  In his celebrated textbook, \textit{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. This left-right symmetry of tunneling probability holds
regardless of the shape of the potential barrier. However, there are a variety
of known cases that break this symmetry, e.g. when observing composite
particles. We computationally (and analytically, in the simplest case) show
this breaking of the left-right tunneling symmetry for Bose-Einstein
condensates (BEC) in 1D, modelled by the Gross-Pitaevskii equation (GPE). By
varying $g$, the parameter of inter-particle interaction in the BEC, we
demonstrate that 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, Maxwell's demons, and black-hole
analogues.
