colloid systems. Two types of interparticle potential were used to represent the colloid-colloid interactions in the suspension. One potential, due to Marcus and Rice, is designed to describe the interaction of sterically stabilized colloid particles. This potential has a term that represents the attraction between colloid particles when there is incipient overlap between the stabilizing brushes on their surfaces, a (soft repulsion) term that represents the entropy cost associated with interpenetration of the stabilizing brushes, and a term that represents core-core repulsion. The other potential we used is an almost hard core repulsion with continuous derivatives. Our results clearly show that the character of the reconstructive hexagonal to square lattice conversion in bilayer colloid systems is potential dependent. For a system with colloid-colloid interactions of the Marcus-Rice type, the packing of particles in the square array exhibits a large interlayer lattice spacing, with the particles located at the minima of the attractive well. In this case the hexagonal to square lattice transition is first order. For a system with hard core colloid-colloid interactions there are two degenerate stable intermediate phases, linear and zigzag rhombic, that are separated from the square lattice by strong first order transitions, and from the hexagonal lattice by either weak first or second order transitions. 相似文献
16.
We investigate the stability properties of breather solitons in a three-dimensional Bose-Einstein condensate with Feshbach resonance management of the scattering length and confined only by a one-dimensional optical lattice. We compare regions of stability in parameter space obtained from a fully 3D analysis with those from a quasi-two-dimensional treatment. For moderate confinement we discover a new island of stability in the 3D case, not present in the quasi-2D treatment. Stable solutions from this region have non-trivial dynamics in the lattice direction; hence, they describe fully 3D breather solitons. We demonstrate these solutions in direct numerical simulations and outline a possible way of creating robust 3D solitons in experiments in a Bose-Einstein condensate in a one-dimensional lattice. We point out other possible applications. 相似文献
17.
Starting with a Gaussian variational ansatz, we predict anisotropic bright solitons in quasi-2D Bose-Einstein condensates consisting of atoms with dipole moments polarized perpendicular to the confinement direction. Unlike isotropic solitons predicted for the moments aligned with the confinement axis [Phys. Rev. Lett. 95, 200404 (2005)10.1103/PhysRevLett.95.200404], no sign reversal of the dipole-dipole interaction is necessary to support the solitons. Direct 3D simulations confirm their stability. 相似文献
18.
19.
We demonstrate the existence of higher-order solitons occurring at an interface separating two one-dimensional (1D) Bessel
optical lattices with different orders or modulation depths in a defocusing medium. We show that, in contrast to homogeneous
waveguides where higher-order solitons are always unstable, the Bessel lattices with an interface support branches of higher-order
structures bifurcating from the corresponding linear modes. The profiles of solitons depend remarkably on the lattice parameters
and the stability can be enhanced by increasing the lattice depth and selecting higher-order lattices. We also reveal that
the interface model with defocusing saturable Kerr nonlinearity can support stable multi-peaked solitons. The uncovered phenomena
may open a new way for soliton control and manipulation. 相似文献
20.
M. Holtschneider W. Selke 《The European Physical Journal B - Condensed Matter and Complex Systems》2008,62(2):147-154
Classical uniaxially anisotropic Heisenberg and XY antiferromagnets
in a field along the easy axis on a square lattice
are analysed, applying ground state
considerations and Monte Carlo techniques. The models are known to
display antiferromagnetic and spin-flop phases. In the Heisenberg
case, a single-ion anisotropy is added to the XXZ antiferromagnet,
enhancing or competing with the uniaxial exchange anisotropy. Its
effect on the stability of non-collinear structures of biconical
type is studied. In the case of the anisotropic XY antiferromagnet,
the transition region between the antiferromagnetic and spin-flop
phases is found to be dominated by degenerate bidirectional
fluctuations. The phase diagram is observed to resemble closely
that of the XXZ antiferromagnet without single-ion anisotropy. 相似文献