Adiabatic Splitting, Transport, and Self-Trapping of a Bose-Einstein Condensate in a Double-Well Potential

We show that the adiabatic dynamics of a Bose-Einstein condensate (BEC) in a double well potential can be described in terms of a dark variable resulting from the combination of the population imbalance and the spatial atomic coherence between the two wells. By means of this dark variable, we extend, to the non-linear matter wave case, the recent proposal by Vitanov and Shore [Phys. Rev. A 73, 053402 (2006)] on adiabatic passage techniques to coherently control the population of two internal levels of an atom/molecule. We investigate the conditions to adiabatically split or transport a BEC as well as to prepare an adiabatic self trapping state by the optimal delayed temporal variation of the tunneling rate via either the energy bias between the two wells or the BEC non-linearity. The emergence of non-linear eigenstates and unstable stationary solutions of the system as well as their role in the breaking down of the adiabatic dynamics is investigated in detail.

💡 Research Summary

This paper extends the concept of adiabatic passage, originally developed for coherent internal‑state transfer in atoms and molecules, to the nonlinear dynamics of a Bose‑Einstein condensate (BEC) confined in a double‑well potential. Starting from the Gross‑Pitaevskii equation, the authors adopt the standard two‑mode approximation, which reduces the many‑body problem to two complex amplitudes (c_{L}(t)) and (c_{R}(t)) describing the left and right wells. From these amplitudes they define the population imbalance (z=|c_{L}|^{2}-|c_{R}|^{2}) and the relative phase (\phi=\arg(c_{L})-\arg(c_{R})). The resulting equations of motion are the nonlinear Josephson equations, containing the tunneling rate (\Omega(t)), the energy bias (\Delta(t)), and the interaction strength (U) (the non‑linearity).

The central theoretical innovation is the introduction of a “dark variable”
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