Coherent Control of Angular Momentum Transfer in Resonant Two-Photon Light-Matter Interaction

We show experimentally and theoretically that a polarization-shaped femtosecond laser pulse with a zero net angular momentum creates a net angular momentum in atomic rubidium during resonant two-photon excitation. The necessary conditions for the creation of a nonzero angular momentum as well as the excitation efficiencies are analyzed in the framework of second-order time-dependent perturbation theory.

Figure 1

(a) The level scheme of rubidium. The spontaneous emission from $6p$ to $5s$ state at 420 nm is measured. (b) The excitation scheme, including $m$ sublevels. The linear polarization is a superposition of circularly polarized components, and quantization axis is the $k$ vector of the laser light. (c) Scheme of the experimental setup. The pulse shaper has a $4f$ geometry. The mirror after the shaper is set close to Brewster’s angle. The fluorescence detection system has a $\lambda /4$ plate, a polarizer, and a PMT with attached narrow-band filter.

Figure 2

(a) Scheme of the change in polarization in the spectrum. In experiment ${\omega }_{\mathrm{step}}$ is scanned. (b) Observed total fluorescence intensity and circular polarization contrast indicate induced angular momentum. (c) The calculations, taking into account spectral resolution of the shaper and experimentally verified reduction in polarization contrast.

Figure 3

(a) Scheme of the change in polarization in the spectrum. The resonant frequency at 776 nm (${\omega }_{fi}$) is blocked. In experiment ${\omega }_{\mathrm{step}}$ is scanned. (b) Observed circular polarization contrast. An extra $\pi /2$ phase shift between orthogonal spectrum parts restores polarization contrast, inducing angular momentum. (c) The calculations, taking into account the spectral resolution of the shaper and experimentally verified reduction in polarization contrast.

Figure 4

(a) Electric field envelope and helicity $\overrightarrow{h}=i[\overrightarrow{E}\times {\overrightarrow{E}}^{*}]/E^2$ of the central part of the excitation pulse for polarization step at 780.2 nm (${\omega }_{ig}$). (b) and (d) Population dynamics of the $5d$ $m=\pm 2$ states and $5p$ $m=\pm 1$ states follow dynamics of the helicity during the pulse. (c) and (e) Angular momentum survives on a long time scale in the $5d$ level and disappears asymptotically in the $5p$ level.