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The concept of a near superposition [Othman A, Yevick D. Int. J. Theor. Phys. 2018; 57:2293–2308] has recently been introduced as the superposition of two semi-identical states and has, in particular, been realized with coherent states. This paper provides a higher-order generalization of this procedure and, in particular, examines the ‘derivative limit’ for which the phases of all the lower-order states are identical and equal to a particular constant. In the derivative limit, the near coherent state superposition is transformed after successive derivative operations into a high-order Derivative Coherent State (DCS). The DCS is accordingly generated by constructing and subsequently displacing a certain stationary seed state formed by superimposing only even or odd Fock states. The mathematical and statistical properties of the DCS display several behaviours and non-classical features that are pronounced for high-order states. These non-classical properties include the Q-Mandel, higher-order antibunching, linear squeezing, and amplitude squared squeezing.

The characteristics of higher-order derivative coherent states (DCS)