January 2025
Volume 93, Issue No. 1
Special Collection: Celebrating the International Year of Quantum Science and Technology
Over the past 100 years, our understanding and use of quantum mechanics have grown substantially. Numerous Nobel Prizes have been awarded for advances in the field, from how atoms are built up from constituents, to how solids conduct electricity, to how strange phase transitions may happen at sufficiently low temperatures, to the very basis of how to measure time to unprecedented accuracy using atoms. Simultaneously, the educational landscape of quantum science and technology has been changing rapidly, and quantum mechanical concepts are being introduced into secondary school curricula and public outreach activities.
In order to celebrate and reflect on the development of quantum mechanics, the United Nations has declared 2025 the International Year of Quantum Science and Technology. In this special issue, we join the celebration, showing how this field is relevant to our lives and especially to modern physics education. We hope to provide inspiration for how to celebrate it in your classrooms. Our contributors shared so many good ideas that we are printing papers from the special collection not only in this issue, but also in the February issue.
EDITORIAL
In this issue: January 2025 In Special Collection: Celebrating the International Year of Quantum Science and Technology by Joanna Behrman; Pierre-François Cohadon; Gina Passante; Daniel Schumayer; Beth Parks. DOI: 10.1119/5.0251764
PAPERS
Quantum mechanics: A historical-linguistic perspective In Special Collection: Celebrating the International Year of Quantum Science and Technology
In Special Collection: Celebrating the International Year of Quantum Science and Technology by Helge Kragh. DOI: 10.1119/5.0202443
Editor's note: Such a specialized field as quantum mechanics naturally uses many specialized terms. Words such as “spin,” “degeneracy,” and “quantum jump,” have come out of a variety of contexts, and some have even taken on new meanings in the general public. This paper discusses the origins and linguistic history of quantum terminology. Readers will especially enjoy learning how certain words came to be the dominant, established, terms in the field. For example, why do we talk about “eigenvalues” today when we could be speaking of “proper values” or “eigenwerts?”
The 1925 revolution of matrix mechanics and how to celebrate it in modern quantum mechanics classes
In Special Collection: Celebrating the International Year of Quantum Science and Technology by J. Tran; L. Doughty; J. K. Freericks. DOI: 10.1119/5.0195658
Editor's Note: The finite spacetime manifold in which outgoing waves reach infinity in a finite spacetime interval was introduced in the 1960s by Roger Penrose. It plays an important role in the analysis of gravitational waves. In this work the author shows how to construct a temporal foliation using spacelike slices with hyperbolic geometry in compactified Minkowski space. Instructors in special relativity will be able to make these ideas accessible to their students, including an application to massless fields in flat spacetime.
A glimpse of matrix mechanics via the harmonic oscillator by Elina Palmgren; Ricardo Karam. DOI: 10.1119/5.0141573
Editor's Note: Introductory quantum mechanics courses typically discuss only the early history of the quantum era, including the experiments that differed from classical predictions, such as black body radiation spectra, and the rough heuristic rules invented to describe these unexpected results, such as the Rydberg formula for atomic emission spectra and Bohr's correspondence principle. This “old quantum theory” built the conceptual foundations that then enabled the development of several complete mathematical formalisms, with matrix mechanics first emerging in 1925, and wave mechanics in 1926. Introductory courses typically skip this history and present only the modern formalism. Here, the arguments of Heisenberg's “magical” 1925 paper that quickly inspired Born and Jordan's matrix mechanics are used to find the energy spectrum of the quantum harmonic oscillator in a presentation appropriate for upper-level undergraduates.
Introducing quantum mechanics with a two-mode Mach–Zehnder interferometer
In Special Collection: Celebrating the International Year of Quantum Science and Technology by Gauthier Rey; Renaud Mathevet; Sébastien Massenot; Benoit Chalopin. DOI: 10.1119/5.0211194
Editor's Note: Recent progress in laser optics, high-speed electronics, and low-noise photon counting has significantly simplified what used to be either thought experiments or state-of-the-art quantum optics experiments. In this paper, the authors take advantage of this progress to present a Mach–Zehnder interferometer operated at the single-photon counting level in order to introduce undergraduate students to quantum concepts, building upon their previous knowledge of wave optics. The simplicity of the Mach–Zehnder configuration allows for an easy introduction to the formalism of quantum states in two-dimensional Hilbert spaces. Anyone teaching introductory quantum mechanics should have a look at this paper, either to perform such experiments or simply to discuss them in class.
Decoherence, entanglement, and information in the electron double-slit experiment with monitoring
In Special Collection: Celebrating the International Year of Quantum Science and Technology by Frederick W. Strauch. DOI: 10.1119/5.0210117
Editor's Note: Richard Feynman famously said of the two-slit experiment that it contained “all of the mystery of quantum mechanics.” While such an experiment has been performed with all kinds of quantum systems over the past century, some of the mystery at the heart of the Einstein–Bohr debates still remains. In this paper, the author revisits the famous argument by Einstein of the movable slits used to monitor the paths of the interfering particles, with a tractable model of path monitoring by Coulomb scattering. This example illustrates the relationship between entanglement and the loss of coherence of the interference fringes. Any physicist with an interest in fundamental quantum mechanics will benefit from this discussion, which has profound consequences in many fields of physics, from photoionization to quantum information.
