Photoassociation of ultracold LiRb molecules with short pulses near a Feshbach resonance

Marko Gacesa; Kazuto Noda; Kazuto Noda; Robin C\^{o}t\&#039;{e}

Photoassociation of ultracold LiRb molecules with short pulses near a Feshbach resonance

POSTER

Abstract

Ultracold diatomic molecules prepared in the lowest ro-vibrational state are a required first step in many experimental studies aimed at investigating the properties of cold quantum matter. We propose a novel approach to produce such molecules in a two-color photoassociation experiment with short pulses performed near a Feshbach resonance. Specifically, we report the results of a theoretical investigation of formation of $^6$Li$^{87}$Rb molecules in a magnetic field. We show that the molecular formation rate can be significantly increased if the pump step is performed near a magnetic Feshbach resonance due to the strong coupling between the energetically open and closed hyperfine states. In addition, the dependence of the nodal structure of the total wave function on the magnetic field allows for enhanced control over the shape and position of the wave packet. The proposed approach is applicable to different systems that have accessible Feshbach resonances.

Authors

Marko Gacesa

University of Connecticut - Storrs, Department of Physics, University of Connecticut, Storrs, CT
Kazuto Noda

California Institute of Technology, JILA, National Institute of Standards and Technology and University of Colorado, Department of Physics, Boulder, CO 80309, USA., National Institute of Standards and Technology, Gaithersburg, MD 20899, USA., Lawrence Berkeley National Lab, Department of Physics, National Tsing Hua University, Chemical Sciences Division, Lawrence Berkeley Natl Lab, Chemical Sciences Division, Lawrence Berkeley National Laboratory, Advanced Light Source, Lawrence Berkeley National Laboratory, University of Frankfurt, Department of Physics, Auburn University, J.R. Macdonald Laboratory, Kansas State University, Lawrence Berkeley National Laboratory, Department of Analytical Chemistry, Institute of Chemical Technology, Prague Technick\'{a}, Czech Republic, J.R. Macdonald Laboratory, Department of Physics, Kansas State University, Manhattan, KS 66506, USA, Budapest University of Technology and Economics, ICREA \& Fisica Teorica, Informacio i Fenomens Quantics, Universitat Autonoma de Barcelona, Spain, Department of Physics and Astronmoy and Center for Computation and Technology, Louisiana State University, USA, Ecole Polytechnique de Bruxelles, Universite Libre de Bruxelles, Belgium and Max-Planck Institut fuer Quantenoptik, Germany, LMU Munich, University of Massachusetts Boston, Stony Brook University, Universit\'e Paris 13, Universitat Polit\`ecnica de Catalunya, University of Heidelberg, Aalto University, University of Innsbruck, University of KwaZulu-Natal, Physics Department, Harvard University, USA, Perimeter Institute for Theoretical Physics, Waterloo, Canada and Institute for Quantum Computing, Waterloo, Canada, Columbia University, University of Washington, Kent State Univ, Case Western Reserve Univ, SLAC National Accelerator Laboratory, TU Berlin, University of Southern California, Ultrafast X-ray Science Laboratory, Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States, Northwestern University, Joint Quantum Institute, University of Maryland and National Institute of Standards and Technology, Univ of California - Berkeley, JILA, National Institute of Standards and Technology and University of Colorado, Joint Quantum Institute and the National Institute of Standards and Technology, National Institute of Standards and Technology, JQI, University of Maryland and NIST, College Park, MD 20742, University of Cambridge, Joint Quantum Centre Durham-Newcastle (Durham University), Sandia National Laboratories, Sandia National Labs, University of New Mexico, Technische Universit\"at Kaiserslautern, MPQ \& LMU M{\"u}nchen, 80799 M{\"u}nchen, Germany, MPQ, Max-Planck-Institut f{\"u}r Physik komplexer Systeme, 01187 Dresden, Germany, Laboratoire Charles Fabry - Institut d'Optique, Palaiseau, France, Max-Planck-Institut f{\"u}r Quantenoptik (MPQ), 85748 Garching, Germany, Schulich Faculty of Chemistry, Russell-Berrie Nanotechnology Institute, and Department of Physics, Technion-Israel Institute of Technology, Schulich Faculty of Chemistry, Technion-Israel Institute of Technology, Schulich Faculty of Chemistry and Faculty of Physics, Technion-Israel Institute of Technology, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA, Department of Physics, Auburn University, Auburn, Alabama 36849, Department of Physics, Purdue University, West Lafayette, Indiana 47907, USA, Department of Physics, Auburn University, Auburn, Alabama 36849, USA, Northwest Missouri State University, QUEERI, Doha, Qatar, Georgia State University, University of North Alabama, The Australian National University, IIT-Madras, J. R. Macdonald Laboratory, Department of Physics, Kansas State University, Max-Planck-Institut fur Quantenoptik, Garching, Germany, Ludwig Maximillian University, Munich, Germany, J.R. Macdonald Laboratory, Kansas State University, Manhattan, KS 66506 USA, Department of Physics, Augustana College, Sioux Falls, SD 57197 USA, J.R. Macdonald Laboratory, Physics Department, Kansas State University, Santa Fe Institute, Institute of Applied Physics, Friedrich-Schiller-Universit\"at