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Atomic Calculations for Future Technology and Study of Fundamental Problems

ICCMSE 2009 RHODES, GREECE. October 30, 2009. Atomic Calculations for Future Technology and Study of Fundamental Problems. Marianna Safronova. Outline. Selected applications of atomic calculations Study of fundamental symmetries: parity violation Quantum information Atomic clocks

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Atomic Calculations for Future Technology and Study of Fundamental Problems

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  1. ICCMSE 2009 RHODES, GREECE October 30, 2009 Atomic Calculations for Future Technology and Study of Fundamental Problems Marianna Safronova

  2. Outline • Selected applications of atomic calculations • Study of fundamental symmetries: parity violation • Quantum information • Atomic clocks • Methods for high-precision atomic calculations • Overview • Computational challenges • Evaluation of the uncertainty • Development of the LCCSD + CI method • Future prospects

  3. study of Fundamental symmetries Parity violation studies with heavy atoms & search for Electron electric-dipole moment

  4. r  ─ r Parity Violation Parity-transformed world: Turn the mirror image upside down. The parity-transformed world is not identical with the real world. Parity is not conserved.

  5. Searches for New Physics Beyond the Standard Model High energies (1) Search for new processes or particles directly (2) Study (very precisely!) quantities which Standard Model predicts and compare the result with its prediction Weak charge QW Low energies http://public.web.cern.ch/, Cs experiment, University of Colorado

  6. F=4 7s F=3 2 1 F=4 6s F=3 The most precise measurement of PNC amplitude (in cesium) C.S. Wood et al. Science 275, 1759 (1997) 1 0.3% accuracy 2 Stark interference scheme to measure ratio of the PNC amplitude and the Stark-induced amplitude b

  7. a e q Z0 e q Parity violation Nuclear spin-independent PNC: Searches for new physics beyond the Standard Model Nuclear spin-dependent PNC: Study of PNC In the nucleus Nuclear anapole moment Weak Charge QW

  8. F=4 7s F=3 2 1 F=4 6s F=3 Analysis of CS PNC experiment Nuclear spin-dependent PNC Nuclear spin-independent PNC 7s 6s Difference of 1 & 2 Average of 1 & 2 Weak Charge QW Nuclear anapole moment

  9. F=4 7s F=3 2 1 F=4 6s a F=3 Spin-dependent parity violation: Nuclear anapole moment Valence nucleon density Parity-violating nuclear moment Anapole moment Nuclear anapole moment is parity-odd, time-reversal-even E1 moment of the electromagnetic current operator.

  10. Constraints on nuclear weak coupling contants W. C. Haxton and C. E. Wieman, Ann. Rev. Nucl. Part. Sci. 51, 261 (2001)

  11. Nuclear anapole moment:test of hadronic weak interations The constraints obtained from the Cs experiment were found to be inconsistent with constraints from other nuclear PNC measurements, which favor a smaller value of the133Cs anapole moment. All-order (LCCSD) calculation ofspin-dependent PNC amplitude: k = 0.107(16)* [ 1% theory accuracy ] No significant difference with previous value k = 0.112(16) is found. NEED NEW EXPERIMENTS!!! *M.S. Safronova, Rupsi Pal, Dansha Jiang, M.G. Kozlov, W.R. Johnson, and U.I. Safronova, Nuclear Physics A 827 (2009) 411c

  12. Quantum information Quantum communication, cryptography and quantum information processing Need calculations of atomic properties Optimizing the fast Rydberg quantum gate, M.S. Safronova, C. J. Williams, and C. W. Clark, Phys. Rev. A 67, 040303 (2003) . Magic wavelengths for the ns-np transitions in alkali-metal atoms, Bindiya Arora, M.S. Safronova, and C. W. Clark, Phys. Rev. A 76, 052509 (2007).

  13. P1/2 D5/2 „quantum bit“ S1/2 Quantum Computer(Innsbruck)

  14. Quantum communication Need to interconnect flying and stationary qubits ~100 µm Optical dipole traps (ac Stark shift) Thin ion trap inside a cavity (Monroe/Chapman, Blatt)

  15. problem Atom in state B sees potential UB Atom in state A sees potential UA

  16. What is 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 Atomic polarizability

  17. α(l) S State P State wavelength Locating magic wavelength Magic wavelengths for the ns-np transitions in alkali-metal atoms, Bindiya Arora, M.S. Safronova, and C. W. Clark, Phys. Rev. A 76, 052509 (2007).

