Bounds on the spectrum and reducing subspaces of a J-self-adjoint operator

Given a self-adjoint involution J on a Hilbert space H, we consider a J-self-adjoint operator L=A+V on H where A is a possibly unbounded self-adjoint operator commuting with J and V a bounded J-self-adjoint operator anti-commuting with J. We establish optimal estimates on the position of the spectrum of L with respect to the spectrum of A and we obtain norm bounds on the operator angles between maximal uniformly definite reducing subspaces of the unperturbed operator A and the perturbed operator L. All the bounds are given in terms of the norm of V and the distances between pairs of disjoint spectral sets associated with the operator L and/or the operator A. As an example, the quantum harmonic oscillator under a PT-symmetric perturbation is discussed. The sharp norm bounds obtained for the operator angles generalize the celebrated Davis-Kahan trigonometric theorems to the case of J-self-adjoint perturbations.Comment: (http://www.iumj.indiana.edu/IUMJ/FULLTEXT/2010/59/4225

Laser pulses for coherent xuv Raman excitation

We combine multi-channel electronic structure theory with quantum optimal control to derive Raman pulse sequences that coherently populate a valence excited state. For a neon atom, Raman target populations of up to 13% are obtained. Superpositions of the ground and valence Raman states with a controllable relative phase are found to be reachable with up to 4.5% population and phase control facilitated by the pump pulse carrier envelope phase. Our results open a route to creating core-hole excitations in molecules and aggregates that locally address specific atoms and represent the first step towards realization of multidimensional spectroscopy in the xuv and x-ray regimes

Hybrid Optimization Schemes for Quantum Control

Optimal control theory is a powerful tool for solving control problems in quantum mechanics, ranging from the control of chemical reactions to the implementation of gates in a quantum computer. Gradient-based optimization methods are able to find high fidelity controls, but require considerable numerical effort and often yield highly complex solutions. We propose here to employ a two-stage optimization scheme to significantly speed up convergence and achieve simpler controls. The control is initially parametrized using only a few free parameters, such that optimization in this pruned search space can be performed with a simplex method. The result, considered now simply as an arbitrary function on a time grid, is the starting point for further optimization with a gradient-based method that can quickly converge to high fidelities. We illustrate the success of this hybrid technique by optimizing a holonomic phasegate for two superconducting transmon qubits coupled with a shared transmission line resonator, showing that a combination of Nelder-Mead simplex and Krotov's method yields considerably better results than either one of the two methods alone.Comment: 17 pages, 5 figures, 2 table

Charting the circuit QED design landscape using optimal control theory

With recent improvements in coherence times, superconducting transmon qubits have become a promising platform for quantum computing. They can be flexibly engineered over a wide range of parameters, but also require us to identify an efficient operating regime. Using state-of-the-art quantum optimal control techniques, we exhaustively explore the landscape for creation and removal of entanglement over a wide range of design parameters. We identify an optimal operating region outside of the usually considered strongly dispersive regime, where multiple sources of entanglement interfere simultaneously, which we name the quasi-dispersive straddling qutrits (QuaDiSQ) regime. At a chosen point in this region, a universal gate set is realized by applying microwave fields for gate durations of 50 ns, with errors approaching the limit of intrinsic transmon coherence. Our systematic quantum optimal control approach is easily adapted to explore the parameter landscape of other quantum technology platforms.Comment: 13 pages, 5 figures, 2 pages supplementary, 1 supplementary figur

Feedback control optimisation of ESR experiments

Numerically optimised microwave pulses are used to increase excitation efficiency and modulation depth in electron spin resonance experiments performed on a spectrometer equipped with an arbitrary waveform generator. The optimisation procedure is sample-specific and reminiscent of the magnet shimming process used in the early days of nuclear magnetic resonance -- an objective function (for example, echo integral in a spin echo experiment) is defined and optimised numerically as a function of the pulse waveform vector using noise-resilient gradient-free methods. We found that the resulting shaped microwave pulses achieve higher excitation bandwidth and better echo modulation depth than the pulse shapes used as the initial guess. Although the method is theoretically less sophisticated than simulation based quantum optimal control techniques, it has the advantage of being free of the linear response approximation; rapid electron spin relaxation also means that the optimisation takes only a few seconds. This makes the procedure fast, convenient, and easy to use. An important application of this method is at the final stage of the implementation of theoretically designed pulse shapes: compensation of pulse distortions introduced by the instrument. The performance is illustrated using spin echo and out-of-phase electron spin echo envelope modulation experiments. Interface code between Bruker SpinJet arbitrary waveform generator and Matlab is included in versions 2.2 and later of the Spinach library

