Blackbody-radiation shifts in optical frequency standards with trapped ions

ORAL

Abstract

The SI unit of time, the second, is defined in terms of the microwave transition frequency between the two hyperfine levels of the ground state of $^{133}$Cs. Recent advancements in experimental techniques such as laser frequency stabilization, atomic cooling and trapping, etc. have made possible the realization of the second to a precision that is six decades higher than that of the existing standard, by use of optical {\it v.s.} microwave transitions. At optical frequencies, the transition levels are members of different electronic configurations, and one of the largest contributors to the uncertainty budget is the blackbody radiation (BBR) frequency shift. We report BBR shifts of the Ca$^+ 4s - 3d_{5/2}$ and Sr$^+ 5s - 4d_{5/2}$ clock transitions as calculated by the relativistic all-order method, in which all single and double excitations of the Dirac-Fock wave function are included to all orders of perturbation theory. Additional calculations are conducted for the dominant contributions in order to evaluate some omitted high-order corrections and estimate the uncertainty of our final values. Our results for these shifts are an order of magnitude more accurate than previous estimates and are of sufficient accuracy at the present stage of development of trapped-ion optical frequency standards.

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Authors

  • Kawtar Hafidi

    Curry School of Education, University of Virginia, Department of Engineering and Science Education, and Department of Mathematical Sciences, Clemson University, Wayne State University, Rutgers University, University of New Mexico, ANL, JAEA, ORNL, McGill U., Northwestern U., U. of Manitoba, U. of Chicago, McGill, TUM, Maryland, LLNL, Yale, Chicago, Northwestern, Manitoba, University of Kentucky, Colorado School of Mines, University of Tennessee, Ohio University, Louisiana State University, Oak Ridge National Laboratory, Oak Ridge Associated Universities, Los Alamos National Laboratory, University of Illinois, C.U., Southern Methodist University, Osaka City University, Department of Physics, Southern Methodist University, NIST, NASA GSFC, University of Maryland, Institute of Physics of the University of S\~ao Paulo, Polytechnic School of the University of S\~ao Paulo, Physics Department, University of Maryland, University of Washington, Universit\`a di Roma Tor Vergata, MIT, Columbia University, California State University Long Beach, Loyola University Chicago, Longwood University, American Institute of Physics/Society of Physics Students, Texas Christian University, University of Minnesota, Washington State University, Jet Propulsion Laboratory and LIGO, Caltech; Observatoire de la Cote d'Azur, The University of Texas at Brownsville, LIGO Caltech, University of Florida, University of Texas at Brownsville, University of Chicago, Fermilab, Ohio State University, University of Hawaii-Manoa, SLAC, University of Science and Technology of China, Indiana University, Michigan State University, University of Kansas, University of South Carolina, College of William and Mary, University of California, Berkeley, Universite Bordeaux, CNRS/IN2P3, Universite Libre de Bruxelles, Cornell University, University of Illinois at Urbana-Champaign, Bowdoin