摘要
Nonlinear tunneling is investigated by analytically solving the one-dimensional Gross–Pitaevskii equation（GPE）with a strong rectangular potential barrier. With the help of analytical solutions of the GPE, which can be reduced to the solution of the linear case, we find that only the supersonic solution in the downstream has a linear counterpart. A critical nonlinearity is explored as an up limit, above which no nonlinear tunneling solution exists. Furthermore, the density solution of the critical nonlinearity as a function of the position has a step-like structure.
Nonlinear tunneling is investigated by analytically solving the one-dimensional Gross–Pitaevskii equation（GPE）with a strong rectangular potential barrier. With the help of analytical solutions of the GPE, which can be reduced to the solution of the linear case, we find that only the supersonic solution in the downstream has a linear counterpart. A critical nonlinearity is explored as an up limit, above which no nonlinear tunneling solution exists. Furthermore, the density solution of the critical nonlinearity as a function of the position has a step-like structure.
基金
Project supported by the National Natural Science Foundation of China(Grant Nos.11074155 and 11374197)
the Program for Changjiang Scholars and Innovative Research Team in University(PCSIRT),China(Grant No.IRT13076)
the National High Technology Research and Development Program of China(Grant No.2011AA010801)
