Alternative proposal for the generation of the displaced number state

This work presents an alternative method for the generation of the displaced number state. The usual proposal found in the literature requires the generation of this state from a number state |n〉, which still have not been generated in laboratory and is difficult to obtain, because it demands properties of atom-field interactions in microwave cavities in processes with maximum reduction of quantum noise. Here we show that it is possible to generate the displaced number state from the coherent state, which is easily obtained, by means of the passage of this through a non-linear medium. The coefficients of the displaced number states obtained by our alternative definitions are calculated, showing that it is the same obtained by the usual definition in the literature.