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Blackbody radiation shifts and magic wavelengths for atomic clock research

IEEE-IFCS 2010, Newport Beach, CA. June 2, 2010. Blackbody radiation shifts and magic wavelengths for atomic clock research. Marianna Safronova 1 , M.G. Kozlov 1,2 , Dansha Jiang 1 , and U.I. Safronova 3 1 University of Delaware, USA 2 PNPI, Gatchina, Russia

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Blackbody radiation shifts and magic wavelengths for atomic clock research

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  1. IEEE-IFCS 2010, Newport Beach, CA June 2, 2010 Blackbody radiation shifts and magic wavelengths for atomic clock research Marianna Safronova1, M.G. Kozlov1,2, Dansha Jiang1, and U.I. Safronova3 1University of Delaware, USA 2PNPI, Gatchina, Russia 3University of Nevada, Reno, USA

  2. Outline • Black-body radiation shifts • Microwave vs. Optical transitions • BBR shift in Rb frequency standard • How to calculate its uncertainty? • Development of new methodology for precision calculations of Group II-type system properties • Polarizabilities • Magic wavelengths

  3. Blackbody radiation shifts Level B Clock transition Level A DBBR T = 0 K T = 300 K Transition frequency should be corrected to account for the effect of the black body radiation at T=300K.

  4. atomic clocksblack-body radiation ( BBR ) shift Motivation: BBR shift gives large contribution into uncertainty budget for some of the atomic clock schemes. Accurate calculations are needed to achieve ultimate precision goals.

  5. BBR shift and polarizability BBR shift of atomic level can be expressed in terms of a scalar static polarizability to a good approximation [1]: Dynamic correction Dynamic correction is generally small. Multipolar corrections (M1 and E2) are suppressed by a2 [1]. Vector & tensor polarizability average out due to the isotropic nature of field. [1] Sergey Porsev and Andrei Derevianko, Physical Review A 74, 020502R (2006)

  6. microWave transitions optical transitions Cs Sr+ 6s F=4 4d5/2 5s1/2 6s F=3 In lowest (second) order the polarizabilities of ground hyperfine 6s1/2 F=4 and F=3 states are the same. Therefore, the third-order F-dependent polarizability aF (0) has to be calculated. Lowest-order polarizability term terms

  7. BBR shifts for microwave transitions Atom Transition Method Ref. b 7Li 2s (F=2 – F=1) LCCSD[pT] [1] -0.5017  10-14 23Na 3s (F=2 – F=1) LCCSD[pT] [7] -0.5019  10-14 39K 4s (F=2 – F=1) LCCSD[pT] [2] -1.118  10-14 87Rb 5s (F=2 – F=1) CP [3] -1.26(1)  10-14 133Cs 6s (F=3 – F=4) LCCSD[pT] [4] -1.710(6)  10-14 CP [3] -1.70(2)  10-14 Experiment [5] -1.710(3)  10-14 137Ba+ 6s (F=2 – F=1) CP [3] -0.245(2)  10-14 171Yb+ 6s (F=1 – F=0) CP [3] -0.0983  10-14 MBPT3 [6] -0.094(5)  10-14 137Hg+ 6s (F=1 – F=0) CP [3] -0.0102(5)  10-14 [1] W.R. Johnson, U.I. Safronova, A. Derevianko, and M.S. Safronova, PRA 77, 022510 (2008) [2] U.I. Safronova and M.S. Safronova, PRA 78, 052504 (2008) [3] E. J. Angstmann, V.A. Dzuba, and V.V. Flambaum, PRA 74, 023405 (2006) [4] K. Beloy, U.I. Safronova, and A. Derevianko, PRL 97, 040801 (2006) [5] E. Simon, P. Laurent, and A. Clairon, PRA 57, 426 (1998) [6] U.I. Safronova and M.S. Safronova, PRA 79, 022510 (2009) [7] M. S. Safronova et al., IEEE - TUFFC 57, 94 (2010).

  8. BBR shifts for microwave transitions Atom Transition Method Ref. b 7Li 2s (F=2 – F=1) LCCSD[pT] [1] -0.5017  10-14 23Na 3s (F=2 – F=1) LCCSD[pT] [7] -0.5019  10-14 39K 4s (F=2 – F=1) LCCSD[pT] [2] -1.118  10-14 87Rb 5s (F=2 – F=1) CP [3] -1.26(1)  10-14 LCCSD[pT]Present -1.255(4)  10-14 133Cs 6s (F=3 – F=4) LCCSD[pT] [4] -1.710(6)  10-14 CP [3] -1.70(2)  10-14 Experiment [5] -1.710(3)  10-14 137Ba+ 6s (F=2 – F=1) CP [3] -0.245(2)  10-14 171Yb+ 6s (F=1 – F=0) CP [3] -0.0983  10-14 MBPT3 [6] -0.094(5)  10-14 137Hg+ 6s (F=1 – F=0) CP [3] -0.0102(5)  10-14 [1] W.R. Johnson, U.I. Safronova, A. Derevianko, and M.S. Safronova, PRA 77, 022510 (2008) [2] U.I. Safronova and M.S. Safronova, PRA 78, 052504 (2008) [3] E. J. Angstmann, V.A. Dzuba, and V.V. Flambaum, PRA 74, 023405 (2006) [4] K. Beloy, U.I. Safronova, and A. Derevianko, PRL 97, 040801 (2006) [5] E. Simon, P. Laurent, and A. Clairon, PRA 57, 426 (1998) [6] U.I. Safronova and M.S. Safronova, PRA 79, 022510 (2009) [7] M. S. Safronova et al., IEEE - TUFFC 57, 94 (2010).

