The semi-classical model of atom-field interaction has been fully studied for some multilevel atoms, e.g. Vee, L, Cascade X , Y, and inverted Y and so on. This issue is developed into the full-quantum electrodynamics formalism, where the probe and coupling electromagnetic fields are quantized. In this article, we investigate the full-quantum model of absorption and dispersion spectrum of trapped four-levels inverted Y type atoms, interacting with a probe beam of photons as well as two-mode trapped coupling photons. It is shown that the measurement of the maximum of absorption of the probe field and its detuning gives us simply the number of two-mode coupling photons, individually. An experimental setup for this non-demolition photon counting method is proposed and the numbers of coupling photons are obtained analytically.
