Interactive simulations for the learning and teaching of quantum mechanics concepts

Since 2009, we have been developing and evaluating interactive simulations with accompanying activities for the learning and teaching of quantum mechanics concepts at university level. The QuVis simulations build on education research and our lecturing experience, and aim to specifically target student areas of difficulty in quantum mechanics. Simulations are available on a wide range of topics from introductory to advanced level quantum mechanics. This article gives an overview of the three collections of QuVis simulations developed so far. These include simulations for physics students, simulations for physical chemistry students studying introductory quantum mechanics and simulations to support a new introductory quantum mechanics curriculum based on two-level systems. Evaluation with students plays a decisive role in optimizing the educational effectiveness of the simulations and activities. We describe methods used to refine and further develop the resources. We give examples of revisions based on outcomes of individual student observation sessions. 1.Postprin

The memory space: Exploring future uses of Web 2.0 and mobile internet through design interventions.

The QuVis Quantum Mechanics Visualization project aims to address challenges of quantum mechanics instruction through the development of interactive simulations for the learning and teaching of quantum mechanics. In this article, we describe evaluation of simulations focusing on two-level systems developed as part of the Institute of Physics Quantum Physics resources. Simulations are research-based and have been iteratively refined using student feedback in individual observation sessions and in-class trials. We give evidence that these simulations are helping students learn quantum mechanics concepts at both the introductory and advanced undergraduate level, and that students perceive simulations to be beneficial to their learning.Comment: 15 pages, 5 figures, 1 table; accepted for publication in the American Journal of Physic

Investigating student understanding of quantum entanglement

The authors thank the UK Institute of Physics for funding the simulation development.Quantum entanglement is a central concept of quantum theory for multiple particles. Entanglement played an important role in the development of the foundations of the theory and makes possible modern applications in quantum information technology. As part of the QuVis Quantum Mechanics Visualization Project, we developed an interactive simulation Entanglement: The nature of quantum correlations using two-particle entangled spin states. We investigated student understanding of entanglement at the introductory and advanced undergraduate levels by collecting student activity and post-test responses using two versions of the simulation and carrying out a small number of student interviews. Common incorrect ideas found include statements that all entangled states must be maximally entangled (i.e. show perfect correlations or anticorrelations along all common measurement axes), that the spins of particles in a product state must have definite values (cannot be in a superposition state with respect to spin) and difficulty factorizing product states. Outcomes from this work will inform further development of the QuVis Entanglement simulation.Publisher PD

Interactive simulations for quantum key distribution

We thank the UK Institute of Physics and the University of St Andrews for funding the simulation developmentSecure communication protocols are becoming increasingly important, e.g. for internet-based communication. Quantum key distribution (QKD) allows two parties, commonly called Alice and Bob, to generate a secret sequence of 0s and 1s called a key that is only known to themselves. Classically, Alice and Bob could never be certain that their communication was not compromised by a malicious eavesdropper. Quantum mechanics however makes secure communication possible. The fundamental principle of quantum mechanics that taking a measurement perturbs the system (unless the measurement is compatible with the quantum state) also applies to an eavesdropper. Using appropriate protocols to create the key, Alice and Bob can detect the presence of an eavesdropper by errors in their measurements. As part of the QuVis Quantum Mechanics Visualisation Project, we have developed a suite of four interactive simulations that demonstrate the basic principles of three different QKD protocols. The simulations use either polarised photons or spin 1/2 particles as physical realisations. The simulations and accompanying activities are freely available for use online or download, and run on a wide range of devices including tablets and PCs. Evaluation with students over three years was used to refine the simulations and activities. Preliminary studies show that the refined simulations and activities help students learn the basic principles of QKD at both the introductory and advanced undergraduate levels.PostprintPeer reviewe

Characterizing representational learning : a combined simulation and tutorial on perturbation theory

We thank the University of St. Andrews for funding the development of simulations.Analyzing, constructing and translating between graphical, pictorial and mathematical representations of physics ideas and reasoning flexibly through them ("representational competence'') is a key characteristic of expertise in physics but is a challenge for learners to develop. Interactive computer simulations and University of Washington style tutorials both have affordances to support representational learning. This article describes work to characterize students' spontaneous use of representations before and after working with a combined simulation and tutorial on first-order energy corrections in the context of quantum-mechanical time-independent perturbation theory. Data were collected from two institutions using pre-, mid- and post-tests to assess short- and long-term gains. A representational competence level framework was adapted to devise level descriptors for the assessment items. The results indicate an increase in the number of representations used by students and the consistency between them following the combined simulation tutorial. The distributions of representational competence levels suggest a shift from perceptual to semantic use of representations based on their underlying meaning. In terms of activity design, this study illustrates the need to support students in making sense of the representations shown in a simulation and in learning to choose the most appropriate representation for a given task. In terms of characterizing representational abilities, this study illustrates the usefulness of a framework focusing on perceptual, syntactic and semantic use of representations.Publisher PDFPeer reviewe

