We theoretically demonstrate the enhanced and dephasing immune squeezing in the resonance fluorescence of a single quantum dot (QD) confined to a pillar-microcavity and driven by a continuous wave laser. We employ a formalism based on Polaron master equation theory for incorporating the influence of exciton-phonon coupling quite accurately in the dot-cavity system. We show a significant enhancement of squeezing due to cavity coupling of the QD as compared to that of an ideal single two-level system in free space. Particularly, we show a four-fold enhancement in squeezing as compared to that of a single QD without cavity coupling. We further demonstrate the persistence of squeezing even when the pure dephasing becomes greater than the radiative decay rate. These novel features are attributed to the cavity-enhanced coherence causing partial reduction of the deteriorating effects of phonon-induced incoherent rates. We also show that the deteriorating effects of phonon-induced incoherent rates on squeezing can be partially circumvented by properly adjusting the detunings.
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