  A coherent state is defined conventionally in different ways such as a
displaced vacuum state, an eigenket of annihilation operator or as an infinite
dimensional Poissonian superposition of Fock states. In this work, we describe
a superposition $(ta+ra^\dagger)$ of field annihilation and creation operators
acting on a continuous variable coherent state $|{\alpha}\rangle$ and specify
it by $|\psi\rangle$. We analyze the lower- as well as the higher-order
nonclassical properties of $|\psi\rangle$. The comparison is performed by using
a set of nonclassicality witnesses (e.g., higher-order photon-statistics,
higher-order antibunching, higher-order sub-Poissonian statistics, higher-order
squeezing, Agarwal-Tara parameter, Klyshko's condition and a relatively new
concept, matrix of phase-space distribution). It is found that higher-order
criteria are much more efficient to detect the presence of nonclassicality as
compared to lower-order conditions.