Jena, CREOL, University of Central Florida, St. Norbert College, University of North Texas, JQI, University of Maryland Dept. of Physics, Dept. of Physics, Pennsylvania State University, Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Univ of Washington, Univ of Maryland-College Park, Tech-X Corp., Univ. Colorado and NIST, NIST, Harvard University, Massachusetts Institute of Technology, Hebrew University, Harvard-Smithsonian Center for Astrophysics, UC Berkeley, Centre for Quantum Technologies, National University of Singapore, Harvard University, Department of Physics, MIT, Department of Physics and Research Laboratory of Electronics, Center for Photonic Innovations and Department of Engineering Science, UEC Tokyo, The University of Electro-Communications, Harvard University Department of Physics, Harvard University School of Engineering and Applied Sciences, University of Basel Department of Physics, No Company Provided, York University, Department of Physics and Astronomy, Oberlin College, Oberlin, OH 44074, Arizona State University, Leibniz-Universitaet Hannover, Pomona College, Argonne National Laboratory, Technische Universit\"at M\"unchen, University of Chicago/Argonne National Laboratory, Argonne National Laboratory/University of Chicago, University of Kentucky, Yale University, University of California, Los Angeles, University of California, San Diego, University of California at Davis, University of Nebraska-Lincoln, University of Windsor, University of Maryland, Joint Quantum Institute, and National Institute of Standards and Technology, Cornell University, Joint Quantum Institute, and National Institute of Standards and Technology, Quantum Theory Project, University of Florida, Gainesville, FL, USA, Birla Institute of Technology and Science Pilani, Hyderabad, India, Simon Fraser University, ETH Zurich, Johann Wolfgang Goethe University Frankfurt and Singapore University of Technology and Design, Johann Wolfgang Goethe University Frankfurt, Washington State University, Creighton University, Joint Quantum Institute (NIST/UMD), Georgia Southern University, University of Colorado, Department of Physics, University of Connecticut, Penn State University, University of Nevada Las Vegas, Emory University, University of Georgia, Duke University, University of Vienna, QEERI, Doha, Qatar, MBI, Berlin, Germany, KSU, Drake Universuty, Drake University, Chemical Sciences Div., Lawrence Berekeley National Laboratory and UC Davis, Dept. of Chemistry, Chemical Sciences Div., Lawrence Berekeley National Laboratory, Universidad Autonoma de Madrid, Dpto. de Quimica Modulo 13, Michigan State University, LPC-CAEN, Argonne National Lab, Space Dynamics Laboraotory, Institut fuer Quantenoptik, Leibniz Universitaet Hannover, JILA and Department of Physics, University of Colorado at Boulder, GIOE, Universidad de Salamanca, University of Delaware, JILA, University of Colorado at Boulder, National Tsing Hua University, Taiwan, CNR - Istituto di Fotonica e Nanotecnologie, INRS-EMT, University of Oxford, Joint Quantum Institute, University of Maryland Department of Physics and National Institute of Standards and Technology, College Park, Maryland 20742, Argonne National Laboratory; University of Chicago, Bethel University, University of Minnesota, University of Toronto, JILA, University of Colorado, University of Bern, Triad Technology Inc., International Atomic Energy Agency, Lawrence Livermore National Laboratory, JILA and University of Colorado at Boulder, Institute of Applied Physics Jena, CREOL, The College of Optics \& Photonics, Institute of Applied Physics, Abbe Center of Photonics, Friedrich-Schiller-Universit\"at Jena, Max-Wien-Platz 1, 07743 Jena, Germany, Max Planck Institute for the Physics of Complex Systems, Dresden, Stanford University, Tsinghua University, Stanford University, Tsinghua University, Tsinghua University, Ohio State University, JILA, NIST, CU-Boulder, CU-Boulder, Rice University, Swinburne University of Technology, Joint Quantum Institute, University of Maryland and NIST, Univ des Saarlandes, University of Wisconsin-Madison, Syracuse University, HRL Laboratories, Joint Quantum Institute, Dept. of Physics, UMD and NIST, College Park, MD 20742, USA, JQI, UMD and NIST, College Park, MD 20742, USA, Dept. of ECE, UMD, College Park, MD 20742, USA, University of Nevada, Reno, MIT, Ohio State University, The University of Chicago, School of Physics and Astronomy, University of Birmingham, JILA, CU-boulder and NIST, University of Wisconsin, Madison, Indiana University, Bloomington, Northrop Grumman Corp., Theoretical Chemistry, PCI, Heidelberg University, Germany, Institute of Theoretical Physics, Charles University in Prague, Czech Republic, Natl Research Council-Canada, Department of Chemistry and Biochemistry, University of Maryland, College Park, MD 20742, 5. Physikalisches Institut, Universit\"{a}t Stuttgart, Pfaffenwaldring 57 D-70550 Stuttgart, Germany, Stanford Univ - Ginzton Lab, Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, Massachusetts 02138, USA, Jagiellonian University and Nicolaus Copernicus University, AGH University of Science and Technology, University of Oklahoma, 5. Physikalisches Institut, Universit\"{a}t Stuttgart, University of Michigan, National Institute of Standards and Technology (NIST) - Boulder, Massachusetts Institute of Technology, Cambridge, MA 02139, USA, Stanford University, Stanford, CA 