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L = r× p = mv0b
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L = mr2 dϕdt
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The electrons can only travel in certain orbits (called byBohr as the "stationary orbits"): at a certain discrete setof distances from the nucleus with specific energies
2 ªÇ^
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They can only gain and lose energy by jumping fromone allowed orbit to another, absorbing or emittingelectromagnetic radiation with a frequency νdetermined by the energy difference of the levelsaccording to the Planck relation:
E1 − E2 = hνwhere h is Planck’s constant.
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L = n h2π = n~, nλ = 2πr
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1905c§Albert Einstein^ÊKb)º1>ANiels Bohr, Werner Heisenberg, Max Planck, Louis deBroglie, Albert Einstein, Erwin Schrödinger, Max Born,John von Neumann, Paul Dirac, Wolfgang Pauli, DavidHilbert, and othersõgاͶEPR¸→Bell’s Inequality1927c§5th Solvay Conference§þfåÆ2É)º®*ÿf1Ì
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Photograph of the first conference in 1911 at the HotelMetropole.
Seated (L-R): W. Nernst, M. Brillouin, E. Solvay, H. Lorentz,E. Warburg, J. Perrin, W. Wien, M. Skłodowska-Curie, andH. PoincaréStanding (L-R): R. Goldschmidt, M. Planck, H. Rubens, A.Sommerfeld, F. Lindemann, M. de Broglie, M. Knudsen, F.Hasenöhrl, G. Hostelet, E. Herzen, J.H. Jeans, E.Rutherford, H. Kamerlingh Onnes, A. Einstein and P.Langevin.
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Photograph of the fifth conference in 1927
A. Piccard, E. Henriot, P. Ehrenfest, E. Herzen, Th. DeDonder, E. Schrödinger, J.E. Verschaffelt, W. Pauli, W.Heisenberg, R.H. Fowler, L. Brillouin; P. Debye, M. Knudsen,W.L. Bragg, H.A. Kramers, P.A.M. Dirac, A.H. Compton, L.de Broglie, M. Born, N. Bohr; I. Langmuir, M. Planck, M.Skłodowska-Curie, H.A. Lorentz, A. Einstein, P. Langevin,Ch. E. Guye, C.T.R. Wilson, O.W. Richardson
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No Year Title Chair1 1911 The theory of Hendrik Lorentz
radiation and quanta (Leiden)2 1913 The structure of matter3 1921 Atoms and electrons4 1924 Electric conductivity of
metals and related problems5 1927 Electrons and photons6 1930 Magnetism Paul Langevin7 1933 Structure properties of (Paris)
the atomic nucleus8 1948 Elementary particles William Lawrence9 1951 The solid state Bragg (Cambridge)10 1954 Electrons in metals11 1958 The structure and
evolution of the universe12 1961 Quantum field theory
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14 1967 Fundamental Problems in R. MøllerElementary Particle Physics (Copenhagen)
15 1970 Symmetry Properties of Nuclei Edoardo Amaldi16 1973 Astrophysics and Gravitation (Rome)17 1978 Order and Fluctuations in Léon van
Equilibrium and Nonequilibrium Hove (CERN)Statistical Mechanics
18 1982 Higher Energy Physics19 1987 Surface Science F. W. de Wette
(Austin)
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20 1991 Quantum Optics Paul Mandel )21 1998 Dynamical Systems Ioannis Antoniou
and Irreversibility (Brussels)22 2001 The Physics of Communication23 2005 The Quantum Structure David Gross
of Space and Time (Santa Barbara)24 2008 Quantum Theory of Bertrand Halperin
Condensed Matter (Harvard)25 2011 The theory of
the quantum world David Gross26 2014 Astrophysics and Cosmology Roger Blandford
(Stanford)27 2017 The physics of living matter: Boris Shraiman
Space, time and information (Santa Barbara)in biology
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David E Pritchard
David E. Pritchardis physics professor at the Massachusetts Institute of Technology(MIT). Professor Pritchard carried out pioneering experiments on theinteraction of atoms with light that led to the creation of the field ofatom optics. His demonstration of the diffraction of a beam of atomsby a grating made of light waves opened the way to studies of thediffraction, reflection, and focusing of matter waves, similar to thosewith light waves. He has applied atom optics to basic studies ofquantum theory, to new methods for studying the properties ofatoms, and to the creation of devices such as the atom interferometerand atom wave gyroscope.
In 1990, he brought Wolfgang Ketterle to MIT as a postdoctoralresearcher to work on atom cooling, and stepped aside from thatfield to allow Ketterle to be appointed to the faculty in 1992. Ketterlepursued atom cooling to achieve Bose-Einstein condensation in1995, a discovery for which Ketterle was awarded the Nobel Prize inPhysics in 2001, along with Eric Cornell and Carl Wieman of JILA,Boulder, CO. Professor Pritchard also mentored Eric Cornell, whowas his graduate student.
