DOCSLIB.ORG

Laser Spectroscopy to Resolve Hyperfine Structure of Rubidium

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Laser Spectroscopy to Resolve Hyperfine Structure of Rubidium Laser spectroscopy to resolve hyperfine structure of rubidium Hannah Saddler, Adam Egbert, and Will Weigand (Dated: 12 November 2015) This experiment had two main goals: to create an absorption spectrum for rubidium using the technique of absorption spectroscopy and to resolve the hyperfine structures for the two rubidium isotopes using saturation absorption spectroscopy. The absorption spectrum was used to determine the frequency difference between the ground state and first excited state for both isotopes. The calculated frequency difference was 6950 MHz ± 90 MHz for rubidium 87 and 3060 MHz ± 60 MHz for rubidium 85. Both values agree with the literature values. The hyperfine structure for rubidium 87 was able to be resolved using this experimental setup. The energy differences were determined to be 260 MHz ± 10 MHz and 150 MHz ± 10 Mhz MHz. The hyperfine structure for rubidium 85 was unable to be resolved using this experimental setup. Additionally the theory of doppler broadening was used to make measurements of the full width half maximum. These values were used to calculate a temperature of 310K ± 40 K which makes sense because the experiments were performed at room temperature. I. INTRODUCTION in the theory section and how they were manipulated and used to derive the results from the recorded data. Addi- tionally there is an explanation of experimental error and The era of modern spectroscopy began with the in- uncertainty associated the results. Section V is a conclu- vention of the laser. The word laser was originally an sion that ties the results of the experiment we performed acronym that stood for light amplification by stimulated to the usefulness of the technique of laser spectroscopy. emission of radiation. The first functioning laser was built in 1960 by Theodore H. Maiman. Lasers differ from other light sources because they emit light coher- II. THEORY ently; this means that the light is spatially coherent al- lowing it to be tightly focused with minimal scattering. Even though lasers were not successfully built until 1960, The two techniques of laser spectroscopy used in this the theoretical foundations were laid out by Albert Ein- experiment aim to understand and measure the absorp- stein in 1917, Rudolf Landenburg in 1928, Willis Lamb tion spectrum for rubidium and the hyperfine splitting and R.C. Retherford in 1947, and Alfred Kastler in 1950. of the two rubidium isotopes. To understand the pro- The Nobel Prize in Physics in 1981 was jointly received cedure, results, and observations it is important to first by Nicolaas Bloembergen and Arthur Leonard Schawlow look at the classical and quantum physics behind the for their contribution to the development of laser spec- structure of rubidium. With a firm understanding of the troscopy and Kai M Siegbahn for his contribution to basics, it is then important to understand the physics the development of high-resolution electron spectroscopy. behind two more phenomena experienced in this experi- The type of laser used in this experiment is known as a ment: doppler broadening and crossover frequencies. tunable diode laser. This means that its wavelength can be altered by a controller to be tuned over a specific range of wavelengths. A. Basic Physics Laser spectroscopy is a useful technique to learn about the structure and energy levels of atoms and their con- Atoms typically contain a central nucleus with elec- stituent electrons. Spectroscopy has played a critical role trons that orbit the nucleus. The electrons fill into these in furthering quantum mechanics, atomic and nuclear different orbitals based on the Pauli Exclusion Principle. physics, and many other fields. Lasers and laser spec- The Pauli Exclusion Principle states that no two elec- troscopy have even found their ways to cosmology and trons in an atom can have the same four electronic quan- medicine. The two types of spectroscopy used in this ex- tum numbers. The orbitals have different energy states. periment were absorption spectroscopy to observe the ab- Electrons that are in the outermost shell, meaning fur- sorption spectrum of rubidium and saturation absorption thest away from the nucleus, can be excited into higher spectroscopy to try to resolve the hyperfine structures of energy states. They jump into these states excited states both rubidium isotopes. by absorbing photons with energies equal to the energy difference between the two states. This is shown by The second section of this paper will cover the theory necessary to understand the procedure, results, and ob- ∆E = E2 − E1 = hf; (1) servations from the laser spectroscopy