94305, USA, University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia, Princeton University, University of Pittsburgh, NIST, JQI, and University of Maryland, JILA, University of Colorado at Boulder, Institute for Quantum Electronics, ETH Zurich, Osaka City Univ, Department of Physics and Astronomy and Rice Quantum Institute, Rice University, IUPUI, Carmel High School, Institut f\"ur Quantenoptik, Leibniz Universit\"at Hannover, Institut f\"ur Quantenoptik, Leibniz Universit\"at Hannover; Department of Physics, Sofia University, Key Laboratory of Quantum Information, Physics Department, Indian Institute of Technology Roorkee, Roorkee 247 667, India, Univ of Chicago, University of Chicago, Central Michigan University, College of Optical Sciences, University of Arizona, Tucson, Az, 85721, USA, Beihang University, Southeast University, College of Physics and Electronic Engineering, Shanxi University, Science and Technology on Inertial Laboratory, Beihang University, Institute f{\"u}r Kernphysik, University of Frankfurt, Auburn University, Department of Chemical and Biological Engineering, Drexel University, Philadelphia, Pennsylvania 19104, USA, JILA, NIST and University of Colorado and Department of Physics, University of Colorado, TACC, Vienna University of Technology, Yale University, Department of Physics, York University, Department of Physics and Astronomy, Universitat Innsbruck, Institut fur Experimentalphysik, University of California, Los Angeles, Department of Physics, The University of Melbourne, National University of Defense Technology, Laboratoire Charles Fabry, Institut d'Optique, CNRS, Univ Paris Sud, 2 avenue Augustin Fresnel, 91127 Palaiseau cedex, France, Division of Materials Science, University of Tsukuba, Tsukuba, Japan, ARC Centre of Excellence for Coherent X-Ray Science, University of Melbourne, Melbourne, Australia, Institute of Nuclear Physics, Moscow State University, Moscow, Russia, Department of Physics and Astronomy, Drake University, Des Moines, IA, USA, ARC Centre of Excellence for Coherent X-Ray Science and Australian Attosecond Science Facility, Griffith University, Brisbane, Australia, The University of Texas at Austin, U. Wisconsin Synchrotron Radiation Center, LCLS / SLAC National Accelerator Laboratory, MPQ Garching, Dublin University, European XFEL, Center for Free Electron Laser science/ DESY, NWMSU, The Advanced Light Source, Lawrence Berkeley National Laboratory,, Geothe University Frankfurt, Univ. Giessen, Germany, Hasan Kalyoncu Univ., Sahinbey, Gaziantep, Turkey, Georgia State Univ., Atlanta, USA, Auburn Univ., Alabama, USA, Western Michigan Univ. Kalamazoo, USA, Tbilisi State Univ., Georgia, Univ. of Montana, Missoula, USA, Univ. of Nevada, Reno, USA, ALS, LBNL, Berkeley, USA, JILA, National Institute of Standards and Technology and Department of Physics, University of Colorado, Boulder, Louisiana State Univ - Baton Rouge, Department of Physics, University of Wisconsin, 1150 University Avenue, Madison, Wisconsin 53706, Physics Department, Purdue University, West Lafayette, IN 47907,USA, Department of Physics, University of Connecticut, Storrs, CT 06269, USA, Joint Quantum Institute, University of Maryland, College Park, MD 20742, USA, Drake University and ITAMP, Laboratory of Molecular Fluid Dynamics, Instituto de Estructura de la Materia, CSIC Serrano 121, 28006 Madrid, Spain, Department of Physics \& Astronomy, Rice University, Penn State University at Berks, Clark Atlanta University, ILM Universit\'{e} Lyon 1, Moravian College, Lehigh University, Univ.\ Giessen, Germany, MPIK, Heidelberg, Germany, Columbia Astrophys.\ Lab., New York, Univ.\ of Strathclyde, Glasgow, UK, Kansas State University, University of Wisconsin Stevens Point, Ilia State University, Purdue University, Dept. of Physics \& research center OPTIMAS, University of Kaiserslautern, Germany, Joint Quantum Institute, NIST/University of Maryland, College Park MD, Department of Physics, The Chinese University of Hong Kong, Shatin, Hong Kong, Harvard-MIT Center for Ultracold Atoms, Cambridge, MA 02138, JILA, National Institute of Standards and Technology and the University of Colorado, Boulder, CO 80309, Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 10617, Taiwan, JILA, CU-Boulder, Purdue, School of Physics and Technology, Wuhan University, Wuhan, Hubei 430072, China, NIST - Boulder, NIST - Boulder and Dept. of Physics, University of Colorado, Rice Univ, UC Boulder, Department of Physics and Astronomy and Rice Quantum Institute, Rice University, Houston, TX 77005, Department of Physics, Oklahoma State University, Stillwater, OK 74078, University of Stuttgart, Department of Physics and research center OPTIMAS, University of Kaiserslautern, Germany, JILA, University of Colorado Boulder, University of Gothenburg, Sweden, Denison University, Granville, OH, Carleton College, Carleton College, Rice University, Centre for Optical Quantum Technologies, University of Hamburg, Luruper Chaussee 149, 22761 Hamburg, Department of Physics and Astronomy, University of British Columbia, Department of Chemistry, University of British Columbia, University of Hong Kong, McMaster University, JILA, NIST and University of Colorado at Boulder, JILA, UC Boulder, JILA, University of Colorado and NIST, Department of Physics, Purdue University, JILA, NIST, and the University of Colorado, Boulder, Peking University, JILA, NIST, and