Low-cost ultrafast eigenstate transition without undergoing an adiabatic process

We introduce a class of non-Hermitian Hamiltonians that offers a dynamical approach to have complete population transfer from the ground state of a system to the ground state of a new system in no time. In particular, in our proposed 2×2 Hamiltonians, one eigenvalue is absolutely real and the other one is complex. This specific form of the eigenvalues helps us to exponentially amplify or decay the population
in an undesired eigenfunction while keeping the probability amplitude in the other eigenfunction conserved. This provides us with a powerful method to have a diabatic process with the same outcome as its corresponding adiabatic process. In contrast to standard shortcuts to adiabaticity, our Hamiltonian has a much simpler form with a lower thermodynamic cost. Our proposed Hamiltonians not only have
application in rapid population transfer but also can be used for tunable mode selection and filtering in acoustics, electronics, and optics.