We propose and demonstrate the method of population transfer by piecewise adiabatic passage between two quantum states. Coherent excitation of a two-level system with a train of ultrashort laser pulses is shown to reproduce the effect of an adiabatic passage, conventionally achieved with a single frequency-chirped pulse. By properly adjusting the amplitudes and phases of the pulses in the excitation pulse train, we achieve complete and robust population transfer to the target state. The effect is demonstrated experimentally by observing piecewise excitation of Rubidium atoms from 5s_1/2 to 5p_1/2 electronic state. We show that similarly to the conventional adiabatic passage, the piecewise process is insensitive to the total excitation energy as long as the adiabaticity conditions are satisfied. The piecewise nature of the process suggests that robust and selective population transfer could be implemented in a variety of complex quantum systems beyond the two-level approximation.
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