In this paper, we have introduced the concept of higher-order atomic d
ipole squeezing (HOADS) and have, as an example, applied it to a quant
um optical model known as Jaynes-Cummings model (JCM) which could gene
rate second-order atomic dipole squeezing (SOADS). We have shown that
the JCM could also generate HOADS when it is restricted to the followi
ng initial condition: the field in a thermal state and the atom in an
appropriate coherent state. We have studied in detail the influence of
initial atomic coherence or thermal photons on HOADS, the important c
onnection of HOADS with SOADS and second-order field squeezing (SOFS),
and the possibility of realization of HOADS in micromaser experiments
with Rydberg atoms in a high-Q cavity.