College, Brunswick, ME, Canadian Institute for Theoretical Astrophysics, HEPHY Vienna, CERN, Vanderbuilt University, Princeton University, Duke University, University of Wisconsin, Stockholm University, Santa Clara University, Stanford, University of California Berkeley, Department of Chemistry, Stony Brook University, Retired Chairman and CEO, Lockheed Martin Corporation, Universidad Nacional Autonoma de Mexico, State University of New York at Buffalo, Hope College, University of Wisconsin - River Falls, Sciprint.org, Inha University, APS President and Princeton University, Drexel University, Laboratory for Physical Sciences, University of Maryland, Joint Quantum Institute, Tokyo University of Science, UNAM, Rowan University, Duke U., Temple U./Jefferson Lab, U. of Virginia, U. of Saskatchewan, Insitute of Modern Physics, CAS, TUNL/Duke, University of Notre Dame, Yale University, Hofstra University, Texas A\&M University, Indiana Univeristy, Al-Farabi Kazakh National University, Joint Institute for Nuclear Reserach, Georgia State University, North Carolina Central University, North Carolina State University, Gettysburg College, National Institute of Standards and Technology, The George Washington University, Indiana University/IUCF, Joint Institute for Nuclear Research, George Washington University, North Carolina State University/TUNL, IUCF/NIST, Georga State University, National Institute of Standards and Technology NIST, ORAU, TTU, Rutgers, CO School of Mines, UTK, University of Naples and INFN Naples, Italy, Second University of Naples and INFN Naples, Italy, NASA Goddard Space Flight Center, 8800 Greenbelt Rd., Greenbelt, MD 20771, Rudolph Peierls Center for Theoretical Physics, Oxford University, UCSD, Boston University, JAEA, 1233 Watanuki, Takasaki, Gunma 370-1292, Japan, IMR, Tohoku University, 2-1-1 Katahira, Sendai 980-8577, Japan, ADMX Collaboration, ADMX collaboration, Argonne National Laboratory, The Algebra Project, American Association for the Advancement of Science, Acting Executive Officer of the Education and Human Resources Directorate, NSF, University of Michigan, Tulane Univ., Univ. of Wisconsin Madison, NIST; Indiana Univ., Univ. of North Carolina at Wilmington, UNC-Wilmington, Tulane U., University of Delaware, ITER Cadarache Joint Work Site, Lawrence Livermore National Laboratory, George E. Wahlen Department of Veterans Affairs Medical Center, Harvard-Smithsonian Center for Astrophysics, Harvard-Smithsonian Center for Asstrophysics, Bethel College, Kansas, Wheaton College, Wheaton, IL USA, Pr, Dr, Superconix Inc, University of Maryland, Universidad de la Republica, Montevideo. Uruguay, Univ. Paris Diderot, Univ. Pierre et Marie Curie, University of Jena, University of Wisconsin -- Milwaukee, NASA Goddard Space Flight Center, U. of Connecticut, Jefferson Lab, Los Alamos National Lab, Departments of Chemisitry and Physics University of Rochester, Cyclotron Institute, Texas A\&M University, Texas A\&M University, College Station, Texas, IN2P3 Orsay, France, A. Soltan Institute for Nuclear Studies, Warsaw, Poland, Department of Physics, Florida State University, University of Manchester, Manchester, Bonn University, Commissioner for Human Resources, Science and Technology, African Union Headquarters, NASA GSFC, U.C. Berkeley, Stanford University, Caltech, Brandeis, BU, UPenn

