Chaos-assisted tunnelling in the absence of reflexion symmetry

It has been shown previously that a novel tunnelling behaviour, dubbed chaos-assisted tunnelling, can arise in bound, mixed phase space systems possessing reflection symmetries. As with the usual, direct tunnelling problem of a double well, even a very weak symmetry breaking typically quenches the ability of certain probability densities to tunnel resonantly back and forth. Experiments lacking exact reflexion symmetry will fail to exhibit tunnelling. We show here how chaos-assisted tunnelling can be re-established experimentally and distinguished from direct tunnelling through the variation of two external system parameters, and demonstrate the applicability of a generalized three-level model of the tunnelling process with the coupled quartic oscillators.