experiment. Sec- tion III is an overview of the experimental design and ap- where f is the frequency of light that is required to make paratus used. Section IV further details the experimental the transition between the states. Figure 1 is an energy procedure and the results of the experiment. This section level diagram that shows the energy levels for rubidium includes a discussion of the various equations presented 85 and rubidium 87. This energy level diagram show the 2 energy difference between the ground and first excited = 3,2,1,0 for rubidium 87 and F = 4,3,2,1 for rubidium states. The diagram also shows the hyperfine splitting 85. Using Equation 5 and the quantum numbers, the caused by non-time dependent energy perturbations that energy differences between the hyperfine splittings can remove the degeneracy of the states. From the figure it be determined1. is obvious that a frequency of 384x106 MHz is required To understand the quantum addition of angular mo- to excite both of the rubidium isotopes from the ground mentum from a more classical perspective is may be use- state to the second excited state. ful to think of the electron as a bar magnet. The magnet can either be aligned or antialigned. The aligned state is a lower energy state that refers to the subtraction of J from I. The antialigned state is a higher energy state that refers to the addition of J and I. B. Doppler Broadening In the laser spectroscopy experiment , the tunable diode laser is directed through a cell of rubidium gas to allows us to make observation of the absorption spec- trum and hyperfine structure of the two rubidium iso- topes. The rubidium gas cell does not contain a station- ary sample to be measured. As a result of the thermal motion of the rubidium atoms in the gas sample, doppler broadening occurs. Doppler broadening is the broaden- ing of spectral lines due to the doppler effect caused by a FIG. 1. Energy diagram for rubidium 87 and rubidium 85. distribution of velocities of the atoms. The different ve- The diagram shows the difference between the ground state locities of the rubidium particles result in doppler shifts and the excited state. The diagram also shows the hyperfine based upon the direction and speed of the particle rela- splitting of both states for both isotopes. tive to the incoming light waves. The expected frequency with the doppler shift is given by To understand the hyperfine splitting of the energy v ! = ! (1 − ); (6) states we must turn to quantum mechanics. The mul- 0 c tiple substates that both energy levels split into are the result of energy perturbations that are explained by the where !0 is the resonant frequency of light the rubid- perturbing hamiltonian operator. The perturbing hamil- ium atom would experience if it was not moving relative tonian operator is given by to the incoming light beam. Therefore doppler broaden- ing stems from the fact that instead of receiving a single Hhfs = A(J • I); (2) spectral line at the resonant frequency, there is a spread of frequencies measured. The spread of frequencies is a where I is the nuclear angular momentum and J is the gaussian distribution given by sum of the electronic orbital and spin angular momen- 2 2 2 −m0e (!0−!) =2KT −! tum. The total angular momentum, F, is then given by I(!) = I0e 0 : (7) F = I + J: (3) As seen above in Equation 7 the thermal doppler broad- ening is dependent of frequency of spectral line, mass By combining Equation 2 and Equation 3, the Hamilto- of emitting particle, and the temperature. Therefore the nian can be rewritten as doppler broadening of the absorption spectrum peaks can be used to determine the temperature of the emitting A ^2 ^2 ^2 body. The equation to do this is known as the equation Hhfs = [F − I − J ]; (4) 2 for full width half maximum and is given by which yields p 2 ∆!fwhm = 2!0 2ln(2KT=m0)=c : (8) A 2 Hhfs = ~ [F (F + 1) − I(I + 1) − J(J + 1)]: (5) 2 C. Crossover Frequencies The ground state of rubidium 85 has I = 5/2 and J = 1/2 which leaves us with F = 2 and F = 3. The ground state When analyzing the results of this experiment it is im- of rubidium 87 have I = 3/2 and J = 1/2 which leaves us portant to know what crossover frequencies are, what with F = 2 and F = 1. For the excited states there are they represent, and what they look like. Crossover fre- four allowed J values (J = ±3=2; ±1=2). This yields F quencies, νc, occur when the laser frequency, is such that 3 the moving rubidium atoms see the pump beam red- pump beam and the remaining 10 percent to be the probe shifted to a frequency of ν1 and at the same time the beam. The probe beam was then directed through the moving rubidium atoms see the probe beam blueshifted rubidium sample and into a PIN detector. The PIN de- to a frequency of ν2. tector was then used to make absorption measurements.
