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Atomic calculations: recent advances and modern applications

July 8, 2010. JQI seminar. Atomic calculations: recent advances and modern applications. Marianna Safronova. Outline. Selected applications of atomic calculations Study of fundamental symmetries Atomic clocks Optical cooling and trapping and quantum information Examples: magic wavelengths

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Atomic calculations: recent advances and modern applications

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  1. July 8, 2010 JQI seminar Atomic calculations: recent advances and modern applications Marianna Safronova

  2. Outline • Selected applications of atomic calculations • Study of fundamental symmetries • Atomic clocks • Optical cooling and trapping and quantum information • Examples: magic wavelengths • Present status of theory • How accurate are theory values? • Present challenges • Development of CI+all-order method for group II atoms • Future prospects

  3. Atomic calculations for study of fundamental symmetries

  4. Transformations and symmetries Translation Momentum conservation Translation in time Energy conservation Rotation Conservation of angular momentum [C] Charge conjugation C-invariance [P] Spatial inversion Parity conservation (P-invariance) [T] Time reversal T-invariance [CP] [CPT]

  5. Transformations and symmetries Translation Momentum conservation Translation in time Energy conservation Rotation Conservation of angular momentum [C] Charge conjugation C-invariance [P] Spatial inversion Parity conservation (P-invariance) [T] Time reversal T-invariance [CP] [CPT]

  6. 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.

  7. a e q Z0 e q Parity violation in atoms 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. Standard Model

  9. 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

  10. 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

  11. a Parity violation in atoms Nuclear spin-dependent PNC: Study of PNC In the nucleus Nuclear spin-independent PNC: Searches for new physics beyond the Standard Model Nuclear anapole moment Present status: agreement with the Standard Model

  12. 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.

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

  14. 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. Fr, Yb, Ra+ 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

  15. Why do we need Atomic calculations to study parity violation? • Present experiments can not be analyzed without theoretical value of PNC amplitude in terms of Qw. • Theoretical calculation of spin-dependent PNC amplitude is needed to determine anapole moment from experiment. • Other parity conserving quantities are needed. Note: need to know theoretical uncertainties!

  16. Transformations and symmetries Translation Momentum conservation Translation in time Energy conservation Rotation Conservation of angular momentum [C] Charge conjugation C-invariance [P] Spatial inversion Parity conservation (P-invariance) [T] Time reversal T-invariance [CP] [CPT]

  17. Permanent electric-dipole moment ( EDM ) Time-reversal invariance must be violated for an elementary particle or atom to possess a permanent EDM. S d d S

  18. EDM and New physics Many theories beyond the Standard Model predict EDM within or just beyond the present experimental capabilities. David DeMille, Yale PANIC 2005

  19. Atomic calculations and search for EDM • EDM effects are enhanced in some heavy atoms and molecules. • Theory is needed to calculate enhancement factors and search for new systems for EDM detection. • Recent new limit on the EDM of 199Hg | d(199Hg) | < 3.1 x 10-29e cm Phys. Rev. Lett. 102, 101601 (2009)

  20. 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, Special Issue of IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control 57, 94 (2010).

  21. Atomic calculations & more precise clocks • Prediction of atomic properties required for new clock proposals • New clock proposals require both estimation of the atomic properties for details of the proposals (transition rates, lifetimes, branching rations, magic wavelength, scattering rates, etc.) and evaluation of the systematic shifts (Zeeman shift, electric quadruple shift, blackbody radiation shift, ac Stark shifts due to various lasers fields, etc.). • (2)Determination of the quantities contributing to the uncertainty budget of the existing schemes. • In the case of the well-developed proposals, one of the main current uncertainty issues is the blackbody radