The turn of the century has brought new perspectives for teaching Quantum Optics. Recent research results provide opportunities to educate specialists in the area with considerable less efforts than in the recent past. Important experiments can now be performed using cheaper optical sources. Full quantum electrodynamics approaches are often simpler to understand, and indeed more comprehensive than the semi-classical ones used before. This correlates well with the fact that it is easier to introduce quantum mechanics using Feynman's many path approach, the root of quantum electrodynamics, instead of the traditional picture based on a set of postulates. A set of cases is presented to demonstrate that full quantization of radiation and matter is not that hard to grasp by physics students with a background in quantum mechanics. The strong motivation achieved is reinforced with a set of medium cost experiments in which matter and radiation are seeing to interact, sometimes in surprising ways. Not to mention the motivating applications and high-technology potential of present quantum optics, the teaching of both introductory and advanced quantum optics can now be performed at the highest level with an effort which, if not less, is comparable with the required when using the semi-classical approach.
The turn of the century has brought new perspectives for teaching Quantum Optics. Recent research results provide opportunities to educate specialists in the area with considerable less efforts than in the recent past. Important experiments can now be performed using cheaper optical sources. Full quantum electrodynamics approaches are often simpler to understand, and indeed more comprehensive than the semi-classical ones used before. This correlates well with the fact that it is easier to introduce quantum mechanics using Feynman's many path approach, the root of quantum electrodynamics, instead of the traditional picture based on a set of postulates. A set of cases is presented to demonstrate that full quantization of radiation and matter is not that hard to grasp by physics students with a background in quantum mechanics. The strong motivation achieved is reinforced with a set of medium cost experiments in which matter and radiation are seeing to interact, sometimes in surprising ways. Not to mention the motivating applications and high-technology potential of present quantum optics, the teaching of both introductory and advanced quantum optics can now be performed at the highest level with an effort which, if not less, is comparable with the required when using the semi-classical approach.
Covering a number of important subjects in quantum optics, this textbook is an excellent introduction for advanced undergraduate and beginning graduate students, familiarizing readers with the basic concepts and formalism as well as the most recent advances. The first part of the textbook covers the semi-classical approach where matter is quantized, but light is not. It describes significant phenomena in quantum optics, including the principles of lasers. The second part is devoted to the full quantum description of light and its interaction with matter, covering topics such as spontaneous emission, and classical and non-classical states of light. An overview of photon entanglement and applications to quantum information is also given. In the third part, non-linear optics and laser cooling of atoms are presented, where using both approaches allows for a comprehensive description. Each chapter describes basic concepts in detail, and more specific concepts and phenomena are presented in 'complements'.
Quantum mechanics (QM) has taken on a paradigmatic role in how physics describes and builds new knowledge about the world. It also has a growing role in our society thanks to recent and rapid developments in the field of new quantum technologies. These are becoming increasingly important in our society, in the world of work and which will also decisively influence future socio-economic choices. Also for this reason QM has an increasing role in the education of young people and has been introduced in many different ways also in secondary school in all continents. The change in the theoretical and cultural frame has profound implications that are often not intuitive, which involve the appropriation of a specific way of thinking. Neither macroscopic phenomenology, nor intuition help, because there is no simple evidence of how quantum objects must be thought to interpret that unobservable microscopic world and for which we must enter another interpretative paradigm even if we want to limit ourselves to describe it. PER has carried out several studies on the learning of key concepts, on the learning nodes, the ways of reasoning, the difficulties of the students, their spontaneous ideas, according to two main strands: above all at university level, conceptual difficulties and misunderstandings often linked to a formal approach, which, moreover, underpins the very nature of the entities involved; at secondary school level in relation to how students acquire a quantum view of phenomena on the basis of specific approaches adopted to address QM. In particular, a vast literature, which has increased considerably and especially in relatively recent times, has studied how university students deal with certain concepts such as that of state, superposition, measurement in quantum mechanics rather than how quantum quantities evolve over time. These studies are based on the use of questionnaires that allow to explore different levels: the verbal, formal and representative one, with different representations (eg. wave function, Dirac notation), rather than different representative modes (eg. Graphs of probability amplitudes, or probability distributions). At the secondary school level, the most important studies on student learning were instead conducted evaluating the educational impact and outlining the learning paths of students who had followed formative activities based on differentiated innovative research-based educational paths. In particular, the learning outcomes were compared to those activated by proposals based on the historical reconstruction approach of quantum physics. This approach is privileged in traditional curricula and school texts and consequently in the ways of teachers approaching the topic. It was developed in schools with a narrative or descriptive dimension of solutions based on old physics of quanta for the interpretation of phenomena not explained by classical physics. The innovative approaches instead make use of contexts whose formal treatment is simple (quantum properties described in a two-state space such as polarization or spin) with the aid of simulations that compensate for the problem of students” limited mathematical-formal skills, avoiding any historical reference. In particular, there is a significant difference between the survey tools and the survey contexts in the high school environment compared to surveys conducted with university students. This paper presents a review of the research literature, focusing in particular on the learning processes of secondary school students and outlining how research perspectives have evolved.