Load more

Recommended publications
  • Fotonica Ed Elettronica Quantistica
    Fotonica ed elettronica quantistica http://www.dsf.unica.it/~fotonica/teaching/fotonica.html Fotonica ed elettronica quantistica Quantum optics - Quantization of electromagnetic field - Statistics of light, photon counting and noise; - HBT and correlation; g1 e g2 coherence; antibunching; single photons - Squeezing - Quantum cryptography - Quantum computer, entanglement and teleportation Light-matter Interaction - Two-level atom - Laser physics - Spectroscopy - Electronics and photonics at the nanometer scale - Cold atoms - Photodetectors - Solar cells http://www.dsf.unica.it/~fotonica/teaching/fotonica.html Energy Temperature LHC at CERN, Higgs, SUSY, ??? TeV 15 q q particle accelerators 10 K q GeV proton rest mass - quarks 1012K MeV electron rest mass / gamma rays 109K keV Nuclear Fusion, x rays, Sun center 106K Atoms ionize - visible light eV Sun surface fundamental components components fundamental room temperature 103K meV Liquid He, superconductors, space 1K dilution refrigerators, quantum Hall µeV laser-cooled atoms 10-3K neV Bose-Einstein condensates 10-6K peV low T record 480 picokelvin 10-9K -12 complexity, organization organization complexity, 10 K Nobel Prizes in Physics 2010 - Andre Geims, Konstantin Novoselov 2009 - Charles K. Kao, Willard S. Boyle, George E. Smith 2007 - Albert Fert, Peter Gruenberg 2005 - Roy J. Glauber, John L. Hall, Theodor W. Hänsch 2001 - Eric A. Cornell, Wolfgang Ketterle, Carl E. Wieman 1997 - Steven Chu, Claude Cohen-Tannoudji, William D. Phillips 1989 - Norman F. Ramsey, Hans G. Dehmelt, Wolfgang Paul 1981 - Nicolaas Bloembergen, Arthur L. Schawlow, Kai M. Siegbahn 1966 - Alfred Kastler 1964 - Charles H. Townes, Nicolay G. Basov, Aleksandr M. Prokhorov 1944 - Isidor Isaac Rabi 1930 - Venkata Raman 1921 - Albert Einstein 1907 - Albert A.
    [Show full text]
  • Laboratoire Kastler Brossel, LKB, ENS PARIS, Sorbonne Université, COLL DE FRANCE, CNRS, Mr Antoine HEIDMANN
    Research evaluation REPORT ON THE RESEARCH UNIT: Kastler Brossel Laboratory LKB UNDER THE SUPERVISION OF THE FOLLOWING INSTITUTIONS AND RESEARCH BODIES: École Normale Supérieure Sorbonne Université Collège de France Centre National de la Recherche Scientifique - CNRS EVALUATION CAMPAIGN 2017-2018 GROUP D In the name of Hcéres1 : In the name of the expert committee2 : Michel Cosnard, President Vahid Sandoghdar, Chairman of the committee Under the decree No.2014-1365 dated 14 November 2014, 1 The president of HCERES "countersigns the evaluation reports set up by the expert committees and signed by their chairman." (Article 8, paragraph 5); 2 The evaluation reports "are signed by the chairman of the expert committee". (Article 11, paragraph 2). Laboratoire Kastler Brossel, LKB, ENS PARIS, Sorbonne Université, COLL DE FRANCE, CNRS, Mr Antoine HEIDMANN This report is the sole result of the unit’s evaluation by the expert committee, the composition of which is specified below. The assessments contained herein are the expression of an independent and collegial reviewing by the committee. UNIT PRESENTATION Unit name: Laboratoire Kastler-Brossel Unit acronym: LKB Requested label: UMR Application type: Renewal Current number: UMR 8552 Head of the unit Mr Antoine HEIDMANN (2017-2018): Project leader Mr Antoine HEIDMANN (2019-2023): Number of teams: 12 COMMITTEE MEMBERS Chair: Mr Vahid SANDOGHDAR, Max Planck Institute, Germany Experts: Mr Jean-Claude BERNARD, CNRS (supporting personnel) Mr Benoît BOULANGER, Université Grenoble Alpes (representative
    [Show full text]
  • Charles Hard Townes (1915–2015)
    ARTICLE-IN-A-BOX Charles Hard Townes (1915–2015) C H Townes shared the Nobel Prize in 1964 for the concept of the laser and the earlier realization of the concept at microwave frequencies, called the maser. He passed away in January of this year, six months short of his hundredth birthday. A cursory look at the archives shows a paper as late as 2011 – ‘The Dust Distribution Immediately Surrounding V Hydrae’, a contribution to infrared astronomy. To get a feel for the range in time and field, his 1936 masters thesis was based on repairing a non-functional van de Graaf accelerator at Duke University in 1936! For his PhD at the California Institute of Technology, he measured the spin of the nucleus of carbon-13 using isotope separation and high resolution spectroscopy. Smythe, his thesis supervisor was writing a comprehensive text on electromagnetism, and