Nonlinear propagation of polarized light pulses in a medium of atoms with degenerate energy levels: Adiabatic approach

We develop a general method allowing one to construct the consistent theory of light pulse propagation through an atomic medium in arbitrary nonlinear regime with respect to the field strength, taking into account the light polarization, temporal (frequency), and spatial dispersions. The method is based on the reduced Maxwell equation, atomic density matrix formalism, and adiabatic approximation. In order to demonstrate the efficiency of our method we investigate in detail the case of propagation of the pulses under conditions of coherent population trapping in a medium of two-level atoms with degenerate energy levels. Equations describing the evolution of various field parameters are derived. It is shown that pulses of ellipticity and spatial orientation of polarization ellipse propagate with slowing. Analytical expressions for the slowing factor are obtained. Previously unknown effects of the stimulated phase modulation and the generation of a phase pilot pulse by the variation of spatial orientation of the polarization ellipse are predicted.

Figure 1

Scheme of light-induced transitions.

Figure 2

Parametrization of the polarization vector e (28).

Figure 3

The degenerate $\Lambda$ system.

Figure 4

Scheme of light-induced transitions for the dark transitions of type $J_g=J\to J_e=J$ ($J$ is integer) with single dark state, which corresponds to the $\Lambda$ chain of Zeeman sublevels (solid line). Particular case: $J_g=2\to J_e=2$.

Figure 5

Slowing factor $m_{\perp }$ as a function of ellipticity angle $\varepsilon$ for the transitions $J_g=J\to J_e=J$ ($J$ is integer).

Figure 6

Scheme of light-induced transitions for the dark transitions of type $J_g=J\to J_e=J-1$ ($J$ is arbitrary) with two dark states, which correspond to the two independent $\Lambda$ chains of Zeeman sublevels (solid and dashed lines). Particular case: $J_g=5/2\to J_e=3/2$.

Figure 7

Slowing factor $m_{\perp }$ as a function of ellipticity angle $\varepsilon$ for the transitions $J_g=J\to J_e=J-1$: $J$ is integer (solid line) and $J$ is half-integer (dashed line).