University of Colorado, Boulder, NIST, Boulder, JILA, NIST and University of Colorado, Boulder, IQOQI of the Austrian Academy of Sciences, Innsbruck, Austria, JQI, NIST and the University of Maryland, Institute for Quantum Optics and Quantum Information, Austria, JQI, Institute for Quantum Information and Matter, Caltech, JQI (Joint Quantum Institute, University of Maryland Dept. of Physics and NIST), University of Illinois at Urbana-Champaign, University of Hamburg, University of California - Los Angeles, Department of Physics, Harvard University and Harvard-MIT Center for Ultracold Atoms, KMLabs, Inc., Boulder, Colorado 80301, USA, J. R. Macdonald Laboratory, Physics Department, Kansas State University, Manhattan, KS 66506, USA, JILA, NIST and Department of Physics, University of Colorado, Boulder, Colorado, NIST-Boulder, NIST-Boulder and Dept. of Physics, University of Colorado, JILA, Colorado University at Boulder, University of Miami, Coral Gables, Universidad de los Andes, Department of Physics, Purdue Universty, West Lafayette IN 47907, University of Munich, CUNY, Univ of Illinois - Urbana, State Polytechnic University, Florida State University, Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, P. R. China, Max-Planck-Institut f\"ur Quantenoptik, University of Cambridge, United Kingdom, Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, USA and Department of Physics, University of Strathclyde, Glasgow, Scotland, JILA, NIST, Department of Physics, University of Colorado, 440 UCB, Boulder, CO 80309, USA, Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA, LENS, Istituto Nazionale di Ottica-CNR and Dipartimento di Fisica, Universita' di Firenze, LENS, LENS and Dipartimento di Fisica, Universita' di Firenze, LENS and Scuola Normale Superiore, Istituto Nazionale di Ottica-CNR and LENS, JILA, CU Boulder \& NIST, Department of Physics, The Chinese University of Hong Kong, Oklahoma State University, Department of Optical Science and Engineering, Fudan University, Shanghai 200433, China, Max-Planck-Institut fuer Physik komplexer Systeme, Dresden, Germany, Institut de Ciencies Fotoniques, Castelldefels, Spain, University of Ottawa, University of Rostock, Davidson College, Denison University, ATOMKI, Debrecen, Hungary, PTB, Braunschweig, Germany, DESY, Hamburg, Germany, Univ. Frankfurt, Germany, FU Berlin, Germany, Univ. Hamburg, Germany, University of Maryland, College Park, SUNY Stony Brook, NIST, JILA, and University of Colorado at Boulder, College of the Holy Cross, University of Wisconsin Madison, Massachusetts General Hospital, Center for Systems Biology, Department of Physics, University of California, Berkeley, Lawrence Berkeley National Laboratory and Helmholtz Institute, JGU, Mainz, Germany, Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois, Excellence Cluster ``Universe,'' Technische Universit\"{a}t M\"{u}nchen, Garching, Germany, Department of Physics, University of California, Berkeley, California, Instituto de Ci\`encias del Espacio (CSIC-IEEC), Barcelona, Spain, York Univ, NIST - Natl Inst of Stds \& Tech, Lehigh Univ., Bethlehem, PA, Rafik Hariri Univ., Meshref, Lebanon, University of Nebraks-Lincoln, Department of Physics and Astronomy, University of Nebraska, Lincoln, Nebraska 68588-0299, USA, Physics Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA, Department of Physics and Astronomy, Northwestern University, JILA, NIST and the University of Colorado, Boulder, Vienna Center for Quantum Science and Technology, Atominstitut, TU Wien, JILA, University of Colorado, Boulder, JILA, University of CO, Boulder, Harvard, U Hannover, Department of Phyiscs, Duquesne University, Pittsburgh, PA 15282, Max-Planck-Institut f{\"u}r Quantenoptik, Hans-Kopfermann-Stra{\ss}e 1, 85748 Garching, Germany, Max-Planck-Institut f{\"u}r Quantenoptik, Garching, Germany\& LMU M{\"u}nchen, Germany, Amherst College, Colby College, State Key Lab of Precision Spectroscopy, East China Normal University, US Army Rsch Lab - Adelphi, University of Maryland-College Park, ITAMP, University of Connecticut, Department of Physics, Harvard University, Laboratoire Charles Fabry de l'Institut d'Optique, CNRS, Department of Physics and Research Center OPTIMAS, University of Kaiserslautern, Germany, Department of Physics, University of Saarland, Germany, Argonne National Laboratory and University of Chicago, Argonne National Laboratory and Technische Universit\"at M\"unchen, George Mason University, Department of Physics, North Carolina State University, Raleigh, NC 27695, USA, North Carolina State University, University of Southampton, \'Ecole Normale Sup\'erieure, University of Massachusetts Amherst, Physik Department, Technische Universit\"at M\"unchen, U Paris 13, UMass Boston, University of Illinois, University of Peradeniya, Peradeniya, Sri Lanka, Helmholtz-Zentrum Berlin fur Materialien und Energie, D-14109, Berlin, Germany, Western Michigan University, Lawrence Berkeley National Lab, Berkeley, USA, Sophia University, Tokyo, Japan, Jagiellonian University Krakow, Johannes Gutenberg Universitat Mainz, Forschungzentrum Juelich, Max Planck Institute Erlangen, University of Virginia, Institut des Sciences Moleculaires, CNRS, Universite Bordeaux 1, UMR 5255, 33405 Talence, France, Institute fur Laser-Physik, Universitat Hamburg, University of Maryland, ITAMP / Harvard, NTT Basic Research Labs., NTT Secure Platform Labs.