Townes solved every problem in it – it must have stood him in good stead in what followed. In 1939, even a star student like him did not get an academic job. The industrial job he took set him on his lifetime course. This was at the legendary Bell Telephone Laboratories, the research wing of AT&T, the company which set up and ran the first – and then the best – telephone system in the world. He was initially given a lot of freedom to work with different research groups. During the Second World War, he worked in a group developing a radar based system for guiding bombs. But his goal was always physics research. After the War, Bell Labs, somewhat reluctantly, let him pursue microwave spectroscopy, on the basis of a technical report he wrote suggesting that molecules might serve as circuit elements at high frequencies which were important for communication.
    [Show full text]
  • Slides for 1920 and 1928)
    Quantum Theory Matters with thanks to John Clarke Slater (1900{1976), Per-Olov L¨owdin(1916{2000), and the many members of QTP (Gainesville, FL, USA) and KKUU (Uppsala, Sweden) Nelson H. F. Beebe Research Professor University of Utah Department of Mathematics, 110 LCB 155 S 1400 E RM 233 Salt Lake City, UT 84112-0090 USA Email: [email protected], [email protected], [email protected] (Internet) WWW URL: http://www.math.utah.edu/~beebe Telephone: +1 801 581 5254 FAX: +1 801 581 4148 Nelson H. F. Beebe (University of Utah) QTM 11 November 2015 1 / 1 11 November 2015 The periodic table of elements All from H (1) to U (92), except Tc (43) and Pm (61), are found on Earth. Nelson H. F. Beebe (University of Utah) QTM 11 November 2015 2 / 1 Correcting a common misconception Scientific Theory: not a wild @$$#% guess, but rather a mathematical framework that allows actual calculation for known systems, and prediction for unknown ones. Nelson H. F. Beebe (University of Utah) QTM 11 November 2015 3 / 1 Scientific method Theories should be based on minimal sets of principles, and be free of preconceived dogmas, no matter how widely accepted. [Remember Archimedes, Socrates, Hypatia, Galileo, Tartaglia, Kepler, Copernicus, Lavoisier, . ] Open publication and free discussion of physical theories and experimental results, so that others can criticize them, improve them, and reproduce them. Know who pays for the work, and judge accordingly! Science must have public support. History shows that such support is paid back many times over. If it ain't repeatable, it ain't science! Nelson H.
    [Show full text]
  • Wolfgang Pauli Niels Bohr Paul Dirac Max Planck Richard Feynman
    Wolfgang Pauli Niels Bohr Paul Dirac Max Planck Richard Feynman Louis de Broglie Norman Ramsey Willis Lamb Otto Stern Werner Heisenberg Walther Gerlach Ernest Rutherford Satyendranath Bose Max Born Erwin Schrödinger Eugene Wigner Arnold Sommerfeld Julian Schwinger David Bohm Enrico Fermi Albert Einstein Where discovery meets practice Center for Integrated Quantum Science and Technology IQ ST in Baden-Württemberg . Introduction “But I do not wish to be forced into abandoning strict These two quotes by Albert Einstein not only express his well­ more securely, develop new types of computer or construct highly causality without having defended it quite differently known aversion to quantum theory, they also come from two quite accurate measuring equipment. than I have so far. The idea that an electron exposed to a different periods of his life. The first is from a letter dated 19 April Thus quantum theory extends beyond the field of physics into other 1924 to Max Born regarding the latter’s statistical interpretation of areas, e.g. mathematics, engineering, chemistry, and even biology. beam freely chooses the moment and direction in which quantum mechanics. The second is from Einstein’s last lecture as Let us look at a few examples which illustrate this. The field of crypt­ it wants to move is unbearable to me. If that is the case, part of a series of classes by the American physicist John Archibald ography uses number theory, which constitutes a subdiscipline of then I would rather be a cobbler or a casino employee Wheeler in 1954 at Princeton. pure mathematics. Producing a quantum computer with new types than a physicist.” The realization that, in the quantum world, objects only exist when of gates on the basis of the superposition principle from quantum they are measured – and this is what is behind the moon/mouse mechanics requires the involvement of engineering.