  • Kawtar Hafidi

    Curry School of Education, University of Virginia, Department of Engineering and Science Education, and Department of Mathematical Sciences, Clemson University, Wayne State University, Rutgers University, University of New Mexico, ANL, JAEA, ORNL, McGill U., Northwestern U., U. of Manitoba, U. of Chicago, McGill, TUM, Maryland, LLNL, Yale, Chicago, Northwestern, Manitoba, University of Kentucky, Colorado School of Mines, University of Tennessee, Ohio University, Louisiana State University, Oak Ridge National Laboratory, Oak Ridge Associated Universities, Los Alamos National Laboratory, University of Illinois, C.U., Southern Methodist University, Osaka City University, Department of Physics, Southern Methodist University, NIST, NASA GSFC, University of Maryland, Institute of Physics of the University of S\~ao Paulo, Polytechnic School of the University of S\~ao Paulo, Physics Department, University of Maryland, University of Washington, Universit\`a di Roma Tor Vergata, MIT, Columbia University, California State University Long Beach, Loyola University Chicago, Longwood University, American Institute of Physics/Society of Physics Students, Texas Christian University, University of Minnesota, Washington State University, Jet Propulsion Laboratory and LIGO, Caltech; Observatoire de la Cote d'Azur, The University of Texas at Brownsville, LIGO Caltech, University of Florida, University of Texas at Brownsville, University of Chicago, Fermilab, Ohio State University, University of Hawaii-Manoa, SLAC, University of Science and Technology of China, Indiana University, Michigan State University, University of Kansas, University of South Carolina, College of William and Mary, University of California, Berkeley, Universite Bordeaux, CNRS/IN2P3, Universite Libre de Bruxelles, Cornell University, University of Illinois at Urbana-Champaign, Bowdoin College, Brunswick, ME, Canadian Institute for Theoretical Astrophysics, HEPHY Vienna, CERN, Vanderbuilt University, Princeton University, Duke University, University of Wisconsin, Stockholm University, Santa Clara University, Stanford, University of California Berkeley, Department of Chemistry, Stony Brook University, Retired Chairman and CEO, Lockheed Martin Corporation, Universidad Nacional Autonoma de Mexico, State University of New York at Buffalo, Hope College, University of Wisconsin - River Falls, Sciprint.org, Inha University, APS President and Princeton University, Drexel University, Laboratory for Physical Sciences, University of Maryland, Joint Quantum Institute, Tokyo University of Science, UNAM, Rowan University, Duke U., Temple U./Jefferson Lab, U. of Virginia, U. of Saskatchewan, Insitute of Modern Physics, CAS, TUNL/Duke, University of Notre Dame, Yale University, Hofstra University, Texas A\&M University, Indiana Univeristy, Al-Farabi Kazakh National University, Joint Institute for Nuclear Reserach, Georgia State University, North Carolina Central University, North Carolina State University, Gettysburg College, National Institute of Standards and Technology, The George Washington University, Indiana University/IUCF, Joint Institute for Nuclear Research, George Washington University, North Carolina State University/TUNL, IUCF/NIST, Georga State University, National Institute of Standards and Technology NIST, ORAU, TTU, Rutgers, CO School of Mines, UTK, University of Naples and INFN Naples, Italy, Second University of Naples and INFN Naples, Italy, NASA Goddard Space Flight Center, 8800 Greenbelt Rd., Greenbelt, MD 20771, Rudolph Peierls Center for Theoretical Physics, Oxford University, UCSD, Boston University, JAEA, 1233 Watanuki, Takasaki, Gunma 370-1292, Japan, IMR, Tohoku University, 2-1-1 Katahira, Sendai 980-8577, Japan, ADMX Collaboration, ADMX collaboration, Argonne National Laboratory, The Algebra Project, American Association for the Advancement of Science, Acting Executive Officer of the Education and Human Resources Directorate, NSF, University of Michigan, Tulane Univ., Univ. of Wisconsin Madison, NIST; Indiana Univ., Univ. of North Carolina at Wilmington, UNC-Wilmington, Tulane U., University of Delaware, ITER Cadarache Joint Work Site, Lawrence Livermore National Laboratory, George E. Wahlen Department of Veterans Affairs Medical Center, Harvard-Smithsonian Center for Astrophysics, Harvard-Smithsonian Center for Asstrophysics, Bethel College, Kansas, Wheaton College, Wheaton, IL USA, Pr, Dr, Superconix Inc, University of Maryland, Universidad de la Republica, Montevideo. Uruguay, Univ. Paris Diderot, Univ. Pierre et Marie Curie, University of Jena, University of Wisconsin -- Milwaukee, NASA Goddard Space Flight Center, U. of Connecticut, Jefferson Lab, Los Alamos National Lab, Departments of Chemisitry and Physics University of Rochester, Cyclotron Institute, Texas A\&M University, Texas A\&M University, College Station, Texas, IN2P3 Orsay, France, A. Soltan Institute for Nuclear Studies, Warsaw, Poland, Department of Physics, Florida State University, University of Manchester, Manchester, Bonn University, Commissioner for Human Resources, Science and Technology, African Union Headquarters, NASA GSFC, U.C. Berkeley, Stanford University, Caltech, Brandeis, BU, UPenn

  • Marianna Safronova

    University of Delaware

  • Charles W. Clark

    Joint Quantum Institute, National Institute of Standards and Technology and University of Maryland