Photoelectron signature of dressed-atom stabilization in intense XUV field

Non-perturbative resonant multiphoton ionization $(1+1)$ is studied using the resolvent operator technique. Scaling parameters for effective two-level Hamiltonians are computed for hydrogen and helium atoms to provide a quantitative description of Rabi oscillations at XUV wavelengths, which were recently observed using a seeded Free-Electron Laser [S. Nandi et al., Nature 608, 488-493 (2022)]. The resulting photoelectron spectra exhibit a range of Autler-Townes doublets, which are studied for different intensities, detunings and interaction times. We identify a photoelectron signature that originates from stabilization against ionization of helium atoms interacting with intense circularly polarized XUV light. Thus, our work shows how it is possible to test the prediction of dressed-atom stabilization by Beers and Armstrong [B. L. Beers and L. Armstrong, Phys. Rev. A 12, 2447 (1975)], without the demanding requirement of atomic saturation in the time domain.Comment: 14 pages, 6 figures, 3 tables; accepted versio

Frustrated tunneling dynamics in ultrashort laser pulses

We study a model for frustrated tunneling ionization using ultrashort laser pulses. The model is based on the strong field approximation and it employs the saddle point approximation to predict quasiclassical trajectories that are captured on Rydberg states. We present a classification of the saddle-point solutions and explore their behavior as functions of angular momentum of the final state, as well as the carrier--envelope phase (CEP) of the laser pulse. We compare the final state population computed by the model to results obtained by numerical propagation of the time-dependent Schr\"odinger equation (TDSE) for the hydrogen atom. While we find qualitative agreement in the CEP dependence of the populations in principal quantum numbers, $n$, the populations to individual angular momentum channels, $\ell$, are found to be inconsistent between model and TDSE. Thus, our results show that improvements of the quasiclassical trajectories are in order for a quantitative model of frustrated tunneling ionizaiton

The maximality principle in singular control with absorption and its applications to the dividend problem

Motivated by a formulation of the classical dividend problem, we develop the maximality principle for singular stochastic control problems with 2-dimensional degenerate dynamics and absorption along the diagonal of the state space. This result is new in the theory of singular control and it unveils deep connections to Peskir's maximality principle in optimal stopping (Ann. Probab. 26, no. 4, 1998). We construct an optimal control as a Skorokhod reflection along a moving barrier. The barrier can be computed analytically as the smallest solution to a certain non-linear ordinary differential equation. Contrarily to the classical 1-dimensional formulation of the dividend problem our framework produces a non-trivial solution when the firm's capital evolves as a geometric Brownian motion. Such solution is also qualitatively different from the one traditionally obtained for the arithmetic Brownian motion.Comment: 23 pages, 3 figures, revised presentation, new section numbering, updated figures, added reference