We demonstrate that the maximum coherent superposition state can be selectively prepared using a sequence of pulse pairs in lambda-type atomic systems, with the final level as a doublet. In each pair, the Stocks pulse comes before the pump pulse, with their back edges overlapping. Numerical results indicate that by tuning the interval of the adjacent pulse pairs, the selective maximum coherent superposition state preparation between the initial and one of the final levels can be achieved. The phenomenon is caused by the accumulative property of the pulse sequence.OCIS codes: 270.1670, 270.6620, 320.7110. doi: 10.3788/COL201109.112701. The coherent superposition state in atoms or molecules plays a crucial role in quantum physics. It has applications in many areas such as electromagnetically induced transparency [1−5] , quantum information [6−8] , and control of chemical reaction [9−11] . Many schemes can prepare the coherent superposition state. For instance, the fractional stimulated Raman adiabatic passage(F-STIRAP) [12] and the coherent population trapping [13] can obtain the maximum coherent superposition state of the two lower levels in lambda-type atoms. Our group also proposed several schemes to achieve this goal, such as the methods based on the STIRAP [14,15] and the pulse train method [16] . Currently, many quantum control schemes prefer employing pulse sequence or pulse train. For example, the direct optical excitation, rapid adiabatic passage, and STIRAP can extend to the multi-level case if the pulse train is adopted [17−19] . When the repetition period of the pulse train is smaller than the decay of the upper levels, it will possess the accumulative property of population and coherence [16,20] . This property has already been investigated by many researchers [21−25] . In lambda-type atomic configurations, if the final level is a doublet, and the pulse couples the two levels with the upper level at the same time, preparing the coherent superposition state between the initial and one of the final levels using the methods mentioned above seems difficult. Here, taking advantage of the accumulative property of the pulse train and based on the method of F-STIRAP, we propose that the selective preparation of the maximum coherent superposition state can be obtained using a sequence of pulse pairs. In this proposal, each pair has a similar pulse order with the F-STIRAP scheme. The Stocks pulse comes first and is followed after a certain time delay by the pump pulse. However, the back edges of the two pulses overlap. Numerical calculations show that an appropriate choice in the interval between the neighboring pulse pair can make the initial and one of the final levels go into the maximum coherent superposition state. The number of pulse pairs is not strictly required, but few pulse pairs are preferred to reduce the population loss through the upper level.Considering the atomic configuration shown in Fig. 1, the final two levels are closely spaced with each other. The Stocks pulse couples the two tra...