Nonlinear semi-coherent states, their nonclassical features and phase properties

Semi-coherent states (semi-CSs) were previously introduced and their nonclassical properties studied. In this paper, we first propose a general formalism for the construction of 'nonlinear semi-CSs' as an extension of semi-CSs and then their explicit form in the number state basis is generally deduced. Next, as some physical appearances of the formalism, after choosing two well-known nonlinearity functions, nonclassical features and quantum statistical properties of the associated states are studied by evaluating quadrature squeezing, higher order squeezing and the Mandel parameter, as well as their phase properties and number and phase squeezing of the introduced states. Finally, the results are compared with the properties of semi-CSs. (paper)