Weak Values and Two-State Vector Formalism in Elementary Scattering and Reflectivity—A New Effect†
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The Concept of Quantum State : New Views on Old Phenomena Michel Paty
The concept of quantum state : new views on old phenomena Michel Paty To cite this version: Michel Paty. The concept of quantum state : new views on old phenomena. Ashtekar, Abhay, Cohen, Robert S., Howard, Don, Renn, Jürgen, Sarkar, Sahotra & Shimony, Abner. Revisiting the Founda- tions of Relativistic Physics : Festschrift in Honor of John Stachel, Boston Studies in the Philosophy and History of Science, Dordrecht: Kluwer Academic Publishers, p. 451-478, 2003. halshs-00189410 HAL Id: halshs-00189410 https://halshs.archives-ouvertes.fr/halshs-00189410 Submitted on 20 Nov 2007 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. « The concept of quantum state: new views on old phenomena », in Ashtekar, Abhay, Cohen, Robert S., Howard, Don, Renn, Jürgen, Sarkar, Sahotra & Shimony, Abner (eds.), Revisiting the Foundations of Relativistic Physics : Festschrift in Honor of John Stachel, Boston Studies in the Philosophy and History of Science, Dordrecht: Kluwer Academic Publishers, 451-478. , 2003 The concept of quantum state : new views on old phenomena par Michel PATY* ABSTRACT. Recent developments in the area of the knowledge of quantum systems have led to consider as physical facts statements that appeared formerly to be more related to interpretation, with free options. -
Light and Matter Diffraction from the Unified Viewpoint of Feynman's
European J of Physics Education Volume 8 Issue 2 1309-7202 Arlego & Fanaro Light and Matter Diffraction from the Unified Viewpoint of Feynman’s Sum of All Paths Marcelo Arlego* Maria de los Angeles Fanaro** Universidad Nacional del Centro de la Provincia de Buenos Aires CONICET, Argentine *[email protected] **[email protected] (Received: 05.04.2018, Accepted: 22.05.2017) Abstract In this work, we present a pedagogical strategy to describe the diffraction phenomenon based on a didactic adaptation of the Feynman’s path integrals method, which uses only high school mathematics. The advantage of our approach is that it allows to describe the diffraction in a fully quantum context, where superposition and probabilistic aspects emerge naturally. Our method is based on a time-independent formulation, which allows modelling the phenomenon in geometric terms and trajectories in real space, which is an advantage from the didactic point of view. A distinctive aspect of our work is the description of the series of transformations and didactic transpositions of the fundamental equations that give rise to a common quantum framework for light and matter. This is something that is usually masked by the common use, and that to our knowledge has not been emphasized enough in a unified way. Finally, the role of the superposition of non-classical paths and their didactic potential are briefly mentioned. Keywords: quantum mechanics, light and matter diffraction, Feynman’s Sum of all Paths, high education INTRODUCTION This work promotes the teaching of quantum mechanics at the basic level of secondary school, where the students have not the necessary mathematics to deal with canonical models that uses Schrodinger equation. -
Origin of Probability in Quantum Mechanics and the Physical Interpretation of the Wave Function
Origin of Probability in Quantum Mechanics and the Physical Interpretation of the Wave Function Shuming Wen ( [email protected] ) Faculty of Land and Resources Engineering, Kunming University of Science and Technology. Research Article Keywords: probability origin, wave-function collapse, uncertainty principle, quantum tunnelling, double-slit and single-slit experiments Posted Date: November 16th, 2020 DOI: https://doi.org/10.21203/rs.3.rs-95171/v2 License: This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License Origin of Probability in Quantum Mechanics and the Physical Interpretation of the Wave Function Shuming Wen Faculty of Land and Resources Engineering, Kunming University of Science and Technology, Kunming 650093 Abstract The theoretical calculation of quantum mechanics has been accurately verified by experiments, but Copenhagen interpretation with probability is still controversial. To find the source of the probability, we revised the definition of the energy quantum and reconstructed the wave function of the physical particle. Here, we found that the energy quantum ê is 6.62606896 ×10-34J instead of hν as proposed by Planck. Additionally, the value of the quality quantum ô is 7.372496 × 10-51 kg. This discontinuity of energy leads to a periodic non-uniform spatial distribution of the particles that transmit energy. A quantum objective system (QOS) consists of many physical particles whose wave function is the superposition of the wave functions of all physical particles. The probability of quantum mechanics originates from the distribution rate of the particles in the QOS per unit volume at time t and near position r. Based on the revision of the energy quantum assumption and the origin of the probability, we proposed new certainty and uncertainty relationships, explained the physical mechanism of wave-function collapse and the quantum tunnelling effect, derived the quantum theoretical expression of double-slit and single-slit experiments. -
Testing the Limits of Quantum Mechanics the Physics Underlying
