Mixed Quantum-Classical Dynamics in Cavity Quantum Electrodynamics

Considering the ultimate limit of molecules interacting with a few photons, the classical description of the electromagnetic field does not suffice anymore and the quantum nature of light needs to be taken into account. Moreover, to describe chemical processes mediated by quantum light, an accurate, flexible and computationally efficient treatment of light-matter interactions is required. Therefore the present work focuses on the theoretical approaches of light-matter interaction in cavity quantum electrodynamics. In particular, we investigate the extension of mixed-quantum classical trajectory methods as well as the concept of time-dependent potential energy surfaces, both traditionally introduced for electron-nuclear problems, to the photonic degrees of freedom. The goal is to pave the way for a full ab initio and computationally feasible description of quantum effects in strongly correlated light-matter systems. We find, that classical Wigner dynamics for photons can be used to describe quantum effects such as spontaneous emission, correlation functions, bound photon states and cavity-induced suppression of proton-coupled electron transfer by properly accounting for the quantum statistics of the vacuum field while using classical/semi-classical trajectories to describe the time-evolution. Additionally, this classical Wigner treatment for the photons allows us to go beyond the usual single-mode picture, and to include the many photon modes supported in most realistic cavities, in a numerically efficient way. Here, we find that as more photon modes are included, cavity-modified phenomena can significantly change and the self-polarization, which is often neglected, has an increasingly crucial impact on the dynamics and even more so presents a potential new tool to control and change chemical reactions. To this end, we introduce the concept of self-polarization-modified Born-Oppenheimer surfaces as an instructive tool for analysis. Furthermore, in order to gain a fundamental understanding of the dynamics obtained by the mixed-quantum classical methods, we investigate the time-dependent potential energy surfaces within the exact factorization framework. Here we find on the one hand that the corresponding time-dependent potential energy surfaces for photons show significant differences to the harmonic potentials used in conventional approaches. On the other hand, analyzing the time-dependent potential energy surface driving the proton motion of a cavity-induced chemical suppression, we show how its features directly correlate to the proton dynamics, in contrast to the polaritonic surfaces. Particularly, within the mixed-quantum classical methods for photons we identify a promising route towards describing quantum effects in realistic correlated light-matter systems. Especially, combining the introduced methods with an existing ab initio electronic structure methods such as time-dependent density functional theory would provide an ab initio computationally feasible way to simulate photon-field fluctuations and