Stability of binary condensates with spatial modulations of quintic nonlinearities in optical lattices

2015 ◽  
Vol 29 (03) ◽  
pp. 1550008 ◽  
Author(s):  
M. D. Mboumba ◽  
A. B. Moubissi ◽  
T. B. Ekogo ◽  
D. Belobo Belobo ◽  
G. H. Ben-Bolie ◽  
...  
Keyword(s):  
Optical Lattice ◽  
Optical Lattices ◽  
Mean Field ◽  
Collective Excitations ◽  
Pitaevskii Equation ◽  
Dependent Potential ◽  
The Mean ◽  
The Stability ◽  
Bose Einstein ◽  
Spatial Modulations

The stability and collective excitations of binary Bose–Einstein condensates with cubic and quintic nonlinearities in variable anharmonic optical lattices are investigated. By using the variational approach, the influences of the quintic nonlinearities and the shape of the external potential on the stability are discussed in details. It is found that the quintic intraspecies and interspecies interatomic interactions profoundly affect the stability criterion and collective excitations of the system. The shape dependent potential form that characterizes the optical lattice deeply alters the stability regions. Direct numerical simulations of the mean-field coupled Gross–Pitaevskii equation describing the system agree well with the analytical predictions.

INTERACTING BOSONIC ATOMS WITH RANDOM POTENTIAL IN OPTICAL LATTICES

2009 ◽  
Vol 23 (11) ◽  
pp. 1391-1404
Author(s):  
WEI LIU ◽  
JIAN-YANG ZHU
Keyword(s):  
Optical Lattice ◽  
Optical Lattices ◽  
Mean Field Theory ◽  
Mean Field ◽  
Temperature Phase ◽  
Optical Parameters ◽  
Xxz Model ◽  
Bose Glass ◽  
The Mean ◽  
Bosonic Atoms

In this paper, we study the ultracold atoms in optical lattice with a weak random external potential by an extended Bose–Hubbard model. When the on-site interaction is strong enough, the model can be mapped to the XXZ model. Then the mean-field theory is applied and we get the zero- and finite-temperature phase diagrams in different optical parameters. The differences between the systems with and without disorder were found, and the Bose-glass phase may exist in the system with disorder.

COLLAPSE OF K-Rb FERMI-BOSE MIXTURES IN OPTICAL LATTICES

2006 ◽  
Vol 20 (30n31) ◽  
pp. 5199-5203
Author(s):  
D. M. JEZEK ◽  
H. M. CATALDO
Keyword(s):  
Low Temperature ◽  
Optical Lattice ◽  
Optical Lattices ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
One Dimensional ◽  
Different Types ◽  
The Mean ◽  
Number Of Particles

We study a confined mixture of Rb and K atoms in a one dimensional optical lattice, at low temperature, in the quanta1 degeneracy regime. This mixture exhibits an attractive boson-fermion interaction, and thus above certain values of the number of particles the mixture collapses. We investigate, in the mean-field approximation, the curve for which this phenomenon occurs, in the space of number of particles of both species. This is done for different types of optical lattices.

scholarly journals Dragging spin-orbit-coupled solitons by a moving optical lattice

2021 ◽  
Author(s):  
Hidetsugu Sakaguchi ◽  
Fumihide Hirano ◽  
Boris A Malomed
Keyword(s):  
Optical Lattice ◽  
Mean Field ◽  
Stability Domain ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Two Dimensional ◽  
Galilean Invariance ◽  
The Stability ◽  
Velocity Interval ◽  
Bose Einstein

Abstract It is known that the interplay of the spin-orbit-coupling (SOC) and mean-field self-attraction creates stable two-dimensional (2D) solitons (ground states) in spinor Bose-Einstein condensates. However, SOC destroys the system's Galilean invariance, therefore moving solitons exist only in a narrow interval of velocities, outside of which the solitons suffer delocalization. We demonstrate that the application of a relatively weak moving optical lattice (OL), with the 2D or quasi-1D structure, makes it possible to greatly expand the velocity interval for stable motion of the solitons. The stability domain in the system's parameter space is identified by means of numerical methods. In particular, the quasi-1D OL produces a stronger stabilizing effect than its full 2D counterpart. Some features of the domain are explained analytically.

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.

scholarly journals The Smoluchowski Ensemble—Statistical Mechanics of Aggregation

Entropy ◽  
2020 ◽  
Vol 22 (10) ◽  
pp. 1181
Author(s):  
Themis Matsoukas
Keyword(s):  
Sol Gel ◽  
Scaling Limit ◽  
Mean Field ◽  
Central Element ◽  
Field Approximation ◽  
Fixed Number ◽  
Mean Field Approximation ◽  
The Mean ◽  
Sol Gel Transition ◽  
The Stability

We present a rigorous thermodynamic treatment of irreversible binary aggregation. We construct the Smoluchowski ensemble as the set of discrete finite distributions that are reached in fixed number of merging events and define a probability measure on this ensemble, such that the mean distribution in the mean-field approximation is governed by the Smoluchowski equation. In the scaling limit this ensemble gives rise to a set of relationships identical to those of familiar statistical thermodynamics. The central element of the thermodynamic treatment is the selection functional, a functional of feasible distributions that connects the probability of distribution to the details of the aggregation model. We obtain scaling expressions for general kernels and closed-form results for the special case of the constant, sum and product kernel. We study the stability of the most probable distribution, provide criteria for the sol-gel transition and obtain the distribution in the post-gel region by simple thermodynamic arguments.

scholarly journals Transition from the mean-field to the bosonic Laughlin state in a rotating Bose-Einstein condensate

2019 ◽  
Vol 100 (2) ◽  
Author(s):  
G. Vasilakis ◽  
A. Roussou ◽  
J. Smyrnakis ◽  
M. Magiropoulos ◽  
W. von Klitzing ◽  
...  
Keyword(s):  
Mean Field ◽  
Einstein Condensate ◽  
Bose Einstein Condensate ◽  
The Mean ◽  
Bose Einstein
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