Testing the limits of quantum mechanics The physics underlying non-relativistic quantum mechanics can be summed up in two postulates. Postulate 1 is very precise, and says that the wave function of a quantum system evolves according to the Schrodinger equation, which is a linear and deterministic equation. Postulate 2 has an entirely different flavor, and can be roughly stated as follows: when the quantum system interacts with a classical measuring apparatus, its wave function collapses, from being in a superposition of the eigenstates of the measured observable, to being in just one of the eigenstates. The outcome of the measurement is random and cannot be predicted; the quantum system collapses to one or the other eigenstates, with a probability that is proportional to the squared modulus of the wave function for that eigenstate. This is the Born probability rule. Since quantum theory is extremely successful, and not contradicted by any experiment to date, one can simply accept the 2nd postulate as such, and let things be. On the other hand, ever since the birth of quantum theory, some physicists have been bothered by this postulate. The following troubling questions arise. How exactly is a classical measuring apparatus defined? How large must a quantum system be, before it can be called classical? The Schrodinger equation, which in principle is supposed to apply to all physical systems, whether large or small, does not answer this question. In particular, the equation does not explain why the measuring apparatus, say a pointer, is never seen in a quantum superposition of the two states `pointer to the left’ and `pointer to the right’? And if the equation does apply to the (quantum system + apparatus) as a whole, why are the outcomes random? Why does collapse, which apparently violates linear superposition, take place? Where have the probabilities come from, in a deterministic equation (with precise initial conditions), and why do they obey the Born rule? This set of questions generally goes under the name `the quantum measurement problem’. -
Finally Making Sense of the Double-Slit Experiment
Finally making sense of the double-slit experiment Yakir Aharonova,b,c,1, Eliahu Cohend,1,2, Fabrizio Colomboe, Tomer Landsbergerc,2, Irene Sabadinie, Daniele C. Struppaa,b, and Jeff Tollaksena,b aInstitute for Quantum Studies, Chapman University, Orange, CA 92866; bSchmid College of Science and Technology, Chapman University, Orange, CA 92866; cSchool of Physics and Astronomy, Tel Aviv University, Tel Aviv 6997801, Israel; dH. H. Wills Physics Laboratory, University of Bristol, Bristol BS8 1TL, United Kingdom; and eDipartimento di Matematica, Politecnico di Milano, 9 20133 Milan, Italy Contributed by Yakir Aharonov, March 20, 2017 (sent for review September 26, 2016; reviewed by Pawel Mazur and Neil Turok) Feynman stated that the double-slit experiment “. has in it the modular momentum operator will arise as particularly signifi- heart of quantum mechanics. In reality, it contains the only mys- cant in explaining interference phenomena. This approach along tery” and that “nobody can give you a deeper explanation of with the use of Heisenberg’s unitary equations of motion intro- this phenomenon than I have given; that is, a description of it” duce a notion of dynamical nonlocality. Dynamical nonlocality [Feynman R, Leighton R, Sands M (1965) The Feynman Lectures should be distinguished from the more familiar kinematical non- on Physics]. We rise to the challenge with an alternative to the locality [implicit in entangled states (10) and previously ana- wave function-centered interpretations: instead of a quantum lyzed in the Heisenberg picture by Deutsch and Hayden (11)], wave passing through both slits, we have a localized particle with because dynamical nonlocality has observable effects on prob- nonlocal interactions with the other slit. -
Wave-Particle Duality Relation with a Quantum Which-Path Detector
entropy Article Wave-Particle Duality Relation with a Quantum Which-Path Detector Dongyang Wang , Junjie Wu * , Jiangfang Ding, Yingwen Liu, Anqi Huang and Xuejun Yang Institute for Quantum Information & State Key Laboratory of High Performance Computing, College of Computer Science and Technology, National University of Defense Technology, Changsha 410073, China; [email protected] (D.W.); [email protected] (J.D.); [email protected] (Y.L.); [email protected] (A.H.); [email protected] (X.Y.) * Correspondence: [email protected] Abstract: According to the relevant theories on duality relation, the summation of the extractable information of a quanton’s wave and particle properties, which are characterized by interference visibility V and path distinguishability D, respectively, is limited. However, this relation is violated upon quantum superposition between the wave-state and particle-state of the quanton, which is caused by the quantum beamsplitter (QBS). Along another line, recent studies have considered quantum coherence C in the l1-norm measure as a candidate for the wave property. In this study, we propose an interferometer with a quantum which-path detector (QWPD) and examine the generalized duality relation based on C. We find that this relationship still holds under such a circumstance, but the interference between these two properties causes the full-particle property to be observed when the QWPD system is partially present. Using a pair of polarization-entangled photons, we experimentally verify our analysis in the two-path case. This study extends the duality relation between coherence and path information to the quantum case and reveals the effect of quantum superposition on the duality relation. -