  18. Atomic clocks Optical Transitions Microwave Transitions Blackbody Radiation Shifts and Theoretical Contributions to Atomic Clock Research, M. S. Safronova, Dansha Jiang, Bindiya Arora, Charles W. Clark, M. G. Kozlov, U. I. Safronova, and W. R. Johnson, to appear in Special Issue of IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control (2009).

  19. motiation: next generation Atomic clocks Next - generation ultra precise atomic clock http://CPEPweb.org Atoms trapped by laser light The ability to develop more precise optical frequency standards will open ways to improve global positioning system (GPS) measurements and tracking of deep-space probes, perform more accurate measurements of the physical constants and tests of fundamental physics such as searches for gravitational waves, etc.

  20. P1/2 D5/2 „quantum bit“ S1/2 applications Parity Violation Atomic Clocks NEED ATOMIC PROPERTIES Quantum information

  21. How to accurately calculate atomic properties? Very precise calculation of atomic properties WANTED! We also need to evaluate uncertainties of theoretical values!

  22. Atomic Properties and others ... Magic wavelength BBR shifts Fine-structure intervals Lifetimes Parity nonconserving amplitudes van der Waals coefficients Derived: Weak charge QW, Anapole moment Electron electric-dipole moment enhancement factors Hyperfine constants Isotope shifts Energies Line strengths Branching ratios Quadrupole moments Oscillator strengths BBR shifts Atom-wall interaction constants ac and dc Polarizabilities Transition probabilities Wavelengths

  23. Theory:All-order method(relativistic linearized coupled-cluster approach)

  24. Perturbation theory:Correlation correction to ground state energies of alkali-metal atoms

  25. Linearized coupled-cluster method The linearized coupled-cluster method sums infinite sets of many-body perturbation theory terms. The wave function of the valence electron v is represented as an expansion that includes all possible single, double, and partial triple excitations. Cs: atom with single (valence) electron outside of a closed core. 1s22s22p63s23p63d104s24p64d105s25p66s valence electron 1s2…5p6 6s core

  26. All-order atomic wave function (SD) core valence electron any excited orbital Core Lowest order Single-particle excitations Double-particle excitations

  27. All-order atomic wave function (SD) core valence electron any excited orbital Core Lowest order Single-particle excitations Double-particle excitations

  28. Triples excitations, non-linear terms, extra perturbation theory terms, … Need for symbolic computing 800 terms! The code was developed to implement Wick’s theorem and simplify the resulting expressions.

  29. Symbolic program for coupled-cluster method & perturbation theory Input: expression of the type in ASCII format. Output: simplified resulting formula in the LaTex format, ASCII output is also generated.

  30. Program features 1) The code is set to work with two or three normal products (all possible cases) with large number of operators. 2) The code differentiates between different types of indices, i.e. core (a,b,c,…), valence (v,w,x,y,...), excited orbitals (m,n,r,s,…), and general case (i, j, k, l,…). 3) The operators are ordered as required in the same order for all terms. 4) The expression is simplified to account for the identical terms and symmetry rules, . 5) The direct and exchange terms are joined together, .

  31. Symbolic computing for program generation The resulting expressions that need to be evaluated numerically contain very large number of terms, resulting in tedious coding and debugging. The symbolic program generator was developed for this purpose to automatically generate efficient numerical codes for coupled-cluster or perturbation theory terms.

  32. Automated code generation Codes that write formulas Codes that write codes Input: list of formulas to be programmed Output: final code (need to be put into a main shell) Features: simple input, essentially just type in a formula!

