Using the Autler-Townes and ac Stark effects to optically tune the frequency of indistinguishable single-photons from an on-demand source

We describe how a coherent optical drive that is near-resonant with the upper rungs of a three-level ladder system, in conjunction with a short pulse excitation, can be used to provide a frequency-tunable source of on-demand single photons. Using an intuitive master equation model, we identify two distinct regimes of device operation: (i) for a resonant drive, the source operates using the Autler-Townes effect, and (ii) for an off-resonant drive, the source exploits the ac Stark effect. The former regime allows for a large frequency tuning range but coherence suffers from timing jitter effects, while the latter allows for high indistinguishability and efficiency, but with a restricted tuning bandwidth due to high required drive strengths and detunings. We show how both these negative effects can be mitigated by using an optical cavity to increase the collection rate of the desired photons. We apply our general theory to semiconductor quantum dots, which have proven to be excellent single-photon sources, and find that scattering of acoustic phonons leads to excitation-induced dephasing and increased population of the higher energy level which limits the bandwidth of frequency tuning achievable while retaining high indistinguishability. Despite this, for realistic cavity and quantum dot parameters, indistinguishabilities of over $90\%$ are achievable for energy shifts of up to hundreds of $\mu$eV, and near-unity indistinguishabilities for energy shifts up to tens of $\mu$eV. Additionally, we clarify the often-overlooked differences between an idealized Hong-Ou-Mandel two-photon interference experiment and its usual implementation with an unbalanced Mach-Zehnder interferometer, pointing out the subtle differences in the single-photon visibility associated with these different setups.