Normalization of photon-added and photon-subtracted states
= Normalization of photon-added and photon-subtracted states
Raw vectors $a^\dagger|\psi\rangle$ and $a|\psi\rangle$ have squared norms $\mu+1$ and $\mu$. Matrix elements of the <number operator> in these vectors must be divided by their squared norms before calling them means. For an <optical squeezed vacuum> with mean $s$, the raw moments are $(3s+1)(s+1)$ and $s(3s+1)$, while both normalized means equal $3s+1$ when subtraction is possible.