Detuning-dependent narrowing of Mollow triplet lines of driven quantum dots

We study the two-time correlation function and the resonance fluorescence spectrum of a semi-conductor quantum dot excited by a strong off-resonant laser pulse. The obtained analytic expressions exhibit a specific detuning-dependent damping of Rabi oscillations of the dressed quantum dot as well as a detuning-dependent width of Mollow triplet lines. In the absence of pure dephasing, the central peak of the triplet is broadened upon increasing detuning, but the blue- and red-side peaks are narrowed. We demonstrate that the pure dephasing processes can invert these dependences. A crossover between the regimes of detuning-dependent narrowing and broadening of the side and central peaks is identified. The predicted effects are consistent with recent experimental results and numerical calculations.