  The technique of shortcuts to adiabaticity (STA) has attracted broad
attention due to their possible applications in quantum information processing
and quantum control. However, most studies published so far have been only
focused on Hermitian systems under the rotating-wave approximation (RWA). In
this paper, we propose a modified STA technique to realize population transfer
for a non-Hermitian system without RWA. We work out an exact expression for the
control function and present examples consisting of two- and three-level
systems with decay to show the theory. The results suggest that the STA
technique presented here is robust for fast passages. We also find that the
decay has small effect on the population transfer in the three-level system. To
shed more light on the physics behind this result, we reduce the quantum
three-level system to an effective two-level one with large detunings. The STA
technique of effective two-level system is studied. Thereby the high-fidelity
population transfer can be implemented in non-Hermitian systems by our method,
and it works even without RWA.
