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Single-level reformulations of (non-convex) distributionally robust optimization (DRO) problems are often intractable, as they contain semiinfinite dual constraints. Based on such a semiinfinite reformulation, we present a safe approximation, that allows for the computation of feasible solutions for DROs that depend on nonconvex multivariate simple functions. Moreover, the approximation allows to address ambiguity sets that can incorporate information on moments as well as confidence sets. The typical strong assumptions on the structure of the underlying constraints, such as convexity in the decisions or concavity in the uncertainty found in the literature were, at least in part, recently overcome in [9]. We start from the duality-based reformulation approach in [9] that can be applied for DRO constraints based on simple functions that are univariate in the uncertainty parameters. We significantly extend their approach to multivariate simple functions which leads to a considerably wider applicability of the proposed reformulation approach. In order to achieve algorithmic tractability, the presented safe approximation is then realized by a discretized counterpart for the semiinfinite dual constraints. The approximation leads to a computationally tractable mixed-integer positive semidefinite problem for which state-of-the-art software implementations are readily available. The tractable safe approximation provides sufficient conditions for distributional robustness of the original problem, i.e., obtained solutions are provably robust., Comment: 18 pages. arXiv admin note: substantial text overlap with arXiv:2301.11185

In this work, we propose a robust optimization approach to mitigate the impact of uncertainties in particle precipitation. Our model incorporates partial differential equations, more particular nonlinear and nonlocal population balance equations to describe particle synthesis. The goal of the optimization problem is to design products with desired size distributions. Recognizing the impact of uncertainties, we extend the model to hedge against them. We emphasize the importance of robust protection to ensure the production of high-quality particles. To solve the resulting robust problem, we enhance a novel adaptive bundle framework for nonlinear robust optimization that integrates the exact method of moments approach for solving the population balance equations. Computational experiments performed with the integrated algorithm focus on uncertainties in the total mass of the system as it greatly influence the quality of the resulting product. Using realistic parameter values for quantum dot synthesis, we demonstrate the efficiency of our integrated algorithm. Furthermore, we find that the unprotected process fails to achieve the desired particle characteristics, even for small uncertainties, which highlights the necessity of the robust process. The latter consistently outperforms the unprotected process in quality of the obtained product, in particular in perturbed scenarios.

Solids exposed to intense electric fields release electrons through tunnelling. This fundamental quantum process lies at the heart of various applications, ranging from high brightness electron sources in DC operation to petahertz vacuum electronics in laser-driven operation. In the latter process, the electron wavepacket undergoes semiclassical dynamics in the strong oscillating laser field, similar to strong-field and attosecond physics in the gas phase. There, the sub-cycle electron dynamics has been determined with a stunning precision of tens of attoseconds, but at solids the quantum dynamics including the emission time window has so far not been measured. Here we show that two-colour modulation spectroscopy of backscattering electrons uncovers the sub-optical-cycle strong-field emission dynamics from nanostructures, with attosecond precision. In our experiment, photoelectron spectra of electrons emitted from a sharp metallic tip are measured as function of the relative phase between the two colours. Projecting the solution of the time-dependent Schr\"odinger equation onto classical trajectories relates phase-dependent signatures in the spectra to the emission dynamics and yield an emission duration of $710\pm30$ attoseconds by matching the quantum model to the experiment. Our results open the door to the quantitative timing and precise active control of strong-field photoemission in solid state and other systems and have direct ramifications for diverse fields such as ultrafast electron sources, quantum degeneracy studies and sub-Poissonian electron beams, nanoplasmonics and petahertz electronics.

In this work, we present algorithmically tractable safe approximations of distributionally robust optimization (DRO) problems. The considered ambiguity sets can exploit information on moments as well as confidence sets. Typically, reformulation approaches using duality theory need to make strong assumptions on the structure of the underlying constraints, such as convexity in the decisions or concavity in the uncertainty. In contrast, here we present a duality-based reformulation approach for DRO problems, where the objective of the adverserial is allowed to depend on univariate indicator functions. This renders the problem nonlinear and nonconvex. In order to be able to reformulate the semiinfinite constraints nevertheless, an exact reformulation is presented that is approximated by a discretized counterpart. The approximation is realized as a mixed-integer linear problem that yields sufficient conditions for distributional robustness of the original problem. Furthermore, it is proven that with increasingly fine discretizations, the discretized reformulation converges to the original distributionally robust problem. The approach is made concrete for a challenging, fundamental task in particle separation that appears in material design. Computational results for realistic settings show that the safe approximation yields robust solutions of high-quality and can be computed within short time., Comment: 28 pages, 7 figures

When two-color femtosecond laser pulses interact with matter, electrons can be emitted through various multiphoton excitation pathways. Quantum interference between these pathways gives rise to a strong oscillation of the photoemitted electron current, experimentally characterized by its visibility. In this work, we demonstrate two-color visibility spectroscopy of multi-photon photoemission from a solid-state nanoemitter. We investigate the quantum pathway interference visibility over an almost octave-spanning wavelength range of the fundamental femtosecond laser pulses and their second-harmonic. The photoemission shows a high visibility of 90% +/- 5%, with a remarkably constant distribution. Furthermore, by varying the relative intensity ratio of the two colors, we find that we can vary the visibility between 0 and close to 100%. A simple but highly insightful theoretical model allows us to explain all observations, with excellent quantitative agreements. We expect this work to be universal to all kinds of photo-driven quantum interference, including quantum control in physics, chemistry and quantum engineering.

We demonstrate coherent control of photoemission from a gold needle tip using a two-color laser field. The relative phase between a fundamental field and its second harmonic imprints a strong modulation on the emitted photocurrent with up to 96.5 % contrast. The contrast as a function of the second harmonic intensity can be described by three interfering quantum pathways. Increasing the bias voltage applied to the tip reduces the maximum achievable contrast and modifies the weights of the involved pathways. Simulations based on the time-dependent Schr\"odinger equation reproduce the characteristic cooperative signal and its dependence on the second harmonic intensity, which further confirms the involvement of three emission pathways.

We report generation of a femtosecond supercontinuum extending from the ultraviolet to the near-infrared and detection of its carrier-envelope phase variation by f-to-2f interferometry. The spectrum is generated in a gas-filled hollow-core photonic crystal fiber where soliton dynamics allows CEP-stable self-compression of OPCPA pump pulses at 800 nm to a duration of 1.7 optical cycles, followed by dispersive wave emission. The source provides up to 1 {\mu}J of pulse energy at 800 kHz repetition rate resulting in 0.8 W of average power, and can be extremely useful for example in strong-field physics, pump-probe measurements and ultraviolet frequency comb metrology., Comment: 4 pages, 4 figures