    [Show full text]
  • Turning Point in the Development of Quantum Mechanics and the Early Years of the Mossbauer Effect*
    Fermi National Accelerator Laboratory FERMILAB-Conf-76/87-THY October 1976 A TURNING POINT IN THE DEVELOPMENT OF QUANTUM MECHANICS AND THE EARLY YEARS OF THE MOSSBAUER EFFECT* Harry J. Lipkin' Weizmann Institute of Science, Rehovot, Israel Argonne National Laboratory, Argonne, Illinois 60^39 Fermi National Accelerator Laboratory"; Batavia, Illinois 60S10 It is interesting to hear about the exciting early days recalled by Professors Wigner and Wick. I learned quantum theory at a later period, which might be called a turning point in its development, when the general attitude toward quantum mechanics and the study of physics was very different from what it is today. As an undergraduate student in electrical engineering in 19^0 in the United States I found a certain disagreement between the faculty and the students about the "relevance'- of the curriculum. Students thought a k-year course in electrical engineering should include more electronics than a one-semester 3-hour course. But the establishment emphasized the study of power machinery and power transmission because 95'/° of their graduates would eventually get jobs in power. Electronics, they said, was fun for students who were radio hams but useless on the job market. Students at that time did not have today's attitudes and did not stage massive demonstrations and protests against the curriculum. Instead a few of us who wished to learn more interesting things satisfied all the requirements of the engineering school and spent as much extra time as possible listening to fascinating courses in the physics building. There we had the opportunity to listen to two recently-arrived Europeans, Bruno Rossi and Hans Bethe.
    [Show full text]
  • Nobel 2012: Trapped Ions and Photons
    FEATURES Nobel 2012: Trapped ions and photons l Michel Brune1, Jean-Michel Raimond1, Claude Cohen-Tannoudji 1,2 - DOI: 10.1051/epn/2012601 l 1 Laboratoire Kastler Brossel, ENS, CNRS, UMPC Paris 6, 24 rue Lhomond, 75005 Paris, France l 2 Collège de France, 11 place Marcelin Berthelot, 75005 Paris, France m This colorized The 2012 Nobel prize in physics has been awarded jointly to Serge Haroche image shows the fluorescence from three (Collège de France and Ecole Normale Supérieure) and David Wineland (National trapped beryllium ions illuminated with Institute for Standards and Technology, USA) “for ground-breaking experimental an ultraviolet laser methods that enable measuring and manipulation of individual quantum systems”. beam. Black and blue areas indicate lower intensity, and red and white higher intensity. hat are these methods, why are they For instance, Einstein and Bohr once imagined weighing NIST physicists used jointly recognized? a photon trapped forever in a box, covered by perfect three beryllium ions to demonstrate a crucial The key endeavour in the last century mirrors. These gedankenexperiments and their “ridicu- step in a procedure that of quantum physics has been the explo- lous consequences”, as Schrödinger once stated, played could enable future ration of the coupling between matter and electromag- a considerable role in the genesis of quantum physics quantum computers W to break today's netic radiation. For a long time, the available experimental interpretation. The technical progress made these most commonly used techniques were limited to a large number of atoms and experiments possible. One can now realize some of the encryption codes.
