Nonclassical properties of states generated by the excitations on a coherent state

We introduce states defined by ‖α,m〉=${\mathit{a}}^{\mathrm{°}\mathit{m}}$‖α〉 up to a normalization constant, where ‖α〉 is a coherent state and m an integer. We study the mathematical and physical properties of such states. We demonstrate phase squeezing and the sub-Poissonian character of the fields in such states. We study in detail the quasiprobability distributions and the distribution of the field quadrature. We also show how such states can be produced in nonlinear processes in cavities.