Kazuto Noda

California Institute of Technology, JILA, National Institute of Standards and Technology and University of Colorado, Department of Physics, Boulder, CO 80309, USA., National Institute of Standards and Technology, Gaithersburg, MD 20899, USA., Lawrence Berkeley National Lab, Department of Physics, National Tsing Hua University, Chemical Sciences Division, Lawrence Berkeley Natl Lab, Chemical Sciences Division, Lawrence Berkeley National Laboratory, Advanced Light Source, Lawrence Berkeley National Laboratory, University of Frankfurt, Department of Physics, Auburn University, J.R. Macdonald Laboratory, Kansas State University, Lawrence Berkeley National Laboratory, Department of Analytical Chemistry, Institute of Chemical Technology, Prague Technick\'{a}, Czech Republic, J.R. Macdonald Laboratory, Department of Physics, Kansas State University, Manhattan, KS 66506, USA, Budapest University of Technology and Economics, ICREA \& Fisica Teorica, Informacio i Fenomens Quantics, Universitat Autonoma de Barcelona, Spain, Department of Physics and Astronmoy and Center for Computation and Technology, Louisiana State University, USA, Ecole Polytechnique de Bruxelles, Universite Libre de Bruxelles, Belgium and Max-Planck Institut fuer Quantenoptik, Germany, LMU Munich, University of Massachusetts Boston, Stony Brook University, Universit\'e Paris 13, Universitat Polit\`ecnica de Catalunya, University of Heidelberg, Aalto University, University of Innsbruck, University of KwaZulu-Natal, Physics Department, Harvard University, USA, Perimeter Institute for Theoretical Physics, Waterloo, Canada and Institute for Quantum Computing, Waterloo, Canada, Columbia University, University of Washington, Kent State Univ, Case Western Reserve Univ, SLAC National Accelerator Laboratory, TU Berlin, University of Southern California, Ultrafast X-ray Science Laboratory, Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States, Northwestern University, Joint Quantum Institute, University of Maryland and National Institute of Standards and Technology, Univ of California - Berkeley, JILA, National Institute of Standards and Technology and University of Colorado, Joint Quantum Institute and the National Institute of Standards and Technology, National Institute of Standards and Technology, JQI, University of Maryland and NIST, College Park, MD 20742, University of Cambridge, Joint Quantum Centre Durham-Newcastle (Durham University), Sandia National Laboratories, Sandia National Labs, University of New Mexico, Technische Universit\"at Kaiserslautern, MPQ \& LMU M{\"u}nchen, 80799 M{\"u}nchen, Germany, MPQ, Max-Planck-Institut f{\"u}r Physik komplexer Systeme, 01187 Dresden, Germany, Laboratoire Charles Fabry - Institut d'Optique, Palaiseau, France, Max-Planck-Institut f{\"u}r Quantenoptik (MPQ), 85748 Garching, Germany, Schulich Faculty of Chemistry, Russell-Berrie Nanotechnology Institute, and Department of Physics, Technion-Israel Institute of Technology, Schulich Faculty of Chemistry, Technion-Israel Institute of Technology, Schulich Faculty of Chemistry and Faculty of Physics, Technion-Israel Institute of Technology, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA, Department of Physics, Auburn University, Auburn, Alabama 36849, Department of Physics, Purdue University, West Lafayette, Indiana 47907, USA, Department of Physics, Auburn University, Auburn, Alabama 36849, USA, Northwest Missouri State University, QUEERI, Doha, Qatar, Georgia State University, University of North Alabama, The Australian National University, IIT-Madras, J. R. Macdonald Laboratory, Department of Physics, Kansas State University, Max-Planck-Institut fur Quantenoptik, Garching, Germany, Ludwig Maximillian University, Munich, Germany, J.R. Macdonald Laboratory, Kansas State University, Manhattan, KS 66506 USA, Department of Physics, Augustana College, Sioux Falls, SD 57197 USA, J.R. Macdonald Laboratory, Physics Department, Kansas State University, Santa Fe Institute, Institute of Applied Physics, Friedrich-Schiller-Universit\"at Jena, CREOL, University of Central Florida, St. Norbert College, University of North Texas, JQI, University of Maryland Dept. of Physics, Dept. of Physics, Pennsylvania State University, Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Univ of Washington, Univ of Maryland-College Park, Tech-X Corp., Univ. Colorado and NIST, NIST, Harvard University, Massachusetts Institute of Technology, Hebrew University, Harvard-Smithsonian Center for Astrophysics, UC Berkeley, Centre for Quantum Technologies, National University of Singapore, Harvard University, Department of Physics, MIT, Department of Physics and Research Laboratory of Electronics, Center for Photonic Innovations and Department of Engineering Science, UEC Tokyo, The University of Electro-Communications, Harvard University Department of Physics, Harvard University School of Engineering and Applied Sciences, University of Basel Department of Physics, No Company Provided, York University, Department of Physics and Astronomy, Oberlin College, Oberlin, OH 44074, Arizona State