Photon-emission spectra of theH2+molecular ion in an intense laser field

Photon-emission spectra of the ${\mathrm{H}}_2^{+}$ molecular ion in an intense, linearly polarized laser field (wavelength λ=1064 nm and intensities ${10}^{13}$≤I≤${10}^{14}$ W/${\mathrm{cm}}^2$) have been calculated using an exact method and compared to two-level models. The exact calculation requires solving a three-dimensional time-dependent Schrödinger equation which allows a full treatment of all the electronic states of ${\mathrm{H}}_2^{+}$ as a function of the internuclear separation R. Three separate excitation regions can be defined which are associated with the 1${\mathrm{\sigma }}_{\mathit{g}\mathrm{-}}$1${\mathrm{\sigma }}_{\mathit{u}}$ charge-resonant (CR) transition of the ${\mathrm{H}}_2^{+}$ molecular ion: (1) for small R, the multiphoton excitation region; (2) for intermediate R, the near-resonant excitation region; and (3) for large R, the strong-coupling region. Two- and three-level models are used for the description of these excitations of the CR states. We will show in this work that (a) in the multiphoton excitation region, an approximate solution of the laser-driven CR states is given by WKB solutions of a Mathieu equation; (b) in the near-resonant region, Rabi or Mollow triplets are obtained for all the harmonics; and (c) in the strong-coupling region, an analytic two-level solution for the CR state excitation reproduces well the exact results. The effects of ground-continuum coupling and ionization is shown to be important for laser intensities I≥${10}^{14}$ W/${\mathrm{cm}}^2$.