Laser-driven population transfer in four-level atoms: Consequences of non-Abelian geometrical adiabatic phase factors

We analyze the influence of three pulsed laser fields interacting with a fo ur-state atomic system for which there occur two degenerate population-trap ping dressed states. We present a simple expression for the geometrical pha se acquired by such an atom during a stimulated Pal-nan adiabatic passage ( STIRAP) process using a delay between Stokes and pump pulses, during which the two Rabi frequencies adiabatically traverse a closed path in the parame ter space. We describe: techniques that can produce (geometrical) state-vec tor phases that are independent of the longitudial velocity with which atom s move across a laser beam, and that are insensitive to radiative decay fro m the intermediate excited state. The geometrical phase can be changed by c hanging the relative delay of the pulses. The geometrical phase can be meas ured by observing the population in atomic stares. We show that when the pu mp and Stokes pulses are properly timed, high population transfer from the initial state to the target state is achieved. In the adiabatic limit the r obustness of the population transfer is equivalent to that of STIRAP. [S105 0-2947(99)05104-5].