Tunneling is one of the most fundamental manifestations of quantum mechanics. For 1D systems, the theoretical description is well established by the Wentzel-Kramers-Brillouin (WKB) method and related approaches [1,2]. However, for higher dimensional systems no such simple description exists. In these systems, typically regular and chaotic motion coexists and in the two-dimensional case regular tori are absolute barriers to the motion. Quantum mechanically, the eigenfunctions either concentrate within the regular islands or in the chaotic sea, as expected from the semiclassical eigenfunction hypothesis [3-5]. These eigenfunctions are coupled by so-called dynamical tunneling  through the dynamically generated barriers in phase space. In particular, this leads to a substantial enhancement of tunneling rates between phase-space regions of regular motion due to the presence of chaotic motion, which was termed chaos-assisted tunneling [7-9]. Such dynamical tunneling processes are ubiquitous in molecular physics and were realized with microwave cavities  and cold atoms in periodically modulated optical lattices [11,12].