scholarly journals THEORY OF NONLINEAR MATTER WAVES IN OPTICAL LATTICES

2004 ◽  
Vol 18 (14) ◽  
pp. 627-651 ◽  
Author(s):  
V. A. BRAZHNYI ◽  
V. V. KONOTOP
Keyword(s):  
Optical Lattices ◽  
Evolution Equations ◽  
Modulational Instability ◽  
Spatial Scales ◽  
Tight Binding ◽  
Matter Wave ◽  
Pitaevskii Equation ◽  
Tight Binding Approximation ◽  
Matter Waves ◽  
Bose Einstein

We consider several effects of the matter wave dynamics which can be observed in Bose–Einstein condensates embedded into optical lattices. For low-density condensates, we derive approximate evolution equations, the form of which depends on relation among the main spatial scales of the system. Reduction of the Gross–Pitaevskii equation to a lattice model (the tight-binding approximation) is also presented. Within the framework of the obtained models, we consider modulational instability of the condensate, solitary and periodic matter waves, paying special attention to different limits of the solutions, i.e. to smooth movable gap solitons and to strongly localized discrete modes. We also discuss how the Feshbach resonance, a linear force and lattice defects affect the nonlinear matter waves.

scholarly journals DYNAMICS OF BISOLITONIC MATTER WAVES IN A BOSE–EINSTEIN CONDENSATE SUBJECTED TO AN ATOMIC BEAM SPLITTER AND GRAVITY

2010 ◽  
Vol 24 (30) ◽  
pp. 2911-2920 ◽  
Author(s):  
ALAIN MOÏSE DIKANDÉ ◽  
ISAIAH NDIFON NGEK ◽  
JOSEPH EBOBENOW
Keyword(s):  
Einstein Condensate ◽  
Matter Wave ◽  
Pitaevskii Equation ◽  
Transform Method ◽  
Perturbative Approach ◽  
Matter Waves ◽  
Bose Einstein Condensate ◽  
Scattering Transform ◽  
Experimental Implementation ◽  
Bose Einstein

A theoretical scheme for an experimental implementation involving bisolitonic matter waves from an attractive Bose–Einstein condensate, is considered within the framework of a non-perturbative approach to the associate Gross–Pitaevskii equation. The model consists of a single condensate subjected to an expulsive harmonic potential creating a double-condensate structure, and a gravitational potential that induces atomic exchanges between the two overlapping post condensates. Using a non-isospectral scattering transform method, exact expressions for the bright-matter–wave bisolitons are found in terms of double-lump envelopes with the co-propagating pulses displaying more or less pronounced differences in their widths and tails depending on the mass of atoms composing the condensate.

Integrability and Multi-Soliton Solutions for a Variable-Coefficient Coupled Gross–Pitaevskii System for Atomic MatterWaves

2012 ◽  
Vol 67 (10-11) ◽  
pp. 525-533
Author(s):  
Zhi-Qiang Lin ◽  
Bo Tian ◽  
Ming Wang ◽  
Xing Lu
Keyword(s):  
Variable Coefficient ◽  
Soliton Solutions ◽  
Variable Coefficients ◽  
Einstein Condensate ◽  
Matter Wave ◽  
Bilinear Method ◽  
Matter Waves ◽  
Bose Einstein Condensate ◽  
Bose Einstein ◽  
Hirota Bilinear

Under investigation in this paper is a variable-coefficient coupled Gross-Pitaevskii (GP) system, which is associated with the studies on atomic matter waves. Through the Painlev´e analysis, we obtain the constraint on the variable coefficients, under which the system is integrable. The bilinear form and multi-soliton solutions are derived with the Hirota bilinear method and symbolic computation. We found that: (i) in the elastic collisions, an external potential can change the propagation of the soliton, and thus the density of the matter wave in the two-species Bose-Einstein condensate (BEC); (ii) in the shape-changing collision, the solitons can exchange energy among different species, leading to the change of soliton amplitudes.We also present the collisions among three solitons of atomic matter waves.

Dynamics of matter-wave solitons in three-component Bose-Einstein condensates with time-modulated interactions and gain or loss effect

2022 ◽  
Author(s):  
Yajie Yang ◽  
Ying Dong
Keyword(s):  
Similarity Transformation ◽  
Soliton Solutions ◽  
Gain Coefficient ◽  
Loss Coefficient ◽  
Matter Wave ◽  
Pitaevskii Equation ◽  
Loss Parameter ◽  
Dynamical Properties ◽  
Bose Einstein ◽  
Loss Effect

Abstract The gain or loss effect on the dynamics of the matter-wave solitons in three-component Bose-Einstein condensates with time-modulated interactions trapped in parabolic external potentials are investigated analytically. Some exact matter-wave soliton solutions to the three-coupled Gross-Pitaevskii equation describing the three-component Bose-Einstein condensates are constructed by similarity transformation. The dynamical properties of the matter-wave solitons are analyzed graphically, and the effects of the gain or loss parameter and the frequency of the external potentials on the matter-wave solitons are explored. It is shown that the gain coefficient makes the atom condensate to absorb energy from the background, while the loss coefficient brings about the collapse of the condensate.