correlations in realistic three-dimensional systems.Zur Analyse der Wechselwirkung von Molekülen mit nur wenigen Photonen, ist die klassische Beschreibung des elektromagnetischen Feldes unzureichend und die Quanteneigenschaften des Lichts müssen berücksichtigt werden. Darüber hinaus erfordert die Simulaton chemischer Prozesse mit starker Quantenlicht- Wechselwirkung eine genaue, flexible und rechnerisch effiziente Beschreibung von Licht-Materie-Wechselwirkung. Die vorliegende Arbeit untersucht daher Theorien der Licht-Matrie-Wechselwirkung für Resonatorquantenelektrodynamik an der Schnittstelle von Quantenoptik und Quantenchemie. Insbesondere betrachten wir die Erweiterung der gemischt quanten-klassischen Trajektorienmethoden, sowie das Konzept der zeitabhängigen Potentialenergieflächen, beides ursprünglich für Elektron-Kern Systeme entwickelt, auf die photonischen Freiheitsgrade. Wir stellen fest, dass die klassische Wigner-Dynamik für Photonen gut geeignet ist, um Quanteneffekte wie spontane Emission, Korrelationsfunktionen, gebundene Photonenzustände und resonatorinduzierte chemische Suppression des Proton-Elektron gekoppelten Ladungstransfers zu beschreiben. Hierbei berücksichtigen wir einerseits die Quantenstatistik des Vakuumfeldes und verwenden andererseits klassische/semi-klassische Trajektorien zur Beschreibung der Zeitevolution. Geht man außerdem über die üblicherweise verwendete Kopplung zu nur einer Photonenmode hinaus, verändern sich die beobachteten resonatormodifizierten Phänomene erheblich und die oft vernachlässigte Selbstpolarisation hat einen immer wichtigeren Einfluss auf die Dynamik und stellt darüber hinaus ein potenzielles neues Werkzeug zur Kontrolle und Veränderung chemischer Reaktionen dar. Zu diesem Zweck stellen wir das Konzept der selbstpolarisationsmodifizierten Born-Oppenheimer-Potentialenergieflächen als instruktives Analysewerkzeug vor. Um ein grundlegendes Verständnis der simulierten Dynamik innerhalb der gemischt quanten-klassischen Trajektorienmethoden zu erhalten, untersuchen wir weiterhin die zeitabhängigen Potentialenergieflächen. Wir stellen fest, dass sich diese für Photonen signifikant von dem üblicherweise verwendeten harmonischen Bild unterscheiden. Darüber hinaus analysieren wir die zeitabhängige Potentialenergiefläche, die die Protonenbewegung einer resonator-induzierten chemischen Suppression des Proton-Elektron gekoppelten Ladungstransfers antreibt, und zeigen wie ihre Charakteristik, im Gegensatz zu polaritonischen Potentialenergieflächen, direkt mit der Protonendynamik zusammenhängen. Wir kommen zu dem Schluss, dass die gemischt quanten-klassischen Methoden für Photonen ein vielversprechender Weg zur Beschreibung von Quanteneffekten in realistischen korrelierten Licht-Materie-Systemen darstellen. Insbesondere die Kombination der vorgestellten Methoden mit einer schon bestehenden ab initio elektronischen Strukturmethode, wie zum Beispiel der zeitabhängigen Dichtefunktionaltheorie, eröffnet die Möglichkeit sowohl Photonenfeldschwankungen als auch Photonkorrelationen in realistischen dreidimensionalen Systemen zu simulieren