Weak Measurements, the Energy-Momentum Tensor and the Bohm Approach Robert Flack and Basil J
6 Weak Measurements, the Energy-Momentum Tensor and the Bohm Approach Robert Flack and Basil J. Hiley Abstract μ In this paper we show how the weak values, x(t)|P |ψ(t0)/x(t)|ψ(t0), are related to the T 0μ(x, t) component of the energy-momentum tensor. This enables the local energy and momentum to be measured using weak measurement techniques. We also show how the Bohm energy and momentum are related to T 0μ(x, t) and there- fore it follows that these quantities can also be measured using the same methods. Thus the Bohm ‘trajectories’ can be empirically determined as was shown by Kocis et al in the case of photons. Because of the difficulties with the notion of a photon trajectory, we argue the case for determining experimentally similar trajectories for atoms where a trajectory does not cause these particular difficulties. 6.1 Introduction The notion of weak measurements introduced by Aharonov, Albert and Vaidman (1988,1990) has opened up a radically new way of exploring quantum phenomena. In contrast to the strong measurement (von Neumann 1955), which involves the collapse of the wave function, a weak measurement induces a more subtle phase change which does not involve any collapse. This phase change can then be ampli- fied and revealed in a subsequent strong measurement of a complementary oper- ator that does not commute with the operator being measured. This amplification explains why it is possible for the result of a weak spin measurement of a spin-1/2 atom to be magnified by a factor of 100 (Aharonov et al. -
Research-Based Interactive Simulations to Support Quantum Mechanics Learning and Teaching
Research-based interactive simulations to support quantum mechanics learning and teaching Antje Kohnle School of Physics and Astronomy, University of St Andrews Abstract Quantum mechanics holds a fascination for many students, but its mathematical complexity can present a major barrier. Traditional approaches to introductory quantum mechanics have been found to decrease student interest. Topics which enthuse students such as quantum information are often only covered in advanced courses. The QuVis Quantum Mechanics Visualization project (www.st-andrews.ac.uk/physics/quvis) aims to overcome these issues through the development and evaluation of interactive simulations with accompanying activities for the learning and teaching of quantum mechanics. Simulations support model-building by reducing complexity, focusing on fundamental ideas and making the invisible visible. They promote engaged exploration, sense-making and linking of multiple representations, and include high levels of interactivity and direct feedback. Some simulations allow students to collect data to see how quantum-mechanical quantities are determined experimentally. Through text explanations, simulations aim to be self-contained instructional tools. Simulations are research-based, and evaluation with students informs all stages of the development process. Simulations and activities are iteratively refined using individual student observation sessions, where students freely explore a simulation and then work on the associated activity, as well as in-class trials using student surveys, pre- and post-tests and student responses to activities. A recent collection of QuVis simulations is embedded in the UK Institute of Physics Quantum Physics website (quantumphysics.iop.org), which consists of freely available resources for an introductory course in quantum mechanics starting from two-level systems. -
Weak Measurement and Feedback in Superconducting Quantum Circuits
1 Weak Measurement and Feedback in Superconducting Quantum Circuits K. W. Murch, R. Vijay, and I. Siddiqi 1 Department of Physics, Washington University, St. Louis, MO, USA [email protected] 2 Tata Institute of Fundamental Research, Mumbai, India [email protected] 3 Quantum Nanoelectronics Laboratory, Department of Physics, University of California, Berkeley, CA, USA [email protected] Abstract. We describe the implementation of weak quantum measurements in su- perconducting qubits, focusing specifically on transmon type devices in the circuit quantum electrodynamics architecture. To access this regime, the readout cavity is probed with on average a single microwave photon. Such low-level signals are detected using near quantum-noise-limited superconducting parametric amplifiers. Weak measurements yield partial information about the quantum state, and corre- spondingly do not completely project the qubit into an eigenstate. As such, we use the measurement record to either sequentially reconstruct the quantum state at a given time, yielding a quantum trajectory, or to close a direct quantum feedback loop, stabilizing Rabi oscillations indefinitely. Measurement-based feedback routines are commonplace in modern elec- tronics, including the thermostats regulating the temperature in our homes to sophisticated motion stabilization hardware needed for the autonomous oper- ation of aircraft. The basic elements present in such classical feedback loops include a sensor element which provides information to a controller, which in turn steers the system of interest toward a desired target. In this paradigm, the act of sensing itself does not a priori perturb the system in a significant way. Moreover, extracting more or less information during the measurement process does not factor into the control algorithm. -
Direct Measurement of the Density Matrix of a Quantum System