University, Leibniz-Universitaet Hannover, Pomona College, Argonne National Laboratory, Technische Universit\"at M\"unchen, University of Chicago/Argonne National Laboratory, Argonne National Laboratory/University of Chicago, University of Kentucky, Yale University, University of California, Los Angeles, University of California, San Diego, University of California at Davis, University of Nebraska-Lincoln, University of Windsor, University of Maryland, Joint Quantum Institute, and National Institute of Standards and Technology, Cornell University, Joint Quantum Institute, and National Institute of Standards and Technology, Quantum Theory Project, University of Florida, Gainesville, FL, USA, Birla Institute of Technology and Science Pilani, Hyderabad, India, Simon Fraser University, ETH Zurich, Johann Wolfgang Goethe University Frankfurt and Singapore University of Technology and Design, Johann Wolfgang Goethe University Frankfurt, Washington State University, Creighton University, Joint Quantum Institute (NIST/UMD), Georgia Southern University, University of Colorado, Department of Physics, University of Connecticut, Penn State University, University of Nevada Las Vegas, Emory University, University of Georgia, Duke University, University of Vienna, QEERI, Doha, Qatar, MBI, Berlin, Germany, KSU, Drake Universuty, Drake University, Chemical Sciences Div., Lawrence Berekeley National Laboratory and UC Davis, Dept. of Chemistry, Chemical Sciences Div., Lawrence Berekeley National Laboratory, Universidad Autonoma de Madrid, Dpto. de Quimica Modulo 13, Michigan State University, LPC-CAEN, Argonne National Lab, Space Dynamics Laboraotory, Institut fuer Quantenoptik, Leibniz Universitaet Hannover, JILA and Department of Physics, University of Colorado at Boulder, GIOE, Universidad de Salamanca, University of Delaware, JILA, University of Colorado at Boulder, National Tsing Hua University, Taiwan, CNR - Istituto di Fotonica e Nanotecnologie, INRS-EMT, University of Oxford, Joint Quantum Institute, University of Maryland Department of Physics and National Institute of Standards and Technology, College Park, Maryland 20742, Argonne National Laboratory; University of Chicago, Bethel University, University of Minnesota, University of Toronto, JILA, University of Colorado, University of Bern, Triad Technology Inc., International Atomic Energy Agency, Lawrence Livermore National Laboratory, JILA and University of Colorado at Boulder, Institute of Applied Physics Jena, CREOL, The College of Optics \& Photonics, Institute of Applied Physics, Abbe Center of Photonics, Friedrich-Schiller-Universit\"at Jena, Max-Wien-Platz 1, 07743 Jena, Germany, Max Planck Institute for the Physics of Complex Systems, Dresden, Stanford University, Tsinghua University, Stanford University, Tsinghua University, Tsinghua University, Ohio State University, JILA, NIST, CU-Boulder, CU-Boulder, Rice University, Swinburne University of Technology, Joint Quantum Institute, University of Maryland and NIST, Univ des Saarlandes, University of Wisconsin-Madison, Syracuse University, HRL Laboratories, Joint Quantum Institute, Dept. of Physics, UMD and NIST, College Park, MD 20742, USA, JQI, UMD and NIST, College Park, MD 20742, USA, Dept. of ECE, UMD, College Park, MD 20742, USA, University of Nevada, Reno, MIT, Ohio State University, The University of Chicago, School of Physics and Astronomy, University of Birmingham, JILA, CU-boulder and NIST, University of Wisconsin, Madison, Indiana University, Bloomington, Northrop Grumman Corp., Theoretical Chemistry, PCI, Heidelberg University, Germany, Institute of Theoretical Physics, Charles University in Prague, Czech Republic, Natl Research Council-Canada, Department of Chemistry and Biochemistry, University of Maryland, College Park, MD 20742, 5. Physikalisches Institut, Universit\"{a}t Stuttgart, Pfaffenwaldring 57 D-70550 Stuttgart, Germany, Stanford Univ - Ginzton Lab, Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, Massachusetts 02138, USA, Jagiellonian University and Nicolaus Copernicus University, AGH University of Science and Technology, University of Oklahoma, 5. Physikalisches Institut, Universit\"{a}t Stuttgart, University of Michigan, National Institute of Standards and Technology (NIST) - Boulder, Massachusetts Institute of Technology, Cambridge, MA 02139, USA, Stanford University, Stanford, CA 94305, USA, University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia, Princeton University, University of Pittsburgh, NIST, JQI, and University of Maryland, JILA, University of Colorado at Boulder, Institute for Quantum Electronics, ETH Zurich, Osaka City Univ, Department of Physics and Astronomy and Rice Quantum Institute, Rice University, IUPUI, Carmel High School, Institut f\"ur Quantenoptik, Leibniz Universit\"at Hannover, Institut f\"ur Quantenoptik, Leibniz Universit\"at Hannover; Department of Physics, Sofia University, Key Laboratory of Quantum Information, Physics Department, Indian Institute of Technology Roorkee, Roorkee 247 667, India, Univ of Chicago, University of Chicago, Central Michigan University, College