Modulational Instability of Dipolar Bose–Einstein Condensates in Optical Lattices with Three-Body Interactions

2018 ◽  
Vol 35 (1) ◽  
pp. 010301 ◽  
Author(s):  
Wei Qi ◽  
Zi-Hao Li ◽  
Zhao-Xin Liang
Keyword(s):  
Optical Lattices ◽  
Modulational Instability ◽  
Three Body ◽  
Bose Einstein

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.

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.

Interplay of three-body and higher-order interactions on the modulational instability of Bose–Einstein condensate

2020 ◽  
Vol 37 (11) ◽  
pp. A54
Author(s):  
Sabari Subramaniyan ◽  
Olivier Tiokeng Lekeufack ◽  
Ramaswamy Radha ◽  
Timoleon Crepin Kofane
Keyword(s):  
Modulational Instability ◽  
Higher Order ◽  
Einstein Condensate ◽  
Bose Einstein Condensate ◽  
Three Body ◽  
Bose Einstein

Quantum corrections to the modulational instability of Bose–Einstein condensates with two- and three-body interactions

2015 ◽  
Vol 76 ◽  
pp. 111-120 ◽  
Author(s):  
O.T. Lekeufack ◽  
S. Sabari ◽  
S.B. Yamgoué ◽  
K. Porsezian ◽  
T.C. Kofané
Keyword(s):  
Modulational Instability ◽  
Quantum Corrections ◽  
Three Body ◽  
Bose Einstein

THREE-BODY INTERACTIONS BEYOND THE GROSS–PITAEVSKII EQUATION AND MODULATIONAL INSTABILITY OF BOSE–EINSTEIN CONDENSATES

2012 ◽  
Vol 26 (32) ◽  
pp. 1250202 ◽  
Author(s):  
DIDIER BELOBO BELOBO ◽  
GERMAIN HUBERT BEN-BOLIE ◽  
TIMOLEON CREPIN KOFANE
Keyword(s):  
Modulational Instability ◽  
Mean Field Theory ◽  
Mean Field ◽  
External Potential ◽  
Pitaevskii Equation ◽  
Theoretical Predictions ◽  
The Mean ◽  
Three Body ◽  
Bose Einstein ◽  
Condensate System

Beyond the mean-field theory, a new model of the Gross–Pitaevskii equation (GPE) that describes the dynamics of Bose–Einstein condensates (BECs) is derived using an appropriate phase-imprint on the old wavefunction. This modified version of the GPE in addition to the two-body interactions term, also takes into account effects of the three-body interactions. The three-body interactions consist of a quintic term and the delayed nonlinear response of the condensate system term. Then, the modulational instability (MI) of the new GPE confined in an attractive harmonic potential is investigated. The analytical study shows that the three-body interactions destabilize more the condensate system while the external potential alleviates the instability. Numerical results confirm the theoretical predictions. Further numerical investigations of the behavior of solitons reveal that the three-body interactions enhance the appearance of solitons, increase the number of solitons generated and deeply change the lifetime of solitons. Moreover, the external potential delays the appearance of solitons. Besides, a new initial condition is introduced which enables to increase the number of solitons created and deeply affects the trail of chains of solitons generated. Moreover, the MI of a condensate without the external potential, and in a repulsive potential is also investigated.

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