Mixed Quantum-Classical Dynamics in Cavity Quantum Electrodynamics

Considering the ultimate limit of molecules interacting with a few photons, the classical description of the electromagnetic field does not suffice anymore and the quantum nature of light needs to be taken into account. Moreover, to describe chemical processes mediated by quantum light, an accurate, flexible and computationally efficient treatment of light-matter interactions is required. Therefore the present work focuses on the theoretical approaches of light-matter interaction in cavity quantum electrodynamics. In particular, we investigate the extension of mixed-quantum classical trajectory methods as well as the concept of time-dependent potential energy surfaces, both traditionally introduced for electron-nuclear problems, to the photonic degrees of freedom. The goal is to pave the way for a full ab initio and computationally feasible description of quantum effects in strongly correlated light-matter systems. We find, that classical Wigner dynamics for photons can be used to describe quantum effects such as spontaneous emission, correlation functions, bound photon states and cavity-induced suppression of proton-coupled electron transfer by properly accounting for the quantum statistics of the vacuum field while using classical/semi-classical trajectories to describe the time-evolution. Additionally, this classical Wigner treatment for the photons allows us to go beyond the usual single-mode picture, and to include the many photon modes supported in most realistic cavities, in a numerically efficient way. Here, we find that as more photon modes are included, cavity-modified phenomena can significantly change and the self-polarization, which is often neglected, has an increasingly crucial impact on the dynamics and even more so presents a potential new tool to control and change chemical reactions. To this end, we introduce the concept of self-polarization-modified Born-Oppenheimer surfaces as an instructive tool for analysis. Furthermore, in order to gain a fundamental understanding of the dynamics obtained by the mixed-quantum classical methods, we investigate the time-dependent potential energy surfaces within the exact factorization framework. Here we find on the one hand that the corresponding time-dependent potential energy surfaces for photons show significant differences to the harmonic potentials used in conventional approaches. On the other hand, analyzing the time-dependent potential energy surface driving the proton motion of a cavity-induced chemical suppression, we show how its features directly correlate to the proton dynamics, in contrast to the polaritonic surfaces. Particularly, within the mixed-quantum classical methods for photons we identify a promising route towards describing quantum effects in realistic correlated light-matter systems. Especially, combining the introduced methods with an existing ab initio electronic structure methods such as time-dependent density functional theory would provide an ab initio computationally feasible way to simulate photon-field fluctuations and correlations in realistic three-dimensional systems.Zur Analyse der Wechselwirkung von Molekülen mit nur wenigen Photonen, ist die klassische Beschreibung des elektromagnetischen Feldes unzureichend und die Quanteneigenschaften des Lichts müssen berücksichtigt werden. Darüber hinaus erfordert die Simulaton chemischer Prozesse mit starker Quantenlicht- Wechselwirkung eine genaue, flexible und rechnerisch effiziente Beschreibung von Licht-Materie-Wechselwirkung. Die vorliegende Arbeit untersucht daher Theorien der Licht-Matrie-Wechselwirkung für Resonatorquantenelektrodynamik an der Schnittstelle von Quantenoptik und Quantenchemie. Insbesondere betrachten wir die Erweiterung der gemischt quanten-klassischen Trajektorienmethoden, sowie das Konzept der zeitabhängigen Potentialenergieflächen, beides ursprünglich für Elektron-Kern Systeme entwickelt, auf die photonischen Freiheitsgrade. Wir stellen fest, dass die klassische Wigner-Dynamik für Photonen gut geeignet ist, um Quanteneffekte wie spontane Emission, Korrelationsfunktionen, gebundene Photonenzustände und resonatorinduzierte chemische Suppression des Proton-Elektron gekoppelten Ladungstransfers zu beschreiben. Hierbei berücksichtigen wir einerseits die Quantenstatistik des Vakuumfeldes und verwenden andererseits klassische/semi-klassische Trajektorien zur Beschreibung der Zeitevolution. Geht man außerdem über die üblicherweise verwendete Kopplung zu nur einer Photonenmode hinaus, verändern sich die beobachteten resonatormodifizierten Phänomene erheblich und die oft vernachlässigte Selbstpolarisation hat einen immer wichtigeren Einfluss auf die Dynamik und stellt darüber hinaus ein potenzielles neues Werkzeug zur Kontrolle und Veränderung chemischer Reaktionen dar. Zu diesem Zweck stellen wir das Konzept der selbstpolarisationsmodifizierten Born-Oppenheimer-Potentialenergieflächen als instruktives Analysewerkzeug vor. Um ein grundlegendes Verständnis der simulierten Dynamik innerhalb der gemischt quanten-klassischen Trajektorienmethoden zu erhalten, untersuchen wir weiterhin die zeitabhängigen Potentialenergieflächen. Wir stellen fest, dass sich diese für Photonen signifikant von dem üblicherweise verwendeten harmonischen Bild unterscheiden. Darüber hinaus analysieren wir die zeitabhängige Potentialenergiefläche, die die Protonenbewegung einer resonator-induzierten chemischen Suppression des Proton-Elektron gekoppelten Ladungstransfers antreibt, und zeigen wie ihre Charakteristik, im Gegensatz zu polaritonischen Potentialenergieflächen, direkt mit der Protonendynamik zusammenhängen. Wir kommen zu dem Schluss, dass die gemischt quanten-klassischen Methoden für Photonen ein vielversprechender Weg zur Beschreibung von Quanteneffekten in realistischen korrelierten Licht-Materie-Systemen darstellen. Insbesondere die Kombination der vorgestellten Methoden mit einer schon bestehenden ab initio elektronischen Strukturmethode, wie zum Beispiel der zeitabhängigen Dichtefunktionaltheorie, eröffnet die Möglichkeit sowohl Photonenfeldschwankungen als auch Photonkorrelationen in realistischen dreidimensionalen Systemen zu simulieren

