Abstract

Phase optimized states yield a minimum of ${\left(\Delta \varphi \right)}^2=〈{\widehat{\varphi }}^2〉-{〈\widehat{\varphi }〉}^2(\widehat{\varphi }$ is the hermitian phase operator) under the assumption of a fixed mean photon number N. Note that (Δϕ)2 need not to be identical to the half width of the phase probability distribution. The corresponding variational problem was first formulated in Ref. ¹and solved in different ways in Ref. ²and Ref. ³. For not too small N the minimum phase uncertainty is and it requires a photon number variance of (Δn)²=(1/5)(N+1)².

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