GENERATION OF BRIGHT MATTER-WAVE SOLITON PATTERNS IN MIXTURES OF BOSE–EINSTEIN CONDENSATES WITH CUBIC AND QUINTIC NONLINEARITIES

2014 ◽  
Vol 28 (04) ◽  
pp. 1450003 ◽  
Author(s):  
DIDIER BELOBO BELOBO ◽  
GERMAIN HUBERT BEN-BOLIE ◽  
TIMOLÉON CRÉPIN KOFANÉ
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Numerical Experiments ◽  
Modulational Instability ◽  
Numerical Results ◽  
Matter Wave ◽  
Bright Solitons ◽  
Bose Einstein

The modulational instability (MI) of binary condensates with cubic-quintic nonlinearities is investigated. Using a linear stability analysis, a gain of instability is derived then, effects of the quintic nonlinearities on the instability gain are identified. To be precise, attractive intraspecie quintic nonlinearities enhance the instability, while repulsive quintic intraspecie nonlinearities soften the instability. Besides, small attractive and large repulsive quintic inter-species nonlinearities increase the instability. Numerical experiments quite well corroborate the analytical predictions. Further numerical results show effects of the cubic and the quintic nonlinearities on the propagation of trains of bright solitons generated.

scholarly journals VARIATIONAL ANALYSIS OF FLAT-TOP SOLITONS IN BOSE–EINSTEIN CONDENSATES

2011 ◽  
Vol 25 (18) ◽  
pp. 2427-2440 ◽  
Author(s):  
B. B. BAIZAKOV ◽  
A. BOUKETIR ◽  
A. MESSIKH ◽  
A. BENSEGHIR ◽  
B. A. PUMAROV
Keyword(s):  
Numerical Solution ◽  
Trial Function ◽  
Variational Analysis ◽  
Dynamic Properties ◽  
Matter Wave ◽  
Variational Approximation ◽  
Pitaevskii Equation ◽  
Three Body ◽  
Bose Einstein ◽  
Good Agreement

Static and dynamic properties of matter-wave solitons in dense Bose–Einstein condensates, where three-body interactions play a significant role, have been studied by a variational approximation (VA) and numerical simulations. For experimentally relevant parameters, matter-wave solitons may acquire a flat-top shape, which suggests employing a super-Gaussian trial function for VA. Comparison of the soliton profiles, predicted by VA and those found from numerical solution of the governing Gross–Pitaevskii equation shows good agreement, thereby validating the proposed approach.

Matter-wave solitons of Bose–Einstein condensates with time-dependent complex potentials

2018 ◽  
Vol 32 (15) ◽  
pp. 1850184 ◽  
Author(s):  
Emmanuel Kengne ◽  
Ahmed Lakhssassi
Keyword(s):  
Modulational Instability ◽  
Time Dependent ◽  
Matter Wave ◽  
Linear Potential ◽  
Dissipative Term ◽  
Loss Parameter ◽  
Gain Loss ◽  
Three Body ◽  
External Trapping Potential ◽  
Bose Einstein

To analytically investigate the matter-wave solitons of Bose–Einstein condensates (BECs) in time-dependent complex potential, we consider a cubic-quintic Gross–Pitaevskii (GP) equation with distributed coefficients and a dissipative term. By introducing a suitable ansatz, we establish the criterion of the modulational instability (MI) of the system and present an explicit expression for the growth rate of a purely growing MI. Effects of the parabolic background potential, as well as of the linear potential, the gain/loss parameter, and the two- and three-body interatomic interactions on the MI are investigated. We show how the feeding/loss parameter can be well used to control the instability of the system. The analytical resolution of the considered GP equation leads to exact bright, dark and kink solitary wave solutions which are used to investigate analytically the dynamics of matter-wave solitons in BECs under consideration. These analytical investigations show that the amplitude and the motion of bright, dark and kink solitary waves depend on the strengths of the two- and three-body interatomic interactions, as well as on the strengths of the external trapping potential and the parameter of the gain/loss of atoms in the condensate.

MODULATIONAL INSTABILITY AND EXACT SOLITON AND PERIODIC SOLUTIONS FOR TWO WEAKLY COUPLED EFFECTIVELY 1D CONDENSATES TRAPPED IN A DOUBLE-WELL POTENTIAL

2010 ◽  
Vol 24 (14) ◽  
pp. 2211-2227 ◽  
Author(s):  
E. KENGNE ◽  
R. VAILLANCOURT ◽  
B. A. MALOMED
Keyword(s):  
Periodic Solutions ◽  
Modulational Instability ◽  
Wave Number ◽  
Pitaevskii Equation ◽  
Nonlinear Dispersion ◽  
Nonlinear Dispersion Relation ◽  
Weakly Coupled ◽  
Modulational Stability ◽  
Bose Einstein ◽  
Double Well Potential

The modulational instability of the coupled Gross–Pitaevskii equation (alias nonlinear Schrödinger equation), which describes two Bose–Einstein condensates trapped in an asymmetric double-well potential, is investigated. The nonlinear dispersion relation that relates the frequency and wave number of the modulating perturbations is found and its analysis shows several possibilities for the modulational stability region. Exact soliton and periodic solutions are constructed via elliptic ordinary differential equations.

EXACT SOLITONS IN THE GROSS–PITAEVSKII EQUATION WITH TIME-MODULATED NONLINEARITY

2007 ◽  
Vol 21 (07) ◽  
pp. 383-390
Author(s):  
Z. X. LIANG ◽  
Z. D. ZHANG
Keyword(s):  
Soliton Solution ◽  
Scattering Length ◽  
Pitaevskii Equation ◽  
Matter Waves ◽  
Bose Einstein

Exact solitonic solutions of the Gross–Pitaevskii equation with time-modulated nonlinearity of a(t) = a0 / (t + t0) are obtained. With help of these solutions, we analyze the properties of Feshbach-managed solitons in Bose–Einstein condensates in details. Our results show that the parameters of atomic matter waves can be manipulated by proper variation of the scattering length. In particular, an exact two-soliton solution is given, from which, it is shown that the separation between the neighboring solitons can be effectively maintained by allowing the solitons to have unequal initial amplitudes.

Sign in / Sign up

Export Citation Format

Share Document