Asymmetric Tunneling of Bose-Einstein Condensates

In his celebrated textbook, Quantum Mechanics-Nonrelativistic Theory, Landau argued that, for single particle systems in 1D, tunneling probability remains the same for a particle incident from the left or the right of a barrier regardless of the shape of that potential barrier. We present a proof of this argument, as no rigorous proof currently exists. We then computationally show breaking of the left-right tunneling symmetry for Bose-Einstein condensates (BEC) in 1D, modeled by the Gross-Pitaevskii equation. By varying the parameter, g, of inter-particle interaction in the BEC, we demonstrate the transition from symmetric (g=0) to asymmetric tunneling is a threshold phenomenon. Our computations employ experimentally feasible parameters such that these results may be experimentally demonstrated in the near future. We conclude by suggesting applications of the phenomena to design atomtronic diodes, synthetic gauge fields, and black-hole analogues.