Terrace-like structure in the above-threshold ionization spectrum of an atom in an IR+XUV two-color laser field

Based on the frequency-domain theory, we investigate the above-threshold ionization (ATI) process of an atom in a two-color laser field with infrared (IR) and extreme ultraviolet (XUV) frequencies, where the photon energy of the XUV laser is close to or larger than the atomic ionization threshold. By using the channel analysis, we find that the two laser fields play different roles in an ionization process, where the XUV laser determines the ionization probability by the photon number that the atom absorbs from it, while the IR laser accelerates the ionized electron and hence widens the electron kinetic energy spectrum. As a result, the ATI spectrum presents a terrace-like structure. By using the saddle-point approximation, we obtain a classical formula which can predict the cutoff of each plateau in the terrace-like ATI spectrum. Furthermore, we find that the difference of the heights between two neighboring plateaus in the terrace-like structure of the ATI spectrum increases as the frequency of the XUV laser increases

Data-driven Approximation of Distributionally Robust Chance Constraints using Bayesian Credible Intervals

The non-convexity and intractability of distributionally robust chance constraints make them challenging to cope with. From a data-driven perspective, we propose formulating it as a robust optimization problem to ensure that the distributionally robust chance constraint is satisfied with high probability. To incorporate available data and prior distribution knowledge, we construct ambiguity sets for the distributionally robust chance constraint using Bayesian credible intervals. We establish the congruent relationship between the ambiguity set in Bayesian distributionally robust chance constraints and the uncertainty set in a specific robust optimization. In contrast to most existent uncertainty set construction methods which are only applicable for particular settings, our approach provides a unified framework for constructing uncertainty sets under different marginal distribution assumptions, thus making it more flexible and widely applicable. Additionally, under the concavity assumption, our method provides strong finite sample probability guarantees for optimal solutions. The practicality and effectiveness of our approach are illustrated with numerical experiments on portfolio management and queuing system problems. Overall, our approach offers a promising solution to distributionally robust chance constrained problems and has potential applications in other fields

Pulse-duration dependence of high-order harmonic generation with coherent superposition state

We make a systematic study of high-order harmonic generation (HHG) in a He$^+$-like model ion when the initial states are prepared as a coherent superposition of the ground state and an excited state. It is found that, according to the degree of the ionization of the excited state, the laser intensity can be divided into three regimes in which HHG spectra exhibit different characteristics. The pulse-duration dependence of the HHG spectra in these regimes is studied. We also demonstrate evident advantages of using coherent superposition state to obtain high conversion efficiency. The conversion efficiency can be increased further if ultrashort laser pulses are employed