We study the field-ionization threshold behavior when a Rydberg atom is
ionized by a short single-cycle pulse field. Both hydrogen and sodium atoms are
considered. The required threshold field amplitude is found to scale
\emph{inversely} with the binding energy when the pulse duration becomes
shorter than the classical Rydberg period, and, thus, more weakly bound
electrons require larger fields for ionization. This threshold scaling behavior
is confirmed by both 3D classical trajectory Monte Carlo simulations and
numerically solving the time-dependent Schr\"{o}dinger equation. More
surprisingly, the same scaling behavior in the short pulse limit is also
followed by the ionization thresholds for much lower bound states, including
the hydrogen ground state. An empirical formula is obtained from a simple
model, and the dominant ionization mechanism is identified as a nonzero spatial
displacement of the electron. This displacement ionization should be another
important mechanism beyond the tunneling ionization and the multiphoton
ionization. In addition, an "ionization window" is shown to exist for the
ionization of Rydberg states, which may have potential applications to
selectively modify and control the Rydberg-state population of atoms and
molecules
