Speeding up adiabatic passage by adding Lyapunov control

We propose a scheme to speed up adiabatic passage by using Lyapunov control theory. This is a good choice to solve the problem that may emerge in Berry's transitionless quantum driving [M. V. Berry, J. Phys. A 42, 365303 (2009)10.1088/1751-8113/42/36/365303]. That is, the extra couplings in the counterdiabatic driving Hamiltonian can be avoided by choosing the available control Hamiltonian in an actual physical system. As examples, we shorten the evolution time of adiabatic population transfer in a three-level system and the entanglement generation in a cavity quantum electrodynamics system. Moreover, the occupation of an intermediate state can be sharply suppressed by properly choosing the control Hamiltonian in the three-level system. The scheme can also be generalized to a complex system where the exact expressions of adiabatic eigenstates are difficult to obtain.