Coherent control of light shifts in an atomic medium driven by two orthogonally polarized pulses: Effect of the pulse overlap

We consider a duplicated two-level system where each two-level subsystem is driven by a strong resonant femtosecond pulse and a weak resonant femtosecond pulse connects cross transitions. Strong interference effects are induced in such a configuration leading to a modulation of the medium gain as a function of the relative phase between the pulses []. We study here the influence of the temporal overlap between the pulses on the dynamics of the system and the medium gain. We show that the dynamics is dominated by two competing phenomena: Light shifts (LS) induced by the driving pulse that prevails for small delays and free induction decay (FID) that prevails for large delays. LS enhance the medium gain for and reduce it for , whereas FID always leads to a decrease of the medium gain.

Figure 1

(a) Energy levels and optical transitions involved in our system. (b) Adiabatic representation. (c) Polarization configuration. (d) Absorption and emission paths.

Figure 2

Population dynamics ${\rho }_{22}$ (a) and ${\rho }_{2^{\prime }{2}^{\prime }}$ (b) in excited states $\mid 2⟩$ and $\mid 2^{\prime }⟩$, respectively. Curves are obtained by numerical simulations for the set of parameters ${\theta }_1=1.5\pi$, ${\theta }_2=0.01\pi$, $e_{\mathrm{disp}}=0.18$, ${\tau }_0=90\mathrm{fs}$, $\tau =0$, and $\varphi =\pi ∕2$. In gray and black lines are plotted the populations obtained at the entrance and the exit of the sample, respectively.

Figure 3

Temporal behavior of the (a) driving pulse and (b) $\sigma$ pulse. The parameters are those given in Fig. 2. In gray and black lines are plotted the intensity obtained at the entrance and the exit of the sample, respectively.

Figure 4

Normalized transmitted $\sigma$ pulse energy with ${\theta }_2=0.01\pi$, $e_{\mathrm{disp}}=0.18$, and ${\tau }_0=90\mathrm{fs}$ for (a) ${\theta }_1=0.75\pi$ and (b) ${\theta }_1=1.5\pi$. In gray and black lines are plotted the curves obtained for $\varphi =0$ and $\varphi =\pi ∕2$, respectively.

Figure 5

Experimental results. Dependence of the transmitted $\sigma$ pulse energy with the delay for ${\theta }_1\simeq 1.5\pi$. Inset exhibits the rapid variation of the signal ($1.35\mathrm{fs}$ period) due to interferences between absorption and stimulated emission paths. See text for parameter values.

Figure 6

Theoretical curves obtained by numerical simulations for a set of parameters close to the experimental conditions (Fig. 5). We have ${\theta }_2=0.1\pi$, $e_{\mathrm{disp}}=0.18$, ${\tau }_0=90\mathrm{fs}$, and ${\theta }_1=1.5\pi$. In gray and black lines are plotted the curves obtained for $\varphi =0$ and $\varphi =\pi ∕2$, respectively.