  We discuss a simple and experimentally realizable model for creation of
enhanced Kerr nonlinearities accompanied by vanishing absorption. The model
involves a V-type atom subjected to a strong drive laser, a weak probe laser
and coupled to a single-mode cavity field. Working in the bad-cavity limit, we
find that the simultaneous coupling of the cavity field to both atomic
transitions creates a coherence between the transitions and thus can lead to
quantum interference effects. We investigate the influences of the cavity field
frequency, the cavity field-atom coupling constants and the atomic decay
constants on the linear and the third-order (Kerr) nonlinear susceptibilities.
We predict giant Kerr nonlinearities with vanishing absorption and attribute
this effect to the combination of the Purcell effect and the cavity-induced
quantum interference.