  33. All-order method:Correlation correction to ground state energies of alkali-metal atoms

  34. Results for alkali-metal atoms: E1 matrix elements (a.u.) Experiment Na,K,Rb: U. Volz and H. Schmoranzer, Phys. Scr. T65, 48 (1996), Cs: R.J. Rafac et al., Phys. Rev. A 60, 3648 (1999), Fr: J.E. Simsarian et al., Phys. Rev. A 57, 2448 (1998) Theory M.S. Safronova, W.R. Johnson, and A. Derevianko, Phys. Rev. A 60, 4476 (1999)

  35. Static polarizabilities of np states Theory [ 1 ] Experiment* (3P1/2) Na 359.9(4) 359.2(6) (3P3/2) 361.6(4) 360.4(7) (3P3/2) -88.4(10) -88.3 (4) (4P1/2) K 606.7(6) 606(6) (4P3/2) 616(6) 614 (10) (4P3/2) -109(2) -107 (2) (5P1/2) Rb 807(14) 810.6(6) 869(14) (5P3/2) 857 (10) -166(3) (5P3/2) -163(3) *Zhu et al. PRA 70 03733(2004) Excellent agreement with experiments ! [1] Bindiya Arora, M.S. Safronova, and Charles W. Clark, Phys. Rev. A 76, 052509 (2007)

  36. Very brief summary of what wecalculated with this approach • Properties • Energies • Transition matrix elements (E1, E2, E3, M1) • Static and dynamic polarizabilities & applications • Dipole (scalar and tensor) • Quadrupole, Octupole • Light shifts • Black-body radiation shifts • Magic wavelengths • Hyperfine constants • C3 and C6 coefficients • Parity-nonconserving amplitudes (derived weak charge and anapole moment) • Isotope shifts (field shift and one-body part of specific mass shift) • Atomic quadrupole moments • Nuclear magnetic moment (Fr), from hyperfine data Systems Li, Na, Mg II, Al III, Si IV, P V, S VI, K, Ca II, In, In-like ions, Ga, Ga-like ions, Rb, Cs, Ba II, Tl, Fr, Th IV, U V, other Fr-like ions, Ra II http://www.physics.udel.edu/~msafrono

  37. how to evaluateuncertainty of theoretical calculations?

  38. Theory: evaluation of the uncertainty HOW TO ESTIMATE WHAT YOU DO NOT KNOW? • I. Ab initio calculations in different approximations: • Evaluation of the size of the correlation corrections • Importance of the high-order contributions • Distribution of the correlation correction • II. Semi-empirical scaling: estimate missing terms

  39. Example:quadrupole moment of 3d5/2 state in Ca+ Electric quadrupole moments of metastable states of Ca+, Sr+, and Ba+,Dansha Jiang and Bindiya Arora and M. S. Safronova, Phys. Rev. A 78, 022514 (2008)

  40. 3D5/2 quadrupole moment in Ca+ Lowest order 2.451

  41. 3D5/2 quadrupole moment in Ca+ Third order 1.610 Lowest order 2.451

  42. 3D5/2 quadrupole moment in Ca+ All order (SD) 1.785 Third order 1.610 Lowest order 2.451

  43. 3D5/2 quadrupole moment in Ca+ All order (SDpT) 1.837 All order (SD) 1.785 Third order 1.610 Lowest order 2.451

  44. 3D5/2 quadrupole moment in Ca+ Coupled-cluster SD (CCSD) 1.822 All order (SDpT) 1.837 All order (SD) 1.785 Third order 1.610 Lowest order 2.451

  45. 3D5/2 quadrupole moment in Ca+ Coupled-cluster SD (CCSD) 1.822 All order (SDpT) 1.837 All order (SD) 1.785 Third order 1.610 Lowest order 2.451 Estimate omitted corrections

  46. Final results: 3d5/2 quadrupole moment All order (SD), scaled 1.849 All-order (CCSD), scaled 1.851 All order (SDpT)1.837 All order (SDpT), scaled 1.836 Third order 1.610 Lowest order 2.454 1.849 (13)

  47. Final results: 3d5/2 quadrupole moment All order (SD), scaled 1.849 All-order (CCSD), scaled 1.851 All order (SDpT)1.837 All order (SDpT), scaled 1.836 Third order 1.610 Lowest order 2.454 1.849 (13) Experiment1.83(1) Experiment: C. F. Roos, M. Chwalla, K. Kim, M. Riebe, and R. Blatt, Nature 443, 316 (2006).

  48. More complicated systems

  49. relativistic All-order method Singly-ionized ions

  50. Summary of theory methods for PNC studies • Configuration interaction (CI) • Many-body perturbation theory • Relativistic all-order method (coupled-cluster) • Perturbation theory in the screened Coulomb • interaction (PTSCI), all-order approach • Configuration interaction + second-order MBPT • Configuration interaction + all-order method* *under development

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