Few-photon single ionization of cold rubidium in the over-the-barrier regime

Photoionization of the rubidium (Rb) atoms cooled in a magneto-optical trap, characterized by the coexistence of the ground 5$S_{1/2}$ and the excited 5$P_{3/2}$ states, is investigated experimentally and theoretically with the 400 nm femtosecond laser pulses at intensities of $I=3\times10^9$ W/cm$^2$ - $4.5\times10^{12}$ W/cm$^2$. Recoil-ion momentum distribution (RIMD) of Rb$^+$ exhibits rich ring-like structures and their energies correspond to one-photon ionization of the 5$P_{3/2}$ state, two-photon and three-photon ionizations of the 5$S_{1/2}$ state, respectively. With the increasing of $I$, we find that experimental signals near zero-momentum (NZM) in RIMDs resulted from the 5$P_{3/2}$ state enhance dramatically and its peaked Rb$^+$ momenta dwindle obviously while that from the 5$S_{1/2}$ state is maintained. Meanwhile, the ion-yield ratio of the 5$S_{1/2}$ over the 5$P_{3/2}$ states varies from $I$ to $I^{1.5}$ as $I$ increases. These features indicate a transition from perturbative ionization to strong-perturbative ionization for the 5$P_{3/2}$ state. Numerical simulations by solving the time-dependent Schr\"odinger equation (TDSE) can qualitatively explain the measurements of RIMD, photoion angular distributions, as well as ion-yield ratio. However, some discrepancies still exist, especially for the NZM dip, which could stem from the electron-electron correlation that is neglected in the present TDSE simulations since we have adopted the single-active-electron approximation