Effect of a transient light shift on the propagation of an ultrashort pulse in a resonant atomic medium

An ultrashort weak pulse that propagates resonantly on the $\mid a⟩\to \mid b⟩$ transition of a three-level system $(\mid a⟩,\mid b⟩,\mid c⟩)$ experiences reshaping effects on a time scale longer than its duration. When a strong field is applied (nonresonantly) on the $\mid b⟩\to \mid c⟩$ transition, important light shifts are induced. We have theoretically studied the novel behavior of both the medium and weak propagating laser pulses in such conditions. For the transmitted field profile, drastic changes occur: at long times, efficient reduction of the distortion is obtained, while strong oscillations appear for short times, mapping out the dynamical light shift. These shaping effects, which are accompanied by new features in the spectrum for the propagating pulse, are interpreted as the result of the interference between incident field and induced dipole radiated field, whose frequency sweeps in time because of the induced light shift.

Figure 1

(a) Schematic representation of the three-level system in the bare-state picture. (b) The equivalent scheme in the dressed-states picture of the strong driving pulse.

Figure 2

Temporal evolution of the population in the excited states $\mid b⟩$ (solid line) and $\mid c⟩$ (dotted line) for two strengths of the pumping pulse: (a) ${\theta }_2=0$ and (b) ${\theta }_2=60$. We also represent in (a) the envelope of the propagating (dot-dashed curve) and driving (dashed curve) pulses with arbitrary units. See text for the values of the other parameters.

Figure 3

Temporal behavior of the radiated field intensity at the output of the atomic medium for two different strengths of the pumping pulse. The laser and atomic parameters are the same as in Fig. 2.

Figure 4

Solid line: temporal behavior of the transmitted intensity for two different strengths of the pumping pulse. Dotted line: intensity of the incident pulse. The laser and atomic parameters are the same as in Figs. 2, 3. The insets represent the modulus of the Fourier transform of the transmitted field for the corresponding situations.