Stability of trapped Bose—Einstein condensates in one-dimensional tilted optical lattice potential

Abstract

Using the direct perturbation technique, this paper obtains a general perturbed solution of the Bose-Einstein condensates trapped in one-dimensional tilted optical lattice potential. We also gave out two necessary and sufficient conditions for boundedness of the perturbed solution. Theoretical analytical results and the corresponding numerical results show that the perturbed solution of the Bose-Einstein condensate system is unbounded in general and indicate that the Bose-Einstein condensates are Lyapunov-unstable. However, when the conditions for boundedness of the perturbed solution are satisfied, then the Bose-Einstein condensates are Lyapunov-stable.

Synchronization Analysis of a Master-Slave BEC System via Active Control

“…where 𝐹 is the internal force, and 𝐹𝑥 produce a tilted potential, accelerates the bosons in the x axis and causes bosons tunnelling out of the traps [4,5,24]. Also 𝑉(𝑥) is the optical lattice potential and given by…”

“…A BEC system with an external potential exhibits many rich results such a nonlinear system [2,3]. The chaotic dynamics of a BEC system depends on the applied external potential and interaction parameters between the atoms that create the condensation [4][5][6][7]. The BEC is given by Ψ(x, t) macroscopic wave function and it is governed the Gross-Pitaevskii equation (GPE).…”

Master-slave synchronization of Bose-Einstein condensate in 1D tilted bichromatical optical lattice

“…where the constant force F describes F = ma. Here, m is the mass of atoms and a is the acceleration wich generates a tilted optical potential as shown in figure 2, accelerates the atoms in the x direction with linearly increasing flow density and leads to the atoms tunnelling out of the traps [24][25][26][27]. Moreover, V(x) is the optical potential.…”

Classical-field description of Bose–Einstein condensation of parallel light in a nonlinear optical cavity*

“…It is a common quantum property also a natural consequence of the statistics of many-particle boson system. Since its theoretical prediction, [1] the phenomenon of BEC has been observed in a wide variety system, [2][3][4][5][6][7][8] from ultracold atomic gases, to quasiparticles such as polaritions, excitons, and magnons. Photons have played a vital role for the experimental realization of BEC of these particles.…”