Single-mode photon number measurement for the squeezed two-mode number state
Xuefen Xu, Zhu Shi-Qun · Chinese Physics B · 2009
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 ⟩ is discussed. It is found that a remaining field-mode simultaneously collapses into a number state | n – m + l ⟩ 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.