  We propose an experimental scheme to detect macroscopic Klein tunneling with
spin-orbit coupled Bose-Einstein condensates (BECs). We show that a nonlinear
Dirac equation with tunable parameters can be realized with such BECs. %in a
simple configuration to generate the artificial spin-orbit coupling. Through
numerical calculations, we demonstrate that macroscopic Klein tunneling can be
clearly detected under realistic conditions. Macroscopic quantum coherence in
such relativistic tunneling is clarified and a BEC with a negative energy is
shown to be able to transmit transparently through a wide Gaussian potential
barrier.
