Rabi oscillations of Morris-Shore–transformed $N$-state systems by elliptically polarized ultrafast laser pulses

We present an experimental investigation of ultrafast laser-driven Rabi oscillations of atomic rubidium. Because the broadband spectrum of an ultrafast laser pulse simultaneously couples all of the electronic hyperfine transitions between the excited and ground states, the complex excitation linkages involved with the $D_1$ or $D_2$ transition are energy degenerate. By application of the Morris-Shore transformation, this study shows that the considered multistate system is reduced to a set of independent two-state systems and dark states. In experiments performed by ultrafast laser interactions of atomic rubidium in the strong interaction regime, we demonstrate that the ultrafast dynamics of the considered system are governed by no more than two decoupled Rabi oscillations when it interacts with ultrafast laser pulses of any polarization state. We further show the implications of this result with regard to possible control of photoelectron polarizations.

Figure 1

(a) Schematic diagram of the experimental setup. (b) Magneto-optical trapping apparatus for ${}^{85}\mathrm{Rb}$. (c) Energy level diagram of ${}^{85}\mathrm{Rb}$ atoms.

Figure 2

Ultrafast Rabi oscillations of ${}^{85}\mathrm{Rb}$ atoms between $5S_{1/2}$ and $5P_{1/2}$ energy states. Experimental results for ultrafast laser pulses with linear ($\pi$ transition) and circular ($\sigma$ transition) polarization are shown with open blue circles and filled red circles, respectively. Both results are scaled along the vertical axis by the maximal excitation probability of the $\pi$ transition and along the horizontal axis by the $\pi$-transition Rabi oscillation phase (${\mathrm{\Theta }}_{\pi }$). The black dotted lines are the theoretical calculation on the basis of Eq. (18) for the corresponding Rabi oscillations. The new calculations that take into account the spatial average effect are represented by solid lines.

Figure 3

Experimental results (blue circled lines) for $D_1$ transitions with elliptically polarized lights for (a) $\epsilon =0.3$, (b) $\epsilon =0.4$, and (c) $\epsilon =0.45$. Black dotted lines represent the ideal Rabi oscillation curves, and blue solid lines represent their spatially averaged oscillations. (d) Calculated Rabi oscillations for various ellipticities are represented in a two-dimensional plot. (e) Experimental data for the first peak position are shown close up for various ellipticities.

Figure 4

(a) Experimental results for $D_2$ transitions for circular (blue open circles) and linear (red closed circles) polarization. In comparison, theoretical calculations and their spatially averaged results are represented by dotted and solid lines, respectively. (b) Coupling strengths defined in $|J,m_J\rangle$ bases. (c) Schematic comparison between the ionization schemes for $5P_{1/2}$ and $5P_{3/2}$ states.