Robustness of high-fidelity Rydberg gates with single-site addressability

Controlled phase (CPHASE) gates can in principle be realized with trapped neutral atoms by making use of the Rydberg blockade. Achieving the ultra-high fidelities required for quantum computation with such Rydberg gates is however compromised by experimental inaccuracies in pulse amplitudes and timings, as well as by stray fields that cause fluctuations of the Rydberg levels. We report here a comparative study of analytic and numerical pulse sequences for the Rydberg CPHASE gate that specifically examines the robustness of the gate fidelity with respect to such experimental perturbations. Analytical pulse sequences of both simultaneous and stimulated Raman adiabatic passage (STIRAP) are found to be at best moderately robust under these perturbations. In contrast, optimal control theory is seen to allow generation of numerical pulses that are inherently robust within a predefined tolerance window. The resulting numerical pulse shapes display simple modulation patterns and their spectra contain only one additional frequency beyond the basic resonant Rydberg gate frequencies. Pulses of such low complexity should be experimentally feasible, allowing gate fidelities of order 99.90 - 99.99% to be achievable under realistic experimental conditions.Comment: 12 pages, 14 figure

A mountain-induced moist baroclinic wave test case for the dynamical cores of atmospheric general circulation models

Idealized test cases for the dynamical cores of atmospheric general circulation models are informative tools to assess the accuracy of the numerical designs and investigate the general characteristics of atmospheric motions. A new test case is introduced that is built upon a baroclinically unstable base state with an added orographic barrier. The topography is analytically prescribed and acts as a trigger of both baroclinic Rossby waves and inertia–gravity waves on a rotating, regular-sized planet. Both dry and idealized moist configurations are suggested. The latter utilizes the Kessler warm-rain precipitation scheme. The test case enhances the complexity of the existing test suite hierarchy and focuses on the impacts of two midlatitudinal mountain ridges on the circulation. Selected simulation examples from four dynamical cores are shown. These are the Spectral Element and Finite Volume dynamical cores, which are part of the National Center for Atmospheric Research (NCAR) Community Earth System Model (CESM), versions 2.1.3 and 2.2, and the Cubed-Sphere Finite Volume dynamical cores, which is new to CESM version 2.2. In addition, the Model for Prediction Across Scales (MPAS) is tested. The overall flow patterns agree well in the four dynamical cores, but the details can vary greatly. The examples highlight the broad palette of use cases for the test case and reveal physics–dynamics coupling issues.</p

The effects of human-induced pollution on the replenishment of coral reefs

Coral reefs are suffering severe declines world-wide caused by multiple anthropogenic disturbances combined with natural events such as storms. Their future depends on the resilience of replenishment processes. However, few studies exist on the effects of multiple stresses on early life history of corals. This review describes coral early life history processes including reproduction, settlement and post-settlement survival. Relevant literature is then reviewed, focusing on the effects of four major human-induced threats, sedimentation, eutrophication, fishing and rising sea water temperature on reproduction, settlement and post-settlement survival. Research shows that in many cases different stresses affect the same replenishment process. Using two simple models results show that additive and synergistic stress can harm not only the energy budget of a single coral colony, but could also drive a species to extinction. A coral confronted by a disturbance may show a decrease in its energy budget due to either a change in environmental conditions such as reduced light penetration, or increased energy use for defensive mechanisms such as increased sediment rejecting activities. Adding other disturbances may reduce growth and/or reproductive output. If the energy budget decreases even further, processes involved in basal metabolism may suffer and the coral might finally die. Multiple stresses decrease maximum per capita growth of coral populations due to, for example, lower larval survival and decreased settlement success. Coral population extinctions may occur when interacting stresses are combined with Allee effects. Reduced coral densities and reduced reproductive output can lead to decreased fertilisation success. Hence, multiple stresses threaten not only adult corals, but also impact upon replenishment of coral reefs. This is a severe concern and highlights the importance of long-term studies of coral reef recovery and stress mitigation, particularly at a time where threats to reefs are expected to increase further in number, frequency and severity

Gender equality in marine sciences in Kiel, Germany: how project-funded measures can urge institutions to act

In Kiel, in the north of Germany, marine research is rooted in a lively research community hosted mainly at Kiel University and the GEOMAR Helmholtz Centre. While the ratio of women and men is more or less balanced on all qualification levels with mainly nonpermanent junior positions, women are generally underrepresented in leading research positions. The problem of gender imbalance and inequality has been well-known for a long time. Especially in the last decade, however, manifold efforts were initiated to improve gender equality on a political and institutional level as well as within the research community itself. In our article we focus on the gender equality activities of the two large externally funded marine sciences research alliances: the Cluster of Excellence “The Future Ocean” and the Collaborative Research Centre 754 “Climate–Biogeochemistry Interactions in the Tropical Ocean”. For about a decade they offered both financial provisions and a structural framework to tackle the problem of women's underrepresentation in science and came up with innovative measures. In the following case study, we not only introduce the situation of women in marine sciences in Kiel and the structural arrangement to improve gender equality in general, but we also discuss three specific measures developed within the two collaborative research projects in detail: (i) the mentoring program via:mento_ocean for female postdocs, (ii) hiring policies integrating a gender quota for recruiting postdoctoral researchers and (iii) a code of conduct. Based on these best-practice examples we can show that progress towards gender equality has been made despite some obstacles faced when implementing the measures. This was especially the case for attracting female researchers to work in Kiel marine sciences and bringing the relevance of the topic to the surface of debates within the community. Looking at gender equality activities from a managerial point of view, we conclude from the situation in Kiel, where external funding for both research alliances ended in 2019, that even time-bound activities can initiate change. Initiatives developed by the marine sciences community were taken up by other research groups and inspired new activities at the level of the institution