Number-operator-annihilation-operator uncertainty as an alternative for the number-phase uncertainty relation

Research Institute for Solid State Physics and Optics, Hungarian Academy of Sciences,P.O. Box 49, H-1525 Budapest, Hungary(Dated: June 8, 2010)We consider a number operator-annihilation operator uncertainty as a well behaved alternative tothe number-phase uncertainty relation, and examine its properties. We find a formulation in whichthe bound on the product of uncertainties depends on the expectation value of the particle number.Thus, while the bound is not a constant, it is a quantity that can easily be controlled in manysystems. The uncertainty relation is approximately saturated by number-phase intelligent states.This allows us to define amplitude squeezing, connecting coherent states to Fock states, without areference to a phase operator. We propose several setups for an experimental verification.