  Since the introduction of binomial state as an intermediate state, different
intermediate states have been proposed. Different nonclassical effects have
also been reported in these intermediate states. But till now higher order
antibunching or higher order subpoissonian photon statistics is predicted only
in one type of intermediate state, namely shadowed negative binomial state.
Recently we have shown the existence of higher order antibunching in some
simple nonlinear optical processes to establish that higher order antibunching
is not a rare phenomenon (J. Phys. B 39 (2006) 1137). To establish our earlier
claim further, here we have shown that the higher order antibunching can be
seen in different intermediate states, such as binomial state, reciprocal
binomial state, hypergeometric state, generalized binomial state, negative
binomial state and photon added coherent state. We have studied the possibility
of observing the higher order subpoissonian photon statistics in different
limits of intermediate states. The effect of different control parameters have
also been studied in this connection and it has been shown that the depth of
nonclassicality can be tuned by controlling various physical parameters.
