Single-mode photon number measurement for the squeezed two-mode number state

Based on the fact that a two-mode squeezed number state is a two-variable Hermite polynomial excitation of the two-mode squeezed vacuum state, the result of one-mode l-photon measurement for the two-mode squeezed number state S_2|m,n\rangle is discussed. It is found that a remaining field-mode simultaneously collapses into a number state |n-m+l\rangle with the coefficient being a Jacobi polynomial of n, m and l, which manifestly exhibits the entanglement between the two modes, i.e. it depends on the number-difference between the two modes. The second mode collapses into an excited coherent state when the first mode is measured as a coherent state.