Shortcuts to adiabatic passage for population transfer and maximum entanglement creation between two atoms in a cavity

We use the approach of ``transitionless quantum driving'' proposed by Berry to construct shortcuts to the population transfer and the creation of maximal entanglement between two $\ensuremath{\Lambda}$-type atoms based on the cavity quantum electronic dynamics system. An effective Hamiltonian is designed by resorting to an auxiliary excited level, a classical driving field, and an extra cavity field mode to supplement or substitute the original reference Hamiltonian, and steer the system evolution along its instantaneous eigenstates in an arbitrarily short time, speeding up the rate of population transfer and creation of maximal entanglement between the two atoms inside a cavity. Numerical simulation demonstrates that our shortcuts are robust against the decoherences caused by atomic spontaneous emission and cavity photon leakage.