Dynamics of Bose-Einstein Condensate in Linear and Non-Linear Regime

Kalai Kumar Rajagopal, Gafurjan Ismailovich Ibragimov

Chuanwei Zhang

Yao-Jun Ying, Lizhen 李真 Sun 孙, Haibin 海彬 Li 李

We investigate dynamics of Bose–Einstein condensates (BECs) in a single-well potential using the mode-coupling method. Symmetry is shown to play a key role in the coupling between modes. A proper mode-coupling theory of the dynamics of BECs in a single-well potential should include at least four modes. In this context, the ideal BEC system can be decomposed into two independent subsystems when the coupling is caused by external potential perturbation and is linear. The mode dynamics of non-ideal BECs with interaction shows rich behavior. The combination of nonlinear coupling and initial condition leads to the different regimes of mode dynamics, from regularity to non-regularity, which also indicates a change of the dependence of coupling on the symmetry of modes.

Wu‐Ming Liu

Aaron Wirthwein, Stephan Haas, Sheng‐wey Chiow

We study the collision dynamics of two Bose-Einstein condensates with their dynamical wave functions modeled by a set of coupled, time-dependent Gross-Pitaevskii equations. Beginning with an effective one-dimensional system, we identify regimes characterized by the relationship between inter- and intra-atomic interactions and the initial configuration of the system, akin to the equilibrium phase diagram of two interacting Bose condensates. We consider a dynamical setup in which two wave packets are initially at rest with a small separation about the center of an asymmetric harmonic trap. Upon release, we observe a rapid approach to dynamical equilibrium in the limits of very large and very small inter-particle repulsion, characterized by periodic transmission or reflection of the condensates as distinguishable units, whereas the intermediate, critical regime is characterized by extended transient dynamics, density fracturing, and dynamical mixing. We therefore have reason to believe that non-trivial behavior may exist during the collisions of Bose-Einstein condensates as a result of their non-linear interactions, and these effects may be observable in a suitable laboratory environment.

V. A. Stepanyan

Recently Bose-Einstein condensation has gathered a popularity and interest. An interesting theoretical phenomenon closely related to BEC and condensation is Frohlich's dynamic condensation phenomenon, proposed as a reoccurring mechanism in biophysics. This phenomenon studied classically brings forth a hypothesis that dynamic emergence of condensation requires nonlinear interactions. Working in the purely quantum regime I show the correctness of the hypothesis for a broad class of initial states as well as show a way for condensation to emerge from linear dynamics if the initial state has very large or very long-range quantum correlations.