    [Show full text]
  • Laser Spectroscopy Experiments
    Hyperfine Spectrum of Rubidium: laser spectroscopy experiments Physics 480W (Dated: Sp19 Paper #4) I. OBJECTIVES FOR THESE EXPERIMENTS We wish to use the technique of absorption spec- troscopy to probe and detect the energy level structure of atomic Rubidium, Rb I, whose ground state is split by a tiny amount on account of nuclear magnetism. In effect, the spectroscopy we do today tells us about nuclear prop- erties and so combines atomic and nuclear physics. The main result of this experiment, the 4th of the semester, is to 1. measure the hyperfine splitting for each isotope, and compare with accepted values, with the fol- lowing details in mind: (a) what is the hyperfine splitting of the ground 2 state, S1=2 term? Do we need saturation- absorption techniques for this? (b) what are the hyperfine splittings of the ex- 2 cited state, P3=2 term, that can be reached with a nominal wavelength of 780nm from the ground state? Here we need saturation- absorption techniques to perform sub-Doppler FIG. 1. Note the four 'blobs'. Why are there four? Which spectroscopy, certainly. Help the reader un- 85 are associated with Rb37, and so on. If all goes swimm- derstand what is entailed in the technique, ingly, we'll get an absorption spectrum that looks much line both experimentally and theoretically. You the figure below the setup. The etalon data will be needed to will need to explain what `saturation' means. make the abscissa something proportional to frequency. The The saturation intensity is an important fig- accepted value of the gap between the 2 outermost dips is ure of merit.
    [Show full text]
  • Shs-17-2018-14.Pdf
    Science beyond borders Nobukata Nagasawa ORCID 0000-0002-9658-7680 Emeritus Professor of University of Tokyo [email protected] On social and psychological aspects of a negligible reception of Natanson’s article of 1911 in the early history of quantum statistics Abstract Possible reasons are studied why Ladislas (Władysław) Natanson’s paper on the statistical theory of radiation, published in 1911 both in English and in the German translation, was not cited properly in the early history of quantum statistics by outstanding scientists, such as Arnold Sommerfeld, Paul Ehrenfest, Satyendra Nath Bose and Albert Einstein. The social and psychological aspects are discussed as back- ground to many so far discussions on the academic evaluation of his theory. In order to avoid in the future such Natansonian cases of very limited reception of valuable scientific works, it is pro- posed to introduce a digital tag in which all the information of PUBLICATION e-ISSN 2543-702X INFO ISSN 2451-3202 DIAMOND OPEN ACCESS CITATION Nagasawa, Nobukata 2018: On social and psychological aspects of a negligible reception of Natanson’s article of 1911 in the early history of quantum statistics. Studia Historiae Scientiarum 17, pp. 391–419. Available online: https://doi.org/10.4467/2543702XSHS.18.014.9334. ARCHIVE RECEIVED: 13.06.2017 LICENSE POLICY ACCEPTED: 12.09.2018 Green SHERPA / PUBLISHED ONLINE: 12.12.2018 RoMEO Colour WWW http://www.ejournals.eu/sj/index.php/SHS/; http://pau.krakow.pl/Studia-Historiae-Scientiarum/ Nobukata Nagasawa On social and psychological aspects of a negligible reception... relevant papers published so far should be automatically accu- mulated and updated.
    [Show full text]
  • Discerned and Non-Discerned Particles in Classical Mechanics and Convergence of Quantum Mechanics to Classical Mechanics
    Annales de la Fondation Louis de Broglie, Volume 36, 2011 117 Discerned and non-discerned particles in classical mechanics and convergence of quantum mechanics to classical mechanics Michel Gondrana, Alexandre Gondranb aUniversity Paris Dauphine, Lamsade, 75016 Paris, France email: [email protected] bEcole Nationale de l’Aviation Civile, 31000 Toulouse, France email: [email protected] ABSTRACT. We introduce into classical mechanics the concept of non- discerned particles for particles that are identical, non-interacting and prepared in the same way. The non-discerned particles correspond to an action and a density which satisfy the statistical Hamilton-Jacobi equations and allow to explain the Gibbs paradox. On the other hand, a discerned particle corresponds to a particular action that satisfies the special Hamilton-Jacobi equations. We then study the convergence of quantum mechanics to classical mechanics when ~ tends to 0 by considering two cases : the convergence to non-discerned classical par- ticles and the convergence to a classical discerned particle. Based on these convergences, we propose an updated interpretation of quantum mechanics. RÉSUMÉ. Nous introduisons en mécanique classique le concept de par- ticules indiscernées pour des particules qui sont identiques, sans in- teraction et préparées de la même façon. Ces particules indiscernées correspondent à une action et une densité qui satisfassent les équa- tions d’Hamilton-Jacobi statistiques et qui permettent d’expliquer le paradoxe de Gibbs. Par ailleurs, une particule discernée correspond à une action particulière qui satisfait les équations spéciales d’Hamilton- Jacobi. L’étude de la convergence de la mécanique quantique vers la mécnique classique quand ~ → 0 se fait alors simplement en considé- rant deux cas : la convergence vers des particules classiques indiscernées et la convergence vers des particules classiques discernées.
