Chaos control of a Bose–Einstein condensate in a moving optical lattice

2016 ◽  
Vol 30 (19) ◽  
pp. 1650238 ◽  
Author(s):  
Zhiying Zhang ◽  
Xiuqin Feng ◽  
Zhihai Yao
Keyword(s):  
Optical Lattice ◽  
Chaos Control ◽  
Chaotic Behavior ◽  
Control Strategies ◽  
Lyapunov Stability Theory ◽  
Einstein Condensate ◽  
Control Parameters ◽  
Periodic Force ◽  
Bose Einstein Condensate ◽  
Bose Einstein

Chaos control of a Bose–Einstein condensate (BEC) loaded into a moving optical lattice with attractive interaction is investigated on the basis of Lyapunov stability theory. Three methods are designed to control chaos in BEC. As a controller, a bias constant, periodic force, or wavelet function feedback is added to the BEC system. Numerical simulations reveal that chaotic behavior can be well controlled to achieve periodicity by regulating control parameters. Different periodic orbits are available for different control parameters only if the maximal Lyapunov exponent of the system is negative. The abundant effect of chaotic control is also demonstrated numerically. Chaos control can be realized effectively by using our proposed control strategies.

Controlling a class of chaotic quantum system under disturbances and noisy measurements: Application to 1D Bose-Einstein condensate

2016 ◽  
Vol 27 (04) ◽  
pp. 1650040 ◽  
Author(s):  
Ricardo Aguilar-López ◽  
Pablo A. López-Pérez ◽  
Gerardo Lara-Cisneros ◽  
Ricardo Femat
Keyword(s):  
Chaotic Behavior ◽  
Lyapunov Stability Theory ◽  
Einstein Condensate ◽  
Nonlinear Feedback ◽  
Bose Einstein Condensate ◽  
Control Goal ◽  
Control Scheme ◽  
Noisy Measurements ◽  
Bose Einstein ◽  
Stochastic Ordinary Differential Equations

In this paper, a robust nonlinear feedback control scheme with adaptive gain is proposed to control the chaotic behavior in a Bose–Einstein condensate (BEC). The control goal concerns the track or regulation purposes. The BEC system is represented as stochastic ordinary differential equations with measured output perturbed by Gaussian noise, which represents the nature of the quantum systems. The convergence of the BEC control law is analyzed under the frame of the Lyapunov stability theory. Numerical experiments show an adequate performance of the proposed methodology under the required conditions. The results are applicable when the shape of the condensate is sufficiently simple.

ON THE ENERGY OF A BOSE–EINSTEIN CONDENSATE IN AN OPTICAL LATTICE

2007 ◽  
Vol 19 (04) ◽  
pp. 371-384 ◽  
Author(s):  
AMANDINE AFTALION
Keyword(s):  
Optical Lattice ◽  
Critical Case ◽  
Periodic Potential ◽  
Einstein Condensate ◽  
Gamma Convergence ◽  
The Third ◽  
Bose Einstein Condensate ◽  
Delta Functions ◽  
Convergence Type ◽  
Bose Einstein

In this paper, we study the Gross–Pitaevskii energy of a Bose–Einstein condensate in the presence of an optical lattice, modeled by a periodic potential V(x3) in the third direction. We study a simple case where the wells of the potential V correspond to regions where V vanishes, and are separated by small intervals of size δ where V is large. According to the intensity of V, we determine the limiting energy as δ tends to 0. In the critical case, the periodic potential approaches a sum of delta functions and the limiting energy has a contribution due to the value of the wave function between the wells. The proof relies on Gamma convergence type techniques.

Effects of three-body atomic interaction and optical lattice on solitons in quasi-one-dimensional Bose-Einstein condensate

Pramana ◽  
2009 ◽  
Vol 72 (2) ◽  
pp. 445-450
Author(s):  
Sk. Golam Ali ◽  
B. Talukdar ◽  
Aparna Saha
Keyword(s):  
Optical Lattice ◽  
Einstein Condensate ◽  
Atomic Interaction ◽  
One Dimensional ◽  
Bose Einstein Condensate ◽  
Three Body ◽  
Bose Einstein

scholarly journals Spatiotemporal Bloch states of a spin–orbit coupled Bose–Einstein condensate in an optical lattice

2019 ◽  
Vol 28 (5) ◽  
pp. 056701
Author(s):  
Ya-Wen Wei ◽  
Chao Kong ◽  
Wen-Hua Hai
Keyword(s):  
Optical Lattice ◽  
Einstein Condensate ◽  
Spin Orbit ◽  
Bose Einstein Condensate ◽  
Bose Einstein

scholarly journals Velocity of sound in a Bose-Einstein condensate in the presence of an optical lattice and transverse confinement

2005 ◽  
Vol 138 (3-4) ◽  
pp. 729-734 ◽  
Author(s):  
M. Kr�mer ◽  
C. Menotti ◽  
M. Modugno
Keyword(s):  
Optical Lattice ◽  
Einstein Condensate ◽  
Velocity Of Sound ◽  
Bose Einstein Condensate ◽  
Bose Einstein
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