kmos: A lattice kinetic Monte Carlo framework

Kinetic Monte Carlo (kMC) simulations have emerged as a key tool for microkinetic modeling in heterogeneous catalysis and other materials applications. Systems, where site-specificity of all elementary reactions allows a mapping onto a lattice of discrete active sites, can be addressed within the particularly efficient lattice kMC approach. To this end we describe the versatile kmos software package, which offers a most user-friendly implementation, execution, and evaluation of lattice kMC models of arbitrary complexity in one- to three-dimensional lattice systems, involving multiple active sites in periodic or aperiodic arrangements, as well as site-resolved pairwise and higher-order lateral interactions. Conceptually, kmos achieves a maximum runtime performance which is essentially independent of lattice size by generating code for the efficiency-determining local update of available events that is optimized for a defined kMC model. For this model definition and the control of all runtime and evaluation aspects kmos offers a high-level application programming interface. Usage proceeds interactively, via scripts, or a graphical user interface, which visualizes the model geometry, the lattice occupations and rates of selected elementary reactions, while allowing on-the-fly changes of simulation parameters. We demonstrate the performance and scaling of kmos with the application to kMC models for surface catalytic processes, where for given operation conditions (temperature and partial pressures of all reactants) central simulation outcomes are catalytic activity and selectivities, surface composition, and mechanistic insight into the occurrence of individual elementary processes in the reaction network.Comment: 21 pages, 12 figure

Interpretation of the THz-THz-Raman Spectrum of Bromoform

Nonlinear THz-THz-Raman (TTR) liquid spectroscopy offers new possibilities for studying and understanding condensed-phase chemical dynamics. Although TTR spectra carry rich information about the systems under study, the response is encoded in a three-point correlation function comprising of both dipole and polarizability elements. Theoretical methods are necessary for the interpretation of the experimental results. In this work, we study the liquid-phase dynamics of bromoform, a polarizable molecule with a strong TTR response. Previous work based on reduced density matrix (RDM) simulations suggests that unusually large multiquanta dipole matrix elements are needed to understand the measured spectrum of bromoform. Here, we demonstrate that a self-consistent definition of the time coordinates with respect to the reference pulse leads to a simplified experimental spectrum. Furthermore, we analytically derive a parametrization for the RDM model by integrating the dipole and polarizability elements to the 4th order in the normal modes, and we enforce inversion symmetry in the calculations by numerically canceling the components of the response that are even with respect to the field. The resulting analysis eliminates the need to invoke large multiquanta dipole matrix elements to fit the experimental spectrum; instead, the experimental spectrum is recovered using RDM simulations with dipole matrix parameters that are in agreement with independent ab initio calculations. The fundamental interpretation of the TTR signatures in terms of coupled intramolecular vibrational modes remains unchanged from the previous work

Quantum Detector and Process Tomography: Algorithm Design and Optimisation

This thesis develops new algorithms and investigates optimisation in quantum detector tomography (QDT) and quantum process tomography (QPT). QDT is a fundamental technique for calibrating quantum devices and performing quantum engineering tasks. We design optimal probe states based on the minimum upper bound of the mean squared error (UMSE) and the maximum robustness. We establish the lower bounds of the UMSE and the condition number for the probe states, and provide concrete examples that can achieve these lower bounds. In order to enhance the estimation precision, we also propose a two-step adaptive QDT and present a sufficient condition on when the infidelity scales $O(1/{N})$ where $N$ is the number of state copies. We then utilize regularization to improve the QDT accuracy whenever the probe states are informationally complete or informationally incomplete. We discuss different regularization forms and prove the mean squared error scales as $O(1/{N})$ or tends to a constant with $N$ state copies under the static assumption. We also characterize the ideal best regularization for the identifiable parameters. QPT is a critical task for characterizing the dynamics of quantum systems and achieving precise quantum control. We firstly study the identification of time-varying decoherence rates for open quantum systems. We expand the unknown decoherence rates into Fourier series and take the expansion coefficients as optimisation variables. We then convert it into a minimax problem and apply sequential linear programming technique to solve it. For general QPT, we propose a two-stage solution (TSS) for both trace-preserving and non-trace-preserving QPT. Using structure simplification, our algorithm has $O(MLd^2)$ computational complexity where $d$ is the dimension of the quantum system and $M$, $L$ are the type numbers of different input states and measurement operators, respectively. We establish an analytical error upper bound and then design the optimal input states and the optimal measurement operators, which are both based on minimizing the error upper bound and maximizing the robustness characterized by the condition number. A quantum optical experiment test shows that a suitable regularization form can reach a lower mean squared error in QDT and the testing on IBM quantum machine demonstrates the effectiveness of our TSS algorithm for QPT

Ab initio approaches to x-ray cavity QED : From multi-mode theory to nonlinear dynamics of Mössbauer nuclei

In this thesis, a theoretical framework for x-ray cavity QED with Mössbauer nuclei is developed. First, it is shown how Jaynes-Cummings-like few-mode models for open resonators can be derived from first principles, which has been an open question in the quantum optics literature. The resulting ab initio few-mode theory is applied to the x-ray cavity case, generalizing a previous phenomenological model. In addition, a second orthogonal approach is developed to enable the numerically efficient treatment of complex cavity geometries. It is shown that one can thereby directly derive a nuclear ensemble Master equation using Green’s functions to encode the cavity environment. This approach provides an ab initio quantum theory for the system, which resolves previous discrepancies and allows to semianalytically calculate cavity-modified nuclear level schemes without the need for a fitting procedure. On the basis of the two developed theories, multi-mode effects resulting from large losses in leaky resonators are investigated. A general criterion is introduced to identify and classify such multi-mode effects, which demonstrates that they are responsible for previously observed signatures in x-ray cavity experiments and can be harnessed to artificially tune nuclear quantum systems. Further interesting cusp features in nuclear Fano interference trajectories of x-ray cavities with overlapping modes are reported. Finally, the gained insights are employed to investigate nonlinear excitation dynamics of Mössbauer nuclei in the presence of strong x-ray driving fields. The feasibility of inverting nuclear ensembles at upcoming facilities and the possibility of using focused pulses in combination with x-ray cavities for intensity boosting is analyzed