  If the photon energy is much less than the electron binding energy,
ionization of an atom by a strong optical field is often described in terms of
electron tunneling through the potential barrier resulting from the
superposition of the atomic potential and the potential associated with the
instantaneous electric component of the optical field. In the strict tunneling
regime, the electron response to the optical field is said to be adiabatic, and
nonadiabatic effects are assumed to be negligible. Here, we investigate to what
degree this terminology is consistent with a language based on the so-called
adiabatic representation. This representation is commonly used in various
fields of physics. For electronically bound states, the adiabatic
representation yields discrete potential energy curves that are connected by
nonadiabatic transitions. When applying the adiabatic representation to optical
strong-field ionization, a conceptual challenge is that the eigenstates of the
instantaneous Hamiltonian form a continuum; i.e., there are no discrete
adiabatic states. This difficulty can be overcome by applying an
analytic-continuation technique. In this way, we obtain a rigorous
classification of adiabatic states and a clear characterization of
(non)adiabatic and (non)diabatic ionization dynamics. Moreover, we distinguish
two different regimes within tunneling ionization and explain the dependence of
the ionization probability on the pulse envelope.