Optimization Of Simulations And Activities For A New Introductory Quantum Mechanics Curriculum

The Institute of Physics New Quantum Curriculum (quantumphysics.iop.org) consists of online texts and interactive simulations with accompanying activities for an introductory course in quantum mechanics starting from two-level systems. Observation sessions and analysis of homework and survey responses from in-class trials were used to optimize the simulations and activities in terms of clarity, ease-of-use, promoting exploration, sense-making and linking of multiple representations. This work led to revisions of simulations and activities and general design principles which have been incorporated wherever applicable. This article describes the optimization of one of the simulation controls and the refinement of activities to help students make direct connections between multiple representations.Comment: 4 pages, 1 figure; submitted to the Proceedings of the 2013 Physics Education Research Conference. appears in 2013 PERC Proceedings [Portland, OR, July 17-18, 2013], edited by P. V. Engelhardt, A. D. Churukian, and D. L. Jone

A new introductory quantum mechanics curriculum

The Institute of Physics New Quantum Curriculum consists of freely available online learning and teaching materials (quantumphysics.iop.org) for a first course in university quantum mechanics starting from two-level systems. This approach immediately immerses students in inherently quantum mechanical aspects by focusing on experiments that have no classical explanation. It allows from the start a discussion of interpretive aspects of quantum mechanics and quantum information theory. This article gives an overview of the resources available at the IOP website. The core text is presented as around 80 articles co-authored by leading experts that are arranged in themes and can be used flexibly to provide a range of alternative approaches. Many of the articles include interactive simulations with accompanying activities and problem sets that can be explored by students to enhance their understanding. Much of the linear algebra needed for this approach is part of the resource. Solutions to activities are available to instructors. The resources can be used in a variety of ways from supplements to existing courses to a complete programme.Comment: 10 pages, 2 figures, 1 table; submitted to the European Journal of Physic

From single particle to superfuid excitations in a dissipative polariton gas

Using angle-resolved heterodyne four-wave-mixing technique, we probe the low momentum excitation spectrum of a coherent polariton gas. The experimental results are well captured by the Bogoliubov transformation which describes the transition from single particle excitations of a normal fluid to sound-wave-like excitations of a superfluid. In a dense coherent polariton gas, we find all the characteristics of a Bogoliubov transformation, i.e. the positive and negative energy branch with respect to the polariton gas energy at rest, sound-wave-like shapes for the excitations dispersion, intensity and linewidth ratio between the two branches in agreement with the theory. The influence of the non-equilibrium character of the polariton gas is shown by a careful analysis of its dispersion.Comment: 4 pages, 3 figure

2D Fourier Transform Spectroscopy of exciton-polaritons and their interactions

We investigate polariton-polariton interactions in a semiconductor microcavity through two-dimensional Fourier transform (2DFT) spectroscopy. We observe, in addition to the lower-lower and the upper-upper polariton self-interaction, a lower-upper cross-interaction. This appears as separated peaks in the on-diagonal and off-diagonal part of 2DFT spectra. Moreover, we elucidate the role of the polariton dispersion through a fine structure in the 2DFT spectrum. Simulations, based on lower-upper polariton basis Gross-Pitaevskii equations including both self and cross-interactions, result in a 2DFT spectra in qualitative agreement with experiments

Quantum Processes, Systems and Information by Benjamin Schumacher & Michael Westmoreland

Quantum Processes, Systems and Information is a textbook aimed at advanced undergraduate students that brings together more traditional quantum mechanics topics and quantum information theory. The book is novel both in this focus and its presentation of the material. The first five chapters discuss the basics of quantum theory using three isomorphic two-level systems: a photon in a Mach–Zehnder interferometer, a spin ½ particle and a two-level atom. These chapters also develop basic quantum information concepts such as the entropy of a message, interpreting unitary time evolution in terms of information capacity and the difference between distinct and distinguishable states in terms of the basic decoding and distinguishability theorems. The text then continues (chapters 6–9) with two-particle states, including entanglement, hidden variables, the no-cloning theorem, density operators and open systems. The transition to continuous systems, the starting point for many quantum mechanics textbooks, is made only in chapter 10, and the following chapters include standard wave mechanics found in many texts. The final three chapters revert the focus back to quantum information processing