Complex sentence: \\ big\\ where the states\\ big\\ of the field are the states with a definite number n of photons, then the number operator\\ hat counts the "total" number N of quanta in the atom-field system.
Split into simpler sentences: \\ big\\ where the states\\ big\\ of the field are the those with a definite number n of photons. The number operator\\ hat counts the "total" number N of quanta in the atom-field system.