Emission and Absorption Spectrum of Pulse-Driven Two-Level Systems in Dynamic Environments

We study the emission spectrum and absorption spectrum of a quantum emitter when it is driven by various pulse sequences. We consider the Uhrig sequence of $\pi_x$ pulses, the periodic sequence of $\pi_x\pi_y$ pulses and the periodic sequence of $\pi_z$ pulses (phase kicks). We find that, similar to the periodic sequence of $\pi_x$ pulses, the Uhrig sequence of $\pi_x$ pulses has emission and absorption that are, with small variations, analogous to those of the resonance fluorescence spectrum. In addition, while the periodic sequence of $\pi_z$ pulses produces a spectrum that is dependent on the detuning between the emitter and the pulse carrier frequency, the Uhrig sequence of nonequidistant $\pi_x$ pulses and the periodic sequence of $\pi_x\pi_y$ pulses have spectra with little dependence on the detuning as long as it stays moderate along with the number of pulses. This implies that they can also, similar to previously studied periodic sequence of $\pi_x$ pulses, be used to tune the emission or absorption of quantum emitters to specific frequencies, to mitigate inhomogeneous broadening and to enhance the production of indistinguishable photons from emitters the solid state.