Simultaneous electromagnetically induced transparency for two circularly polarized lasers coupled to the same linearly polarized laser in a four-level atomic system in the W scheme

Abstract

Electromagnetic induced transparency (EIT) can be produced in a four-level atomic system in the W scheme using a linearly polarized optical field for simultaneously slowing down two $\ensuremath{\sigma}{}^{+}$ and $\ensuremath{\sigma}{}^{\ensuremath{-}}$ circularly polarized optical fields. This four-level atomic system can be set up with a $|{}^{1}{S}_{0}\ensuremath{\rangle}$ ground state and three Zeeman levels of the $|{}^{1}{P}_{1}\ensuremath{\rangle}$ excited state of any alkali-metal atom placed in a weak magnetic field. We apply our W scheme to ultracold magnesium atoms for neglecting the collisional dephasing. Atomic coherences are reported after solving a density matrix master equation including radiative relaxations from Zeeman states of the $|{}^{1}{P}_{1}\ensuremath{\rangle}$ multiplet to the $|{}^{1}{S}_{0}\ensuremath{\rangle}$ ground state. The EIT feature is analyzed using the transit time between the normal dispersive region and the EIT region. The evolution of the EIT feature with the variation of the coupling field is discussed using an intuitive dressed-state representation. We analyze the sensitivity of an EIT feature to pressure broadening of the excited Zeeman states.