Abstract
In the present paper, we have studied the higher as well as the lower-order nonclassicalities of photon-added-then-subtracted and photon-subtracted-then-added thermal and even coherent states. Different criteria such as Mandel's function (Q_M^(l)), higher-order antibunching (d_h^(l-1)), sub-Poissonian photon statistics (D_h^(l-1)), higher-order squeezing (S^(l)), Husimi function (Q), Agarwal-Tara criteria (A₃) and Klyshko's condition (B(m)) are used to witness the nonclassical feature of these states. Many of these conditions established that the considered states are highly nonclassical. It is also realized that the non-Gaussian photon-addition-then-subtraction operation is preferred over the photon-subtraction-then-addition for developing nonclassicality.