Quantification of dissipation in a multilevel electromagnetically-induced-transparency system

Electromagnetically induced transparency (EIT) in multilevel atomic systems exhibits complex dependencies on optical depth (OD) and polarization configurations, yet their combined effects remain underexplored. Here, we introduce a dissipation factor $\ensuremath{\kappa}$ which quantifies polarization-dependent absorption resulting from the emergence of dissipative channels. Starting from a semiclassical framework, we derive the transmission of a resonant probe as ${T}_{\text{res}}=exp(\ensuremath{-}\ensuremath{\kappa}\ifmmode\cdot\else\textperiodcentered\fi{}d)$, where $d$ denotes the optical depth, demonstrating that $\ensuremath{\kappa}$ and OD jointly govern the transparency. And broadly, $\ensuremath{\kappa}$ is universally applicable across any multilevel system when its value spans a range $\ensuremath{\kappa}\ensuremath{\in}[0,1]$, where $\ensuremath{\kappa}=0$ corresponds to ideal transparency and $\ensuremath{\kappa}=1$ represents pure absorption. Our experimental results in cold $^{87}\mathrm{Rb}$ atomic ensemble across low and high OD regimes confirm the completeness of the theoretical model, with EIT line shapes showing close agreement with simulations. By elucidating the joint effects of OD and polarization-dependent dissipation in EIT, this work is conducive to systemic optimization in multilevel EIT systems such as quantum memory, optical switching, and precision metrology applications.