Nonclassical Properties of Superposition of Two Coherent States Shifted in Phase by 3π/2

We consider the quantum superposition of two coherent states shifted in phase by 3π/2, |α> and |-iα>, as well as special states that are characterized solely with respect to amplitude α. According to analysis of nonclassical properties such as oscillatory and sub-Poissonian distribution of photon numbers, photon antibunching, quadrature squeezing, and negativity of Wigner function, it is concluded that the considered superposition state is a nonclassical state. Also, the special state is found to exhibit even stronger onclassical features when relative phase Ф of the superposition is equal to the average photon number |α|².