Coherent population trapping and electromagnetically induced transparency in multi-Zeeman-sublevel atoms

Abstract

We present a general formalism for studying the interaction between laser fields and degenerate-Zeeman-sublevel atoms correct up to the first order in the weak probe field. We derive from this theory the equations of motion for a \ensuremath{\Lambda}-type system involving ${\mathit{S}}_{1/2}$, F=2\ensuremath{\leftrightarrows}${\mathit{P}}_{1/2}$, F\ensuremath{'}=1\ensuremath{\leftrightarrows}${\mathit{S}}_{1/2}$, F=1 transitions in $^{87}\mathrm{Rb}$ atoms. These equations are used to numerically investigate the coherent population trapping (CPT) schemes in the ${\mathit{S}}_{1/2}$, F=2\ensuremath{\leftrightarrows}${\mathit{P}}_{1/2}$, F\ensuremath{'}=1 transition induced by a linearly polarized pumping field and the electromagnetically induced transparency exhibited in the weak probe spectrum in the ${\mathit{S}}_{1/2}$, F=1\ensuremath{\leftrightarrows}${\mathit{P}}_{1/2}$, F\ensuremath{'}=1 transition. We discuss the effects of the CPT on the probe spectrum with and without the Doppler broadenings by comparing the probe spectrum derived from the real system with that derived from an ideal \ensuremath{\Lambda}-type system. We show that the atoms in the CPT states are shielded from interacting with the probe field while those in the absorbent states make contributions to the weak probe by the Raman anti-Stokes process, and the effect of the real system on the probe field becomes equivalent to the ideal \ensuremath{\Lambda} system only in the strong CPT parameter regime. \textcopyright{} 1996 The American Physical Society.