Lower- versus higher-order nonclassicalities for a coherent superposed quantum state

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 $(ta+r{a}^{†})$ of field annihilation and creation operators acting on a continuous variable coherent state $\mathrm{\mid }\alpha ⟩$ and specify it by $\mathrm{\mid }\psi ⟩$. We analyze the lower- as well as the higher-order nonclassical properties of $\mathrm{\mid }\psi ⟩$. 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.