  9. BBR shift in Rb b = -1.255(4)  10-14 Uncertainty estimate How to determine theoretical uncertainty?

  10. BBR shift in Rb b = -1.255(4)  10-14 Uncertainty estimate How to determine theoretical uncertainty? Scalar Stark shift coefficient

  11. Third-order polarizability calcualtion The third-order static scalar electric-dipole polarizability of the hyperfine level F can be written as: Coefficient Each term involves sums with two electric-dipole and one hyperfine matrix element. The summations in these terms range over core, valence bound and continuum states. Electric-dipole matrix elements Hyperfine matrix elements

  12. Sources of uncertainties • Strategy: dominant terms (m, n=5-12) are calculated with • ``best set’’ matrix elements and experimental energies. • The remaining terms are calculated in Dirac-Hartree-Fock • approximation. • Uncertainty calculation: • Uncertainty of each of the157 matrix elements contributing to dominant terms is estimated. • (2) Uncertainties in all remainders are evaluated.

  13. 157 “Best-set” matrix elements Relativistic all-order matrix elements or experimental data

  14. Uncertainty of the remainders: Term T fast convergence slow convergence 15% of the term T DHF approximation is determined to be accurate to 4% by comparing accurate results for main terms with DHF values. Therefore, we adjust the DHF tail by 4%. Entire adjustment (4%) is taken to be uncertainty in the tail.

  15. Blackbody radiation shifts in optical frequency standards:(1) monovalent systems(2) divalent systems(3) other, more complicated systems Mg, Ca, Zn, Cd, Sr, Al+,In+,Yb, Hg ( ns2 1S0–nsnp3P) Hg+ (5d 106s – 5d 96s2) Yb+ (4f 146s – 4f 136s2)

  16. GOAL of the present project:calculate properties of group II atoms with precision comparable to alkali-metal atoms

  17. Configuration interaction +all-order method CI works for systems with many valence electrons but can not accurately account for core-valence and core-core correlations. All-order (coupled-cluster) method can not accurately describe valence-valence correlation for large systems but accounts well for core-core and core-valence correlations. Therefore, two methods are combined to acquire benefits from both approaches.

  18. CI + ALL-ORDER RESULTS Two-electron binding energies, differences with experiment AtomCI CI + MBPT CI + All-order Mg 1.9% 0.11% 0.03% Ca 4.1% 0.7% 0.3% Zn 8.0% 0.7% 0.4 % Sr 5.2% 1.0% 0.4% Cd 9.6% 1.4% 0.2% Ba 6.4% 1.9% 0.6% Hg 11.8% 2.5% 0.5% Ra 7.3% 2.3% 0.67% Development of a configuration-interaction plus all-order method for atomic calculations, M.S. Safronova, M. G. Kozlov, W.R. Johnson, Dansha Jiang, Phys. Rev. A 80, 012516 (2009).

  19. Cd, Zn, and Sr Polarizabilities, preliminary results (a.u.) *From expt. matrix elements, S. G. Porsev and A. Derevianko, PRA 74, 020502R (2006).

  20. magic wavelength Atom in state B sees potential UB Atom in state A sees potential UA Magic wavelength lmagic is the wavelength for which the optical potential U experienced by an atom is independent on its state

  21. Cd, Zn, Sr, and Hg magic wavelengths, preliminary results (nm) [1] A. D. Ludlow et al., Science 319, 1805 (2008) [2] H. Hachisu et al., Phys. Rev. Lett. 100, 053001 (2008)

  22. Summary of the fractional uncertainties dn/n0 due to BBR shift and the fractional error in the absolute transition frequency induced by the BBR shift uncertainty at T = 300 K in various frequency standards. Present 510-17 M. S. Safronova et al., IEEE - TUFFC 57, 94 (2010).

  23. Conclusion • New BBR shift result for Rb frequency standard is presented. • The new value is accurate to 0.3%. • II. Development of new method for calculating atomic properties of divalent and more complicated systems is reported (work in progress). • Improvement over best present approaches is demonstrated. • Preliminary results for Mg, Zn, Cd, and Sr polarizabilities are presented. • Preliminary results for magic wavelengths in Cd, Zn, and Hg are presented.

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