As quantum computers are becoming available for experiments, their enormous potential is being recognized among college communities. The goal of introducing quantum computing in college level computer science programs is becoming attractive. However, this goal comes with opportunities and challenges. of the challenges is that quantum computing appears to require substantial background in physics as well as in computer science. However, it is hard to convince students to major in these two fields. Computer Science students with a minor in physics can also be considered. Several alternative curriculum structures are possible. A non-consecutive two-course framework is proposed here. A course on Introduction to Quantum Computing may be offered to sophomore level students. This introductory course may teach fundamental ideas about quantum computing with basic concepts behind BQP (Bounded Error Quantum Polynomial) and related topics. This introductory course may be followed up by some physics courses (on related topics such as quantum mechanics) and some computer science courses. Then, a senior level course on Advanced Quantum Computing may be offered that may include some well-known algorithms (such as Shor's Algorithm for Quantum Factorization and Grover's Algorithm for Quantum Search) and their implementation and practices on some simulators (such as QuIDE from http://www.quide.eu/) or some prototype quantum processors (such as IBM's prototype quantum processors). For advanced level courses, some course materials are available from various sources (such as MIT OpenCourseWare). The greater challenge would be in teaching the introductory course mentioned earlier that motivates students towards investing time and efforts in learning quantum computing and related physics, math and computational topics. The challenges of teaching the introductory course should not be underestimated. Some flexible strategies can be suggested for this course so that the biggest challenges can be overcome. Some initial assessments of the students may help adjusting the introduction strategies with student's preparation. What is recommended is that the instructor should be able to adjust the coverage of topics, rigor and depth of treatment. That is, the introductory course should not be rigidly defined. It should be recognized that the main emphasis of the introductory course is actually instilling motivations and curiosity in student's mind about potentials of quantum computing through adaptive teaching of some selected topics where traditional digital computers do not provide tractable solutions. Ideally a balance could be achieved among aspects of depth of treatment, rigor, inspiration, motivation and coverage of topics. Students should be able to realize that the emerging quantum computing technology would be able to provide elegant solutions to some of the classical intractable problems combining ideas from physics, math and computer science in an innovative way. One size fits all is not a good approach and discussion of issues may help us face the challenges better by pragmatically considering a range of possible alternatives. Resources that are currently available may also need to be reviewed for the purpose of introducing quantum computing adequately.
`Quantum Mechanics'' is a comprehensive introduction to quantum mechanics for advanced undergraduate students in physics. It provides the reader with a strong conceptual background in the subject, extensive experience with the necessary mathematical background, as well as numerous visualizations of quantum concepts and phenomena. - ;Quantum Mechanics: Classical Results, Modern Systems, and Visualized Examples is a comprehensive introduction to non-relativistic quantum mechanics for advanced undergraduate students in physics and related fields. It provides students with a strong conceptual background in the most important theoretical aspects of quantum mechanics, extensive experience with the mathematical tools required to solve problems, the opportunity to use quantum ideas to confront modern experimental. realizations of quantum systems, and numerous visualizations of quantum concepts and phenomena. Changes from the First Edition include many new discussions of modern quantum systems (such as Bose-Einstein condensates, the quantum Hall effect, and wave packet revivals) all in the context of familiar. textbook level examples. The book continues to emphasize the many connections to classical mechanics and wave physics to help students use their existing intuition to better learn new quantum concepts. -
In this paper, we present an overview of recent developments in the Feynman sum over paths approach for teaching introductory quantum mechanics to high school students and university undergraduates. A turning point in recent research is identified in the clarification of the distinction between the time-dependent and time-independent approaches, and it is shown how the adoption of the latter has allowed new educational reconstructions to proceed much farther beyond what had previously been achieved. It is argued that sum over paths has now reached full maturity as an educational reconstruction of quantum physics and offers several advantages with respect to other approaches in terms of leading students to develop consistent mental models of quantum phenomena, achieving better conceptual understanding and a higher degree of longitudinal integration of knowledge.
One of the key frameworks for developing the theory of light–matter interactions in modern optics and photonics is quantum electrodynamics (QED). Contrasting with semiclassical theory, which depicts electromagnetic radiation as a classical wave, QED representations of quantized light fully embrace the concept of the photon. This tutorial review is a broad guide to cutting-edge applications of QED, providing an outline of its underlying foundation and an examination of its role in photon science. Alongside the full quantum methods, it is shown how significant distinctions can be drawn when compared to semiclassical approaches. Clear advantages in outcome arise in the predictive capacity and physical insights afforded by QED methods, which favors its adoption over other formulations of radiation–matter interaction.