Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Open Physics

Relation between chaos probability and zero-point number of the Melnikov function for a Bose-Einstein condensate

Qianquan Zhu, Wenhua Hai, Shiguang Rong

Published Jan 18, 2009• 1 citation
Publisher

Abstract

Abstract We investigate an attractive Bose-Einstein condensate perturbed by a weak traveling optical superlattice. It is demonstrated that under a stochastic initial set and in a given parameter region solitonic chaos appears with a certain probability that is tightly related to the zero-point number of the Melnikov function; the latter depends on the potential parameters. Effects of the lattice depths and wave vectors on the chaos probability are studied analytically and numerically, and different chaotic regions of the parameter space are found. The results suggest a feasible method for strengthening or weakening chaos by modulating the potential parameters experimentally.

DOI
10.2478/s11534-008-0159-1

Related papers

Transition probability from matter-wave soliton to chaos

Qianquan Zhu, Wenhua Hai, Shiguang Rong

For a Bose-Einstein condensate loaded into a weak traveling optical superlattice, it is demonstrated that under a stochastic initial set and in a given parameter region, the solitonic chaos appears with a certain probability. Effects of the lattice depths and wave vectors on the chaos probability are investigated analytically and numerically and different chaotic regions associated with different chaos probabilities are found. The results suggest a method for weakening or strengthening chaos by modulating the moving superlattice.

arXiv:0804.0906•Physical Review E•Jul 7, 2009•20 citations

Controlling Chaos Probability of a Bose–Einstein Condensate in a Weak Optical Superlattice

Xu Jun, Xiaobing Luo

The spatial chaos probability of a Bose–Einstein condensate perturbed by a weak optical superlattice is studied. It is demonstrated that the spatial chaotic solution appears with a certain probability in a given parameter region under a random boundary condition. The effects of the lattice depths and wave vectors on the chaos probability are illustrated, and different regions associated with different chaos probabilities are found. This suggests a feasible scheme for suppressing and strengthening chaos by adjusting the optical superlattice experimentally.

Chinese Physics Letters•Mar 31, 2009•4 citations

Transient and stationary chaos of a Bose-Einstein condensate loaded into a moving optical lattice potential

Guishu Chong, Wenhua Hai, Qiongtao Xie

Chaotic space-time evolution is investigated for the particle number density of a Bose-Einstein condensate with attractive interatomic interaction loaded into a traveling optical lattice. Melnikov chaos is studied and the weakly chaotic regime is presented analytically. Transitions from transient to stationary chaos in the space-time evolution are illustrated numerically. The results show that, on increasing the strength of the optical potential, the transient chaos falls onto several different attractors. Meanwhile, these attractors undergo a series of period-doubling bifurcations when the optical potential intensity is increased continuously, and eventually stationary chaos arises for a critical depth of the optical lattice. The obstructions to chaos caused by the damping and the motion of lattice are also demonstrated.

Physical Review E•Sep 27, 2004•55 citations

Boundary-Dependent Chaotic Regions for a Bose–Einstein Condensate Interacting with Laser Field

Zhu Qian-Quan, Hai Wen-Hua, Haiming Deng

Spatial chaos of a Bose–Einstein condensate perturbed by a weak laser standing wave and a weak laser δ pulse is studied. By using the perturbed chaotic solution we investigate the new type of Melnikov chaotic regions, which depend on an integration constant c 0 determined by the boundary conditions. It is shown that when the | c 0 | values are small, the chaotic region corresponds to small values of laser wave vector k , and the chaotic region for the larger k values is related to the large | c 0 | values. The result is confirmed numerically by finding the chaotic and regular orbits on the Poincaré section for the two different parameter regions. Thus, for a fixed c 0 the adjustment of k from a small value to large value can transform the chaotic region into the regular one or on the contrary, which suggests a feasible method for eliminating or generating Melnikov chaos.

Chinese Physics Letters•Oct 17, 2007•2 citations

Suppression of Chaos in a Bose–Einstein Condensate Loaded into a Moving Optical Superlattice Potential

Xiaobing Luo, Xia Xiu-Wen, Zhang Xiao-Fei

We have shown that the application of modulating the secondary lattice is an efficient route to suppressing the generation of chaotic traveling waves of a Bose–Einstein Condensate with attractive interatomic interaction loaded into a moving optical superlattice consisting of two lattices. With the Melnikov method, we obtain the optimal value of the relative phase between the two lattice harmonics for the control of chaos. We also find that the regularization route as the potential depth of the secondary lattice is varied and fairly rich, including the period-doubling bifurcations.

