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Number operator-annihilation operator uncertainty as an alternative of the number-phase uncertainty relation
We consider a number operator-annihilation operator uncertainty as a well
behaved alternative to the number-phase uncertainty relation, and examine its
properties. We find a formulation in which the 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 many systems. 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 a reference to a
phase operator. We propose several setups for an experimental verification.Comment: 8 pages including 3 figures, revtex4; v2: typos corrected,
presentation improved; v3: presentation considerably extended; v4: published
versio