Selected for a Viewpoint in Physics week ending PRL 117, 120401 (2016) PHYSICAL REVIEW LETTERS 16 SEPTEMBER 2016 Direct Measurement of the Density Matrix of a Quantum System G. S. Thekkadath, L. Giner, Y. Chalich, M. J. Horton, J. Banker, and J. S. Lundeen Department of Physics and Max Planck Centre for Extreme and Quantum Photonics, University of Ottawa, 25 Templeton Street, Ottawa, Ontario K1N 6N5, Canada (Received 26 April 2016; revised manuscript received 14 June 2016; published 12 September 2016) One drawback of conventional quantum state tomography is that it does not readily provide access to single density matrix elements since it requires a global reconstruction. Here, we experimentally demonstrate a scheme that can be used to directly measure individual density matrix elements of general quantum states. The scheme relies on measuring a sequence of three observables, each complementary to the last. The first two measurements are made weak to minimize the disturbance they cause to the state, while the final measurement is strong. We perform this joint measurement on polarized photons in pure and mixed states to directly measure their density matrix. The weak measurements are achieved using two walk-off crystals, each inducing a polarization-dependent spatial shift that couples the spatial and polarization degrees of freedom of the photons. This direct measurement method provides an operational meaning to the density matrix and promises to be especially useful for large dimensional states. DOI: 10.1103/PhysRevLett.117.120401 Shortly after the inception of the quantum state, Pauli of the reconstruction algorithm renders the task increasingly questioned its measurability, and in particular, whether or difficult for large dimensional systems. -
Weak Measurements for Quantum Characterization and Control Jonathan A
University of New Mexico UNM Digital Repository Physics & Astronomy ETDs Electronic Theses and Dissertations Summer 7-27-2018 Weak measurements for quantum characterization and control Jonathan A. Gross University of New Mexico Follow this and additional works at: https://digitalrepository.unm.edu/phyc_etds Part of the Atomic, Molecular and Optical Physics Commons, and the Quantum Physics Commons Recommended Citation Gross, Jonathan A.. "Weak measurements for quantum characterization and control." (2018). https://digitalrepository.unm.edu/ phyc_etds/204 This Dissertation is brought to you for free and open access by the Electronic Theses and Dissertations at UNM Digital Repository. It has been accepted for inclusion in Physics & Astronomy ETDs by an authorized administrator of UNM Digital Repository. For more information, please contact [email protected]. Weak measurements for quantum characterization and control by Jonathan A. Gross B.M., Piano Performance, University of Arizona, 2011 B.S., Computer Engineering, University of Arizona, 2011 M.S., Physics, University of New Mexico, 2015 DISSERTATION Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Physics The University of New Mexico Albuquerque, New Mexico December, 2018 c 2018, Jonathan A. Gross iii Dedication The posting of witnesses by a third and other path altogether might also be called in evidence as appearing to beggar chance, yet the judge, who had put his horse forward until he was abreast of the speculants, said that in this was expressed the very nature of the witness and that his proximity was no third thing but rather the prime, for what could be said to occur unobserved? |Cormac McCarthy, Blood Meridian: Or the Evening Redness in the West And he sayde vnto me: my grace is sufficient for the. -
Weak Measurement, Projective Measurement and Quantum-To-Classical Transitions in Free Electron-Photon Interactions
Weak measurement, projective measurement and quantum-to-classical transitions in free electron-photon interactions Yiming Pan1†, Eliahu Cohen2†, Ebrahim Karimi3, Avraham Gover4, Ido Kaminer5 and Yakir Aharonov6,7 1. Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel 2. Faculty of Engineering and the Institute of Nanotechnology and Advanced Materials, Bar Ilan University, Ramat Gan 5290002, Israel 3. Department of Physics, University of Ottawa, Ottawa, Ontario, K1N 6N5, Canada 4. Department of Electrical Engineering Physical Electronics, Tel Aviv University, Ramat Aviv 6997801, Israel 5. Department of Electrical Engineering, Technion – Israel Institute of Technology, Haifa 3200003, Israel 6. School of Physics and Astronomy, Tel Aviv University, Ramat Aviv 6997801, Israel 7. Institute for Quantum Studies, Chapman University, Orange, CA 92866, USA †Correspondence and requests for materials should be addressed to E.C. ([email protected]) and Y.P. ([email protected]). 1 Abstract How does the quantum-to-classical transition of measurement occur? This question is vital for both foundations and applications of quantum mechanics. We developed a new measurement- based framework for characterizing the classical and quantum free electron-photon interactions. We first analyze the transition from projective measurement to weak measurement in generic light- matter interactions, and show that any classical electron-laser-beam interaction can be represented as an outcome of a weak measurement. In particular, the appearance of classical point-particle acceleration is an example of an amplified weak value resulting from weak measurement. A universal decay factor exp(-G2 2), quantifies the measurement regimes and their transition from quantum to classical, where G corresponds to the ratio between the electron wavepacket size and the optical wavelength.