Teaching quantum formalism and postulates to first-year undergraduates
In Special Collection: Celebrating the International Year of Quantum Science and Technology by Jeremy Levy; Chandralekha Singh. DOI: 10.1119/5.0209945
Editor's Note: This paper provides a carefully designed path for teaching Dirac notation, operators, and the Born rule to introductory physics students. The curriculum includes a series of ten classes with no out-of-class exercises. It could easily be extended to teach further aspects of quantum mechanics. Readers may especially wish to adopt the Bloch Cube that provides a tangible system on which rotations act.
Investigating and improving student understanding of time dependence of expectation values in quantum mechanics using an interactive tutorial on Larmor precession
In Special Collection: Celebrating the International Year of Quantum Science and Technology by Ben Brown; Guangtian Zhu; Chandralekha Singh. DOI: 10.1119/5.0186030
Editor's Note: Students face many challenges when studying quantum mechanics at the first time, including how theory and experiment are related. This article explores how expectation values evolve in time, focusing on the Larmor precession of spin-1/2 systems. This choice of system is ideal for a teaching schedule following a classical, history-based approach or a more recent approach where finite-dimensional spin systems are taught first. The authors have designed activities for students and interesting checks for the teachers. Early tests suggest that the interactive tutorials help students apply quantum mechanical concepts and recall the conclusions long after the activity.
Introductory learning of quantum probability and quantum spin with physical models and observations
In Special Collection: Celebrating the International Year of Quantum Science and Technology by Anastasia Lonshakova; Kyla Adams; David Blair. DOI: 10.1119/5.0211456
Editor's Note: This paper presents a learning sequence for teaching quantum mechanics concepts to 10–15-year-olds, making concepts tangible through tools such as the phasor wheel, which is used to calculate measurement probabilities when multiple paths interfere. Quantum spin is then taught through analogies with tops that can change their orientation or stack and sum together. The curriculum could be used by other instructors at this level, and the manipulatives may be appreciated even by more advanced students.
Simple portable quantum key distribution for science outreach
In Special Collection: Celebrating the International Year of Quantum Science and Technology by Pedro Neto Mendes; Paulo André; Emmanuel Zambrini Cruzeiro. DOI: 10.1119/5.0204077
Editor's note: Quantum cryptography is not only a major application of quantum technologies but also an easy gateway to entanglement and modern quantum mechanics in the classroom. Several protocols based upon the exchange of single photons can easily be demonstrated with faint laser pulses. This paper presents a simple and cost-effective quantum key distribution setup based on the BB84 protocol that can be used for science outreach, in the undergraduate laboratory, or in class demonstrations.
Introducing quantum computing to high school students with Grover's search algorithm
In Special Collection: Celebrating the International Year of Quantum Science and Technology by Mark S. Hannum. DOI: 10.1119/5.0228847
Editor's Note: We are witnessing the second quantum revolution, which exploits the quantum world to perform computation. The paper shows how concepts such as qubits and superposition, along with innovative approaches to quantum computation, can be explored by secondary school students. Grover's algorithm is presented and applied to a classical satisfiability problem. In addition to the theoretical underpinning, practical codes are also provided, which novices can try out on publicly available quantum computers. This set of codes offers an open-ended exploration of this rapidly evolving field.
Quantum information science and technology high school outreach: Conceptual progression for introducing principles and programming skills
In Special Collection: Celebrating the International Year of Quantum Science and Technology by Dominik Schneble; Tzu-Chieh Wei; Angela M. Kelly. DOI: 10.1119/5.0211535
Editor's Note: This paper describes the curriculum for a QIST summer program for high school students. In a total of 25 h of instruction, students are introduced to essential classical physics concepts such as waves and polarization, and then to a carefully chosen series of quantum ideas leading through superposition, measurement, entanglement, and Bell's inequality. Quantum computation is introduced using IBM's Quantum Composer, and students learn the process of quantum key distribution. The provided course structure and materials could be used to replicate the instruction in a similar program for high school students, but it can also be used as the basis of more formal instruction at the high school or university level.
Simulating spin dynamics with quantum computers by Jarrett L. Lancaster; D. Brysen Allen. DOI: 10.1119/5.0112717
Editor's Note: Richard Feynman wrote in 1982 that, if we wanted to simulate physics with computers, then we needed quantum computers. The problem, of course, was that they didn't exist then. But now they do! This paper shows how students can use IBM's free quantum hardware to simulate spin systems that we teach about in class, thus reinforcing what they learn in quantum mechanics while simultaneously gaining exposure to the current capabilities of quantum computing.
Testing the necessity of complex numbers in traditional quantum theory with quantum computers
In Special Collection: Celebrating the International Year of Quantum Science and Technology by Jarrett L. Lancaster; Nicholas M. Palladino. DOI: 10.1119/5.0225728
Editor's Note: The concept of complex numbers is often introduced in first-year physics classes, such as when studying wave phenomena, and we tell students that they provide a convenient tool to do calculations. It is also emphasized that the same results could be derived using only real quantities. Hence students might ask whether quantum mechanics inherently needs complex numbers. The researchers show a case where a real-valued quantum theory predicts identical correlations to complex-valued quantum mechanics in certain Bell tests. However, a small modification to the tests shows differing predictions of the real and complex descriptions, with specific devices able to falsify the real-valued quantum theory. Using IBM's quantum hardware, the authors highlight that, despite the limitations of noisy quantum devices, they can still effectively address foundational issues in quantum mechanics.
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