Conjugate priors for Bayesian object tracking

Object tracking refers to the problem of using noisy sensor measurements to determine the location and characteristics of objects of interest in clutter. Nowadays, object tracking has found applications in numerous research venues as well as application areas, including air traffic control, maritime navigation, remote sensing, intelligent video surveillance, and more recently environmental perception, which is a key enabling technology in autonomous vehicles. This thesis studies conjugate priors for Bayesian object tracking with focus on multi-object tracking (MOT) based on sets of trajectories. Finite Set Statistics provides an elegant Bayesian formulation of MOT in terms of the theory of random finite sets (RFSs). Conjugate priors are also of great interest as they provide families of distributions that are suitable to work with when seeking accurate approximations to the true posterior distributions. Many RFS-based MOT approaches are only concerned with multi-object filtering without attempting to estimate object trajectories. An appealing approach to building tracks is by computing the multi-object densities on sets of trajectories. This leads to the development of trajectory filters, e.g., filters based on Poisson multi-Bernoulli mixture (PMBM) conjugate priors.In this thesis, [Paper A] and [Paper B] consider the problem of point object tracking where an object generates at most one measurement per scan. In [Paper A], it is shown that the trajectory MBM filter is the solution to the MOT problem for standard point object models with multi-Bernoulli birth. In addition, the multi-scan implementations of trajectory PMBM and MBM filters are presented. In [Paper B], a solution for recovering full trajectory information, via the calculation of the posterior of the set of trajectories from a sequence of multi-object filtering densities and the multi-object dynamic model, is presented. [Paper C] and [Paper D] consider the problem of ex- tended object tracking where an object may generate multiple measurements per scan. In [Paper C], the extended object PMBM filter for sets of objects is generalized to sets of trajectories. In [Paper D], a learning-based extended ob- ject tracking algorithm using a hierarchical truncated Gaussian measurement model tailored for automotive radar measurements is presented

Octopus, a computational framework for exploring light-driven phenomena and quantum dynamics in extended and finite systems

Over the last few years, extraordinary advances in experimental and theoretical tools have allowed us to monitor and control matter at short time and atomic scales with a high degree of precision. An appealing and challenging route toward engineering materials with tailored properties is to find ways to design or selectively manipulate materials, especially at the quantum level. To this end, having a state-of-the-art ab initio computer simulation tool that enables a reliable and accurate simulation of light-induced changes in the physical and chemical properties of complex systems is of utmost importance. The first principles real-space-based Octopus project was born with that idea in mind, i.e., to provide a unique framework that allows us to describe non-equilibrium phenomena in molecular complexes, low dimensional materials, and extended systems by accounting for electronic, ionic, and photon quantum mechanical effects within a generalized time-dependent density functional theory. This article aims to present the new features that have been implemented over the last few years, including technical developments related to performance and massive parallelism. We also describe the major theoretical developments to address ultrafast light-driven processes, such as the new theoretical framework of quantum electrodynamics density-functional formalism for the description of novel light-matter hybrid states. Those advances, and others being released soon as part of the Octopus package, will allow the scientific community to simulate and characterize spatial and time-resolved spectroscopies, ultrafast phenomena in molecules and materials, and new emergent states of matter (quantum electrodynamical-materials)

Octopus, a computational framework for exploring light-driven phenomena and quantum dynamics in extended and finite systems

Over the last few years, extraordinary advances in experimental and theoretical tools have allowed us to monitor and control matter at short time and atomic scales with a high degree of precision. An appealing and challenging route toward engineering materials with tailored properties is to find ways to design or selectively manipulate materials, especially at the quantum level. To this end, having a state-of-the-art ab initio computer simulation tool that enables a reliable and accurate simulation of light-induced changes in the physical and chemical properties of complex systems is of utmost importance. The first principles real-space-based Octopus project was born with that idea in mind, i.e., to provide a unique framework that allows us to describe non-equilibrium phenomena in molecular complexes, low dimensional materials, and extended systems by accounting for electronic, ionic, and photon quantum mechanical effects within a generalized time-dependent density functional theory. This article aims to present the new features that have been implemented over the last few years, including technical developments related to performance and massive parallelism. We also describe the major theoretical developments to address ultrafast light-driven processes, such as the new theoretical framework of quantum electrodynamics density-functional formalism for the description of novel light–matter hybrid states. Those advances, and others being released soon as part of the Octopus package, will allow the scientific community to simulate and characterize spatial and time-resolved spectroscopies, ultrafast phenomena in molecules and materials, and new emergent states of matter (quantum electrodynamical-materials).This work was supported by the European Research Council (Grant No. ERC-2015-AdG694097), the Cluster of Excellence “Advanced Imaging of Matter” (AIM), Grupos Consolidados (IT1249-19), and SFB925. The Flatiron Institute is a division of the Simons Foundation. X.A., A.W., and A.C. acknowledge that part of this work was performed under the auspices of the U.S. Department of Energy at Lawrence Livermore National Laboratory under Contract No. DE-AC52-07A27344. J.J.-S. gratefully acknowledges the funding from the European Union Horizon 2020 Research and Innovation Program under the Marie Sklodowska-Curie Grant Agreement No. 795246-StrongLights. J.F. acknowledges financial support from the Deutsche Forschungsgemeinschaft (DFG Forschungsstipendium FL 997/1-1). D.A.S. acknowledges University of California, Merced start-up funding.Peer reviewe

