Reverse engineering of a nonlossy adiabatic Hamiltonian for non-Hermitian systems

We generalize the quantum adiabatic theorem to the non-Hermitian system and build a strict adiabaticity condition to make the adiabatic evolution nonlossy when taking into account the effect of the adiabatic phase. According to the strict adiabaticity condition, the nonadiabatic couplings and the effect of the imaginary part of adiabatic phase should be eliminated as much as possible. Also, the non-Hermitian Hamiltonian reverse-engineering method is proposed for adiabatically driving an artificial quantum state. A concrete two-level system is adopted to show the usefulness of the reverse-engineering method. We obtain the desired target state by adjusting extra rotating magnetic fields at a predefined time. Furthermore, the numerical simulation shows that certain noise and dissipation in the systems are no longer undesirable but play a positive role in the scheme. Therefore, the scheme is quite useful for quantum information processing in some dissipative systems.