of Optical Sciences, University of Arizona, Tucson, Az, 85721, USA, Beihang University, Southeast University, College of Physics and Electronic Engineering, Shanxi University, Science and Technology on Inertial Laboratory, Beihang University, Institute f{\"u}r Kernphysik, University of Frankfurt, Auburn University, Department of Chemical and Biological Engineering, Drexel University, Philadelphia, Pennsylvania 19104, USA, JILA, NIST and University of Colorado and Department of Physics, University of Colorado, TACC, Vienna University of Technology, Yale University, Department of Physics, York University, Department of Physics and Astronomy, Universitat Innsbruck, Institut fur Experimentalphysik, University of California, Los Angeles, Department of Physics, The University of Melbourne, National University of Defense Technology, Laboratoire Charles Fabry, Institut d'Optique, CNRS, Univ Paris Sud, 2 avenue Augustin Fresnel, 91127 Palaiseau cedex, France, Division of Materials Science, University of Tsukuba, Tsukuba, Japan, ARC Centre of Excellence for Coherent X-Ray Science, University of Melbourne, Melbourne, Australia, Institute of Nuclear Physics, Moscow State University, Moscow, Russia, Department of Physics and Astronomy, Drake University, Des Moines, IA, USA, ARC Centre of Excellence for Coherent X-Ray Science and Australian Attosecond Science Facility, Griffith University, Brisbane, Australia, The University of Texas at Austin, U. Wisconsin Synchrotron Radiation Center, LCLS / SLAC National Accelerator Laboratory, MPQ Garching, Dublin University, European XFEL, Center for Free Electron Laser science/ DESY, NWMSU, The Advanced Light Source, Lawrence Berkeley National Laboratory,, Geothe University Frankfurt, Univ. Giessen, Germany, Hasan Kalyoncu Univ., Sahinbey, Gaziantep, Turkey, Georgia State Univ., Atlanta, USA, Auburn Univ., Alabama, USA, Western Michigan Univ. Kalamazoo, USA, Tbilisi State Univ., Georgia, Univ. of Montana, Missoula, USA, Univ. of Nevada, Reno, USA, ALS, LBNL, Berkeley, USA, JILA, National Institute of Standards and Technology and Department of Physics, University of Colorado, Boulder, Louisiana State Univ - Baton Rouge, Department of Physics, University of Wisconsin, 1150 University Avenue, Madison, Wisconsin 53706, Physics Department, Purdue University, West Lafayette, IN 47907,USA, Department of Physics, University of Connecticut, Storrs, CT 06269, USA, Joint Quantum Institute, University of Maryland, College Park, MD 20742, USA, Drake University and ITAMP, Laboratory of Molecular Fluid Dynamics, Instituto de Estructura de la Materia, CSIC Serrano 121, 28006 Madrid, Spain, Department of Physics \& Astronomy, Rice University, Penn State University at Berks, Clark Atlanta University, ILM Universit\'{e} Lyon 1, Moravian College, Lehigh University, Univ.\ Giessen, Germany, MPIK, Heidelberg, Germany, Columbia Astrophys.\ Lab., New York, Univ.\ of Strathclyde, Glasgow, UK, Kansas State University, University of Wisconsin Stevens Point, Ilia State University, Purdue University, Dept. of Physics \& research center OPTIMAS, University of Kaiserslautern, Germany, Joint Quantum Institute, NIST/University of Maryland, College Park MD, Department of Physics, The Chinese University of Hong Kong, Shatin, Hong Kong, Harvard-MIT Center for Ultracold Atoms, Cambridge, MA 02138, JILA, National Institute of Standards and Technology and the University of Colorado, Boulder, CO 80309, Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 10617, Taiwan, JILA, CU-Boulder, Purdue, School of Physics and Technology, Wuhan University, Wuhan, Hubei 430072, China, NIST - Boulder, NIST - Boulder and Dept. of Physics, University of Colorado, Rice Univ, UC Boulder, Department of Physics and Astronomy and Rice Quantum Institute, Rice University, Houston, TX 77005, Department of Physics, Oklahoma State University, Stillwater, OK 74078, University of Stuttgart, Department of Physics and research center OPTIMAS, University of Kaiserslautern, Germany, JILA, University of Colorado Boulder, University of Gothenburg, Sweden, Denison University, Granville, OH, Carleton College, Carleton College, Rice University, Centre for Optical Quantum Technologies, University of Hamburg, Luruper Chaussee 149, 22761 Hamburg, Department of Physics and Astronomy, University of British Columbia, Department of Chemistry, University of British Columbia, University of Hong Kong, McMaster University, JILA, NIST and University of Colorado at Boulder, JILA, UC Boulder, JILA, University of Colorado and NIST, Department of Physics, Purdue University, JILA, NIST, and the University of Colorado, Boulder, Peking University, JILA, NIST, and University of Colorado, Boulder, NIST, Boulder, JILA, NIST and University of Colorado, Boulder, IQOQI of the Austrian Academy of Sciences, Innsbruck, Austria, JQI, NIST and the University of Maryland, Institute for Quantum Optics and Quantum Information, Austria, JQI, Institute for Quantum Information and Matter, Caltech, JQI (Joint Quantum Institute, University of Maryland Dept. of Physics and NIST), University of Illinois at