All-optical Raman control of ultracold atomic hyperfine states using pulsed jump protocol

We develop a pulse-driven jump protocol to achieve all-optical Raman control of ultracold atomic hyperfine states. By establishing general conditions for adiabatic evolution between quantum states in parameter space, we derive the essential pulse area and phase conditions necessary for quantum state transfer in a resonant single-$\Lambda$ three-level system. We extend this approach to a double-$\Lambda$ four-level system by incorporating a neighboring intermediate state, which leads to a single-photon detuned $\Lambda$ three-level system. Through numerical simulations of the ultracold $^{87}$Rb atomic system, we demonstrate that high-fidelity and robust control of quantum state transfer can be achieved in the single-$\Lambda$ three-level system using stimulated Raman adiabatic passage (STIRAP) and the pulsed jump protocol. Furthermore, we show that the destructive quantum interference effects between resonant and detuned Raman pathways in the double-$\Lambda$ four-level system can be mitigated by optimizing the pulse area and two-photon detuning parameters within the pulsed jump protocol. This work presents a promising approach for achieving all-optical Raman control of quantum state transfer in ultracold atomic hyperfine states.