  Recently, synthetic spin-orbit coupling has been introduced into cold-atom
systems for more flexible control of the Hamiltonian, which was further made
time-varying through two-photon detuning to achieve dynamic control of the
cold-atom state. While an intraband transition can be adiabatically obtained, a
complete interband transition, rather than a superposition of different bands,
obtained through fast sweeping is usually guaranteed by having the positions of
the initial and final states be far away from any band gap in the quasimomentum
space. Here, by introducing an additional non-Hermitian parameter through an
atom-loss contrast together with two-photon detuning as two controllable
external parameters, both intraband and complete interband transitions can be
achieved independent of the positions of the initial and final states. In
addition, a point-source diagram approach in the 2D external parameter space is
developed to visualize and predict the locations of any nonadiabatic
transitions. This control protocol can have potential applications in quantum
state control and quantum simulations using cold-atom systems.
