Coherent phase control of resonance-mediated two-photon absorption in rare-earth ions

We theoretically and experimentally demonstrate the quantum coherent control of the resonance-mediated two-photon absorption in rare-earth ions by the phase-shaped femtosecond laser pulse. Our theoretical results show that the resonance-mediated two-photon absorption can be effectively controlled, but the control efficiency depends on the laser repetition rate in real experiment due to the long lifetime and the short decoherence time of the excited state, and the larger laser repetition rate yields the lower control efficiency. These theoretical results are experimentally confirmed in glass sample doped with Er 3 + by utilizing the femtosecond lasers with low repetition rate of 1 kHz and high repetition rate of 80 MHz.