Phase-dependent interaction in a four-level atomic configuration

We study a four-level atomic scheme interacting with four lasers in a closed-loop configuration with a $\diamond$ (diamond) geometry. We investigate the influence of the laser phases on the steady state. We show that, depending on the phases and the decay characteristic, the system can exhibit a variety of behaviors, including population inversion and complete depletion of an atomic state. We explain the phenomena in terms of multiphoton interference, and compare our results with the phase-dependent phenomena in the double-$\Lambda$ scheme. This investigation may be useful for developing nonlinear optical devices, and for the spectroscopy and laser cooling of alkali-earth atoms.