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Lene Vestergaard Hau, S. E. Harris, Zachary Dutton, Cyrus H. BehrooziLight speed reduction to 17 metres per second in an ultracold atomic gas,Nature 397, 594-598 (18 February 1999).
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We have already argued that for EIT to be effective ineliminating dissipation, the light pulse spectrum shouldbe contained within a relatively narrow transparencywindow [Fig. 1(b)]. A vanishing control beam intensityimplies that the transparency window would become in-finitely narrow and eventually disappear. How can oneavoid loss in such a case? The essence of adiabatic fol-lowing in polaritons is that a dynamic reduction in groupvelocity is accompanied by narrowing of the polaritonfrequency spectrum, such that it is not destroyed even ifvg50. To see why it happens, we note that during theprocess of adiabatic slowing the spatial profile and, inparticular, the spatial width of the wave packet remainsunaffected (see Fig. 3), as long as the group velocityvg(t) is only a function of time (Fleischhauer and Lukin,2002). At the same time, the amplitude of the electricfield gets reduced and its temporal profile is stretcheddue to the reduction of the group velocity.
The spectrum of the signal field is reduced in propor-tion to vg /c;uVu2, i.e., by exactly the same factor as thetransparency bandwidth Dn. Therefore, the conditionsfor adiabatic following are very simple: the entire pulseshould be within the medium at the beginning of thetrapping procedure, and its spectrum should be con-tained within the original transparency window. Onceagain, these conditions are satisfied only if an opticallydense medium (12) is used. It is also worth noting thatthe rate at which the group velocity is turned to zero canbe quite fast, especially if the initial group velocity of thelight pulse is much smaller than c . The adiabaticity con-ditions have been analyzed in detail by Matsko et al.(2001a), and by Fleischhauer and Lukin (2002).
The concept of adiabatic passage in multilevel systemswas first introduced by Oreg et al. (1984) and was ex-perimentally rediscovered by Gaubatz et al. (1990). Itsapplication for quantum state transfer was first pointedout by Parkins et al. (1993). Extensions and detailed
analysis of such techniques were considered by Parkinsand Kimble (1999). Recent experimental progress to-ward implementation of these ideas (Kuhn et al., 2002)should be especially noted. Csesznegi and Grobe (1997)pointed out that the spatial profile of an atomic Ramancoherence can be mirrored into the electromagnetic fieldby coherent scattering, whereas time-varying fields canbe used to create spatially nonhomogeneous matter ex-citations. These techniques were reviewed by Bergmannet al. (1998). There is by now a considerable literatureinvestigating various aspects of storage in atomic en-sembles (Juzelinas and Carmichael, 2002; Mewes andFleischauer, 2002) as well as nonclassical light genera-tion (Poulsen and Molmer, 2001) using these techniques.See also the review by Fleischhauer and Mewes (2001).
Finally, it should be remarked here that the essentialpoint of this technique is not to store the energy or mo-mentum carried by photons but their quantum states. Infact, in practice almost no energy or momentum is actu-ally stored in the EIT medium. Instead, both are beingtransferred into (or borrowed from) the control beam insuch a way that an entire optical pulse is coherently con-verted into a low-energy spin wave. This is the key fea-ture that distinguishes the present approach from earlierstudies in optics [involving, e.g., traditional photon echotechniques (Boyd, 1992) or nuclear physics (Shvydkoet al., 1996)], and that enables potential applications inquantum information science. A different proposal to‘‘freeze’’ light pulses in a moving medium was suggestedby Kocharovskaya et al. (2001) and the possibility to ob-serve phenomena resembling black holes was consid-ered by Leonhardt (2001).
E. Collective enhancement and stored states
The above considerations indicate that, in principle,complete storage and retrieval of the input state is pos-
FIG. 3. A dark-state polariton can be stoppedand reaccelerated by ramping the control fieldintensity, as shown in (a). The coherent am-plitudes of the polariton C, the electric fieldE , and the spin components s are plotted in(b)–(d).
462 M. D. Lukin: Colloquium: Trapping and manipulating photon states in atomic ensembles
Rev. Mod. Phys., Vol. 75, No. 2, April 2003
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M§§÷?ÍCÔnÆ£12¤¥IÆEâÆѧ2008§ISBN:978-7-312-01883-1.
B. H. Bransden and C. J. JoachainPhysics of atoms and molecules (2nd Edition)Pearson Education Limited, 2003, ISBN: 0-582-35692-X.
Christopher J. FootAtomic PhysicsOxford University Press, 2005, ISBN:978-0-19-850695-9.
D. A. SteckRubidium 87 D Line Datahttp://steck.us/alkalidata/rubidium87numbers.pdf
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R. Grimm, M. Weidemüller, and Y. B. OvchinnikovOptical Dipole Traps for Neutral AtomsAdvances In Atomic, Molecular, and Optical Physics 42,95 (2000).
VideoW. Ketterle,Ultracold atoms,http://video.mit.edu/watch/bose-einstein-condensates-the-coldest-matter-in-the-universe-9889/