Entropic uncertainty relations and the number-phase Wigner function for nonlinear and multiphoton coherent states

Abstract

The number-phase entropic uncertainty relation for the multiphoton coherent state (MCS) and nonlinear coherent state (NCS) are studied and compared with an ordinary coherent state (CS). We show that the MCS has higher (lower) number (phase) entropy while the NCS has lower (higher) number (phase) entropy in comparision to the CS. We also discuss the number-phase Wigner function for these states which gives a graphical representation of the complimentary nature of the number and phase properties for these states. With the help of this Wigner representation a photon number cat formation in the NCS is discussed.