We solve a model with one bound state and two continua.1 Two lasers are used to study the above threshold ionization process. The first laser couples the electron in a bound state to a continuum state. The photons are assumed to be energetic enough to promote the electron directly into the continuum far from the threshold; this avoids complications due to the Rydberg levels and the ponderomotive shifts of the threshold. The second laser mixes the electron wavefunction between two continuum states (C—C transitions); since we avoid the rotating wave approximation, multiple transitions between these continua are allowed. We find that the ionization rate is unaffected by the C—C transitions. Our model of hydrogenic atoms allows redistribution among the continua only during the ionization process and the photoelectron spectra exhibits peak suppression; i.e., the population is not the strongest at the energy of the ionization laser.
An assembly of ground-state two-level atoms with a Maxwellian velocity distribution is considered to be illuminated by a near-resonant train of Gaussian pulses whose pulse separation is of the same order of magnitude as the natural decay time of the upper state by spontaneous emission. The equations of motion of the density matrix, including spontaneous decay, are numerically integrated over the duration of one pulse and are analytically integrated between pulses. In this way, the transition matrix is derived. The time evolution of the system is then followed by successive multiplications of the state vector by the transition matrix. Steady state is attained after a few pulses. Because the pulse train has side bands separated by the pulse repetition frequency, corresponding velocity groups are preferentially excited. The response (defined as the time-average spontaneous emission of the assembly) is found to be a quasi-sinusoidal function of the number of Rabi flops per pulse. Frequency modulation of the pulse train leads to smaller variation in the response and, consequently, to considerably higher response.
Laser excitation of a two-level atom is analytically studied for arbitrary pulse shape, area, and energy. The ionization mechanism is modeled as a homogeneous width $\ensuremath{\gamma}$ of the atomic excited state. A transformation of the optical Bloch equations allows the dynamics to be completely described by a single equation for the area of the pulse at time
t, $\ensuremath{\Phi}(t)$. Analytic solutions for the total bound population for a wide variety of pulse shapes can be found in two regions: $\ensuremath{\Phi}(t)\ensuremath{\approx}sin\ensuremath{\Phi}(t)$ and $\ensuremath{\Omega}(t)>\ensuremath{\gamma}$, where $\ensuremath{\Omega}(t)$ is the resonance Rabi frequency. The generalization of the two-level atom results to the
N-level atom is discussed.
The two-photon resonance ionization probability of atoms in strong extreme-ultraviolet free-electron laser (EUV FEL) pulses has been investigated by the model of time-dependent wave packet propagation of a light-coupled multilevel atom. Under the simulation within the model assuming single-mode FEL pulses, the ionization probability
Pion has shown characteristic dependences on the scaled coupling parameter
Ugi between two levels of the ground (
g) and intermediate (
i) resonance states, namely, ${P}_{\mathrm{ion}}\ensuremath{\propto}{({U}_{gi})}^{n}$, with
n being equal to \ensuremath{\sim}2, less than 1, and \ensuremath{\sim}1 for the small, medium, and large
Ugi regimes, respectively. This power dependence of the ionization probability has been interpreted due to Rabi oscillations between
g and
i states. To compare with recent experimental results on the same condition, the multimode nature of self-amplitude spontaneous emission (SASE) FEL pulses has been managed in the simulation. Then, the recent experimental laser-power dependence of the two-photon resonance ionization of He [Sato et al., J. Phys. B 44, 161001 (2011)] has been well described by that for the large
Ugi regime of the simulation, i.e.,
n \ensuremath{\sim} 1. Thus, the observed linear laser-power dependence has been rationalized as being caused by the strong Rabi oscillations between the (2
p)--(1
s) states.