The robustness of the three-level transitionless quantum driving proposed by Giannelli and Arimondo [L.Giannelli and E. Arimondo, Phys. Rev. A 89, 033419 (2014)] is investigated. In the case when the excited state is barely populated during the evolution, its decay rate has little effect on the adiabatic population transfer. However, the dephasing which is due to collisions or phase fluctuations of the driving fields will produce a significant effect on the evolution. We found that the dephasing reduces the performance of the population transfer and the fidelity can be far below the quantum computation target even for small dephasing rates.

In this paper we investigate the effect of dephasing on the performance of the quantum rotation gate implemented by adiabatic passage and static laser pulses proposed in Lacour et al (2006 Opt. Commun. 264 362). We show that in an open system, where the three-level lambda system is subjected to dephasing of its ground states, the dephasing will introduce additional dynamic phases which cannot be recompensated as in the closed system. We analyse the evolution of the population by using the quantum jump approach. The results are obtained assuming realistic dephasing rates Γ0 ≪ 1.

Stimulated Raman Adiabatic Passage is an important process for population transfer as well as for implementing quantum gates. This process requires large Rabi frequencies, which is an undesirable in many experimental applications. To overcome this problem transitionless (superadiabatic) STIRAP was proposed. In this paper we study the role of superadiabatic STIRAP in two examples, population transfer and quantum rotation gates. The effect of dephasing was also investigated by computing the fidelity. We have shown that the damping of the excited state has a little effect but the dephasing of the ground state leads to imperfect population transfer and imperfect rotation gates.