Studies on nonlinear coherent states

Nonclassical states of light are of fundamental importance in quantum optic s. The properties of these states are due to the quantal nature of the elec tromagnetic held. In recent years there have been many experimental demonst rations of the realizability of nonclassical states in various physical sch emes such as resonance fluorescence, four-wave mixing, centre-of-mass motio n of a trapped ion and manipulation of field in a cavity. It is of interest to introduce new classes of nonclassical states and investigate their prop erties. In this context, generalization of the concept of coherent states ( CSs) has played a major role. New concepts such as the nonlinear coherent s tates (NCSs) and interference in phase space have emerged from such studies . In this tutorial review we are concerned with the construction of new cla sses of nonclassical states by generalizing the notion of CSs. Our investig ations on the photon-added coherent states (PACSs) indicate that these stat es can be interpreted as NCSs. Also, we introduce a new class of nonclassic al states related to the PACSs. Having introduced a realizable example of N CSs, we extend the notion of even and odd CSs to the case of NCSs by introd ucing even and odd NCSs. With this new definition we interrelate some of th e well known states of light. We suggest a scheme to generate a class of ev en and odd NCSs in the centre-of-mass motion of a trapped, laser-cooled, tw o-level ion.