    [Show full text]
  • One Year with the Académie Des Sciences 2012
    One Year with the Académie des Sciences 2012 Encouraging the Science Community Promoting Scientific Teaching Transmitting Knowledge Fostering International Collaboration Playing an Expert and Advisory Role The Académie des Sciences: a modernised institution The Académie des Sciences holds an original position among French scientific institutions: placed under the protection of the President of the French Republic, it is self-governed and only supervised by the French National Audit Office (Cour des comptes). Such independence also stems from the process through which members are appointed: they are peer-elected. Gathering the scientific elite of our country, the Académie des Sciences has adapted to the increasing pace of scientific progress by expanding its membership – now at 245 members aside from Foreign Associate and Corresponding Members – and rejuvenating the profile of the Academy – half of its seats are kept for applicants under 55 years old, which means they are still working – thus making sure the Academy is in direct connection with civil society and economic activities. The Académie des Sciences performs its five missions through finely-tuned coordination between its statutory governance bodies, all members of which have been elected, and Committees providing analysis and advice. Plenary Assembly (Closed-Door Committee - Comité Secret) Permanent Members of the Academy, Corresponding and Foreign Associate Members, spread across Divisions and Division 1 Sections Division 2 Sections Sections Mathematics Select Committee Chemistry
    [Show full text]
  • El Premio Nobel De Fısica De 2012
    El premio Nobel de f´ısica de 2012 Jose´ Mar´ıa Filardo Bassalo* Abstract Palabras clave: Premio nobel de f´ısica de 2012; Haroche y In this article we will talk about the 2012 Nobel Prize in Phy- Wineland, manipulacion´ cuantica.´ sics, awarded to the physicists, the frenchman Serge Haroche and the north-american David Geffrey Wineland for ground- Serge Haroche breaking experimental methods that enable measuring and ma- El premio nobel de f´ısica (PNF) de 2012 fue con- nipulation of individual quantum systems. cedido a los f´ısicos, el frances´ Serge Haroche (n. 1944) y el norteamericano David Geffrey Wine- Keywords: 2012 Physics Nobel Prize; Haroche and Wineland; Quantum Manipulation. land (n. 1944) por el desarrollo de tecnicas´ experimen- tales capaces de medir y manipular sistemas qu´ımi- Resumen cos individuales por medio de la optica´ cuanti-´ En este art´ıculo trataremos del premio nobel de f´ısica de 2012 ca. Con todo, emplearon tecnicas´ distintas y comple- concedido a los f´ısicos, el frances´ Serge Haroche y al norteame- mentarias: Haroche utilizo´ fotones de atomos´ carga- ricano David Geffrey Wineland por el desarrollo de tecnicas´ ex- dos (iones) entrampados; Wineland entrampo´ los io- perimentales capaces de medir y manipular sistemas cuanticos´ nes y empleo´ fotones para modificar su estado individuales. cuantico.´ *http://www.amazon.com.br Recibido: 16 de abril de 2013. Comencemos viendo algo de la vida y del trabajo de es- Aceptado: 09 de octubre de 2013. tos premiados, as´ı como la colaboracion´ en estos temas 5 6 ContactoS 92, 5–10 (2014) por algunas f´ısicos brasilenos,˜ por ejemplo Nicim Za- gury (n.
    [Show full text]