Chinese Physics Letters•Apr 1, 2010•6 citations

Generation and control of chaos in a Bose–Einstein condensate

Xu Jun, Hai Wen-Hua, Hui Li

For a Bose-Einstein condensate (BEC) confined in a double lattice consisting of two weak laser standing waves we find the Melnikov chaotic solution and chaotic region of parameter space by using the direct perturbation method. In the chaotic region, spatial evolutions of the chaotic solution and the corresponding distribution of particle number density are bounded but unpredictable between their superior and inferior limits. It is illustrated that when the relation k 1 ≈ k 2 between the two laser wave vectors is kept, the adjustment from k 2 < k 1 to k 2 ⩾ k 1 can transform the chaotic region into regular one or the other way round. This suggests a feasible scheme for generating and controlling chaos, which could lead to an experimental observation in the near future.

Chinese Physics•Aug 1, 2007•13 citations
Abstract We investigate an attractive Bose-Einstein condensate perturbed by a weak traveling optical superlattice. It is demonstrated that under a stochastic initial set and in a given parameter region solitonic chaos appears with a certain probability that is tightly related to the zero-point number of the Melnikov function; the latter depends on the potential parameters. Effects of the lattice depths and wave vectors on the chaos probability are studied analytically and numerically, and different chaotic regions of the parameter space are found. The results suggest a feasible method for strengthening or weakening chaos by modulating the potential parameters experimentally.
For a Bose-Einstein condensate loaded into a weak traveling optical superlattice, it is demonstrated that under a stochastic initial set and in a given parameter region, the solitonic chaos appears with a certain probability. Effects of the lattice depths and wave vectors on the chaos probability are investigated analytically and numerically and different chaotic regions associated with different chaos probabilities are found. The results suggest a method for weakening or strengthening chaos by modulating the moving superlattice.
The spatial chaos probability of a Bose–Einstein condensate perturbed by a weak optical superlattice is studied. It is demonstrated that the spatial chaotic solution appears with a certain probability in a given parameter region under a random boundary condition. The effects of the lattice depths and wave vectors on the chaos probability are illustrated, and different regions associated with different chaos probabilities are found. This suggests a feasible scheme for suppressing and strengthening chaos by adjusting the optical superlattice experimentally.
Chaotic space-time evolution is investigated for the particle number density of a Bose-Einstein condensate with attractive interatomic interaction loaded into a traveling optical lattice. Melnikov chaos is studied and the weakly chaotic regime is presented analytically. Transitions from transient to stationary chaos in the space-time evolution are illustrated numerically. The results show that, on increasing the strength of the optical potential, the transient chaos falls onto several different attractors. Meanwhile, these attractors undergo a series of period-doubling bifurcations when the optical potential intensity is increased continuously, and eventually stationary chaos arises for a critical depth of the optical lattice. The obstructions to chaos caused by the damping and the motion of lattice are also demonstrated.
Spatial chaos of a Bose–Einstein condensate perturbed by a weak laser standing wave and a weak laser δ pulse is studied. By using the perturbed chaotic solution we investigate the new type of Melnikov chaotic regions, which depend on an integration constant c 0 determined by the boundary conditions. It is shown that when the | c 0 | values are small, the chaotic region corresponds to small values of laser wave vector k , and the chaotic region for the larger k values is related to the large | c 0 | values. The result is confirmed numerically by finding the chaotic and regular orbits on the Poincaré section for the two different parameter regions. Thus, for a fixed c 0 the adjustment of k from a small value to large value can transform the chaotic region into the regular one or on the contrary, which suggests a feasible method for eliminating or generating Melnikov chaos.
We have shown that the application of modulating the secondary lattice is an efficient route to suppressing the generation of chaotic traveling waves of a Bose–Einstein Condensate with attractive interatomic interaction loaded into a moving optical superlattice consisting of two lattices. With the Melnikov method, we obtain the optimal value of the relative phase between the two lattice harmonics for the control of chaos. We also find that the regularization route as the potential depth of the secondary lattice is varied and fairly rich, including the period-doubling bifurcations.
For a Bose-Einstein condensate (BEC) confined in a double lattice consisting of two weak laser standing waves we find the Melnikov chaotic solution and chaotic region of parameter space by using the direct perturbation method. In the chaotic region, spatial evolutions of the chaotic solution and the corresponding distribution of particle number density are bounded but unpredictable between their superior and inferior limits. It is illustrated that when the relation k 1 ≈ k 2 between the two laser wave vectors is kept, the adjustment from k 2 < k 1 to k 2 ⩾ k 1 can transform the chaotic region into regular one or the other way round. This suggests a feasible scheme for generating and controlling chaos, which could lead to an experimental observation in the near future.