  Raman process is used for generation of nonclassical states and subsequent
applications due to its simplicity. In view of the experimental feasibility of
the off-resonant Raman process at single photon level useful in long distance
quantum communication and quantum memory, we perform here a detailed study of
possibility of generation of nonclassical states under off-resonance
conditions. Specifically, we have studied nonclassicality in the off-resonant
Raman process with the help of a characteristic function written using more
general solution than the conventional short-time solution under complete
quantum treatment and established the significance of frequency detuning
parameter in generation of nonclassical states. The obtained characteristic
function remains Gaussian and reveals that larger values of frequency detuning
parameters are favorable to induce nonclassicality in some cases. The single-
and two-mode squeezing and antibunching as well as intermodal entanglement are
reported in terms of experimentally accessible quantum noise fluctuations
considering either phonon mode coherent or chaotic. Subsequently, the joint
photon number and integrated intensity distributions are studied to analyze the
performance of pair generation in Stokes-phonon and pump-phonon modes. The
present study discusses the role of resonance conditions in generation of
nonclassical states and establishes that experimentally controllable detuning
parameter can be used to probe and enhance the generated nonclassicality.
