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

摘要

We consider a number operator-annihilation operator uncertainty as a wellbehaved alternative to the number-phase uncertainty relation, and examine itsproperties. We find a formulation in which the bound on the product ofuncertainties depends on the expectation value of the particle number. Thus,while the bound is not a constant, it is a quantity that can easily becontrolled in many systems. The uncertainty relation is approximately saturatedby number-phase intelligent states. This allows us to define amplitudesqueezing, connecting coherent states to Fock states, without a reference to aphase operator. We propose several setups for an experimental verification.