 Squeezed one-photon state

photon addition to an optical squeezed vacuum gives $a^{†}S|0⟩=\cosh rS|1⟩$; subtraction gives $aS|0⟩=-\sinh rS|1⟩$. After successful-event normalization these are the same state up to phase, with mean occupation $1+3{\sinh }^{2}r$ and odd photon parity. At zero squeezing subtraction never succeeds; the normalized limiting state is not an output at that exact parameter value.