Urbana-Champaign, University of Hamburg, University of California - Los Angeles, Department of Physics, Harvard University and Harvard-MIT Center for Ultracold Atoms, KMLabs, Inc., Boulder, Colorado 80301, USA, J. R. Macdonald Laboratory, Physics Department, Kansas State University, Manhattan, KS 66506, USA, JILA, NIST and Department of Physics, University of Colorado, Boulder, Colorado, NIST-Boulder, NIST-Boulder and Dept. of Physics, University of Colorado, JILA, Colorado University at Boulder, University of Miami, Coral Gables, Universidad de los Andes, Department of Physics, Purdue Universty, West Lafayette IN 47907, University of Munich, CUNY, Univ of Illinois - Urbana, State Polytechnic University, Florida State University, Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, P. R. China, Max-Planck-Institut f\"ur Quantenoptik, University of Cambridge, United Kingdom, Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, USA and Department of Physics, University of Strathclyde, Glasgow, Scotland, JILA, NIST, Department of Physics, University of Colorado, 440 UCB, Boulder, CO 80309, USA, Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA, LENS, Istituto Nazionale di Ottica-CNR and Dipartimento di Fisica, Universita' di Firenze, LENS, LENS and Dipartimento di Fisica, Universita' di Firenze, LENS and Scuola Normale Superiore, Istituto Nazionale di Ottica-CNR and LENS, JILA, CU Boulder \& NIST, Department of Physics, The Chinese University of Hong Kong, Oklahoma State University, Department of Optical Science and Engineering, Fudan University, Shanghai 200433, China, Max-Planck-Institut fuer Physik komplexer Systeme, Dresden, Germany, Institut de Ciencies Fotoniques, Castelldefels, Spain, University of Ottawa, University of Rostock, Davidson College, Denison University, ATOMKI, Debrecen, Hungary, PTB, Braunschweig, Germany, DESY, Hamburg, Germany, Univ. Frankfurt, Germany, FU Berlin, Germany, Univ. Hamburg, Germany, University of Maryland, College Park, SUNY Stony Brook, NIST, JILA, and University of Colorado at Boulder, College of the Holy Cross, University of Wisconsin Madison, Massachusetts General Hospital, Center for Systems Biology, Department of Physics, University of California, Berkeley, Lawrence Berkeley National Laboratory and Helmholtz Institute, JGU, Mainz, Germany, Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois, Excellence Cluster ``Universe,'' Technische Universit\"{a}t M\"{u}nchen, Garching, Germany, Department of Physics, University of California, Berkeley, California, Instituto de Ci\`encias del Espacio (CSIC-IEEC), Barcelona, Spain, York Univ, NIST - Natl Inst of Stds \& Tech, Lehigh Univ., Bethlehem, PA, Rafik Hariri Univ., Meshref, Lebanon, University of Nebraks-Lincoln, Department of Physics and Astronomy, University of Nebraska, Lincoln, Nebraska 68588-0299, USA, Physics Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA, Department of Physics and Astronomy, Northwestern University, JILA, NIST and the University of Colorado, Boulder, Vienna Center for Quantum Science and Technology, Atominstitut, TU Wien, JILA, University of Colorado, Boulder, JILA, University of CO, Boulder, Harvard, U Hannover, Department of Phyiscs, Duquesne University, Pittsburgh, PA 15282, Max-Planck-Institut f{\"u}r Quantenoptik, Hans-Kopfermann-Stra{\ss}e 1, 85748 Garching, Germany, Max-Planck-Institut f{\"u}r Quantenoptik, Garching, Germany\& LMU M{\"u}nchen, Germany, Amherst College, Colby College, State Key Lab of Precision Spectroscopy, East China Normal University, US Army Rsch Lab - Adelphi, University of Maryland-College Park, ITAMP, University of Connecticut, Department of Physics, Harvard University, Laboratoire Charles Fabry de l'Institut d'Optique, CNRS, Department of Physics and Research Center OPTIMAS, University of Kaiserslautern, Germany, Department of Physics, University of Saarland, Germany, Argonne National Laboratory and University of Chicago, Argonne National Laboratory and Technische Universit\"at M\"unchen, George Mason University, Department of Physics, North Carolina State University, Raleigh, NC 27695, USA, North Carolina State University, University of Southampton, \'Ecole Normale Sup\'erieure, University of Massachusetts Amherst, Physik Department, Technische Universit\"at M\"unchen, U Paris 13, UMass Boston, University of Illinois, University of Peradeniya, Peradeniya, Sri Lanka, Helmholtz-Zentrum Berlin fur Materialien und Energie, D-14109, Berlin, Germany, Western Michigan University, Lawrence Berkeley National Lab, Berkeley, USA, Sophia University, Tokyo, Japan, Jagiellonian University Krakow, Johannes Gutenberg Universitat Mainz, Forschungzentrum Juelich, Max Planck Institute Erlangen, University of Virginia, Institut des Sciences Moleculaires, CNRS, Universite Bordeaux 1, UMR 5255, 33405 Talence, France, Institute fur Laser-Physik, Universitat Hamburg, University of Maryland, ITAMP / Harvard, NTT Basic Research Labs., NTT Secure Platform Labs.
Robin C\^{o}t\'{e}

University of Connecticut - Storrs, Department of Physics, University of Connecticut, Storrs, CT, University of Connecticut, Storrs