Effect of dephasing on superadiabatic three-level quantum driving

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.

Figure 1

Three-level $\Lambda$ system driven by two coherent fields, a pump(Stokes) beam with Rabi frequency ${\Omega }_{p\left(s\right)}$. The two fields have the same detuning $\Delta$.

Figure 2

Maximum fidelity as a function of dephasing rate ${\Gamma }_0$ for $\tau =0.5$. The damping rate of the excited state is $\Gamma =0$ for the solid line and $\Gamma =10$ for the dashed line. All parameters are scaled with respect to the width of the pulses $T$.

Figure 3

Fidelity as function of $\Omega$ and the area of the additional pulse for transitionless Gaussian pulses for $\tau =0.5,{\Gamma }_{=}1$, and dephasing rate ${\Gamma }_0=0.002$.