Deep Reinforcement Learning for Robotic Tasks: Manipulation and Sensor Odometry

Research in robotics has frequently focused on artificial intelligence (AI). To increase the effectiveness of the learning process for the robot, numerous studies have been carried out. To be more effective, robots must be able to learn effectively in a shorter amount of time and with fewer resources. It has been established that reinforcement learning (RL) is efficient for aiding a robot's learning. In this dissertation, we proposed and optimized RL algorithms to ensure that our robots learn well. Research into driverless or self-driving automobiles has exploded in the last few years. A precise estimation of the vehicle's motion is crucial for higher levels of autonomous driving functionality. Recent research has been done on the development of sensors to improve the localization accuracy of these vehicles. Recent sensor odometry research suggests that Lidar Monocular Visual Odometry (LIMO) can be beneficial for determining odometry. However, the LIMO algorithm has a considerable number of errors when compared to ground truth, which motivates us to investigate ways to make it far more accurate. We intend to use a Genetic Algorithm (GA) in our dissertation to improve LIMO's performance. Robotic manipulator research has also been popular and has room for development, which piqued our interest. As a result, we researched robotic manipulators and applied GA to Deep Deterministic Policy Gradient (DDPG) and Hindsight Experience Replay (HER) (GA+DDPG+HER). Finally, we kept researching DDPG and created an algorithm named AACHER. AACHER uses HER and many independent instances of actors and critics from the DDPG to increase a robot's learning effectiveness. AACHER is used to evaluate the results in both custom and existing robot environments.In the first part of our research, we discuss the LIMO algorithm, an odometry estimation technique that employs a camera and a Lidar for visual localization by tracking features from their measurements. LIMO can estimate sensor motion via Bundle Adjustment based on reliable keyframes. LIMO employs weights of the vegetative landmarks and semantic labeling to reject outliers. LIMO, like many other odometry estimating methods, has the issue of having a lot of hyperparameters that need to be manually modified in response to dynamic changes in the environment to reduce translational errors. The GA has been proven to be useful in determining near-optimal values of learning hyperparameters. In our study, we present and propose the application of the GA to maximize the performance of LIMO's localization and motion estimates by optimizing its hyperparameters. We test our approach using the well-known KITTI dataset and demonstrate how the GA supports LIMO to lower translation errors in various datasets. Our second contribution includes the use of RL. Robots using RL can select actions based on a reward function. On the other hand, the choice of values for the learning algorithm's hyperparameters could have a big impact on the entire learning process. We used GA to find the hyperparameters for the Deep Deterministic Policy Gradient (DDPG) and Hindsight Experience Replay (HER). We proposed the algorithm GA+DDPG+HER to optimize learning hyperparameters and applied it to the robotic manipulation tasks of FetchReach, FetchSlide, FetchPush, FetchPick\&Place, and DoorOpening. With only a few modifications, our proposed GA+DDPG+HER was also used in the AuboReach environment. Compared to the original algorithm (DDPG+HER), our experiments show that our approach (GA+DDPG+HER) yields noticeably better results and is substantially faster. In the final part of our dissertation, we were motivated to use and improve DDPG. Many simulated continuous control problems have shown promising results for the DDPG, a unique Deep Reinforcement Learning (DRL) technique. DDPG has two parts: Actor learning and Critic learning. The performance of the DDPG technique is therefore relatively sensitive and unstable because actor and critic learning is a considerable contributor to the robot’s total learning. Our dissertation suggests a multi-actor-critic DDPG for reliable actor-critic learning as an improved DDPG to further enhance the performance and stability of DDPG. This multi-actor-critic DDPG is further combined with HER, called AACHER. The average value of numerous actors/critics is used to replace the single actor/critic in the traditional DDPG approach for improved resistance when one actor/critic performs poorly. Numerous independent actors and critics can also learn from the environment in general. In all the actor/critic number combinations that are evaluated, AACHER performs better than DDPG+HER