Laser phase fluctuations in a four-level atomic system in N-configuration

We discuss here the effect of laser phase fluctuations on coherent spectroscopy of four-level N-system interacting with a trichromatic radiation field of frequencies Ω _i , (i = 1?3). The laser phase variables are described by the Wiener-Levy diffusion process to specify the bandwidths (Γ _i ) and cross-correlations (Γ _ij ) that may exist between pairs of laser fields. A general formalism based on the master equation and theory of multiplicative stochastic processes is developed and used to study three-photon and (2+1)-photon absorptive resonances in model N-system of ⁴⁰Ca⁺ ion. It is observed that the resonances are suppressed or broadened by all Γ _i ,(i = 1?3), while their revival is dependent only on Γ ₁₂ and Γ ₂₃, and yet the revival is only partial even when the relevant fields are critically correlated. In contrast Γ ₁₃ is observed to deteriorate the absorptive resonances. The distinctive features of the steady state and time dependent behavior of the system under three-photon and (2 + 1)-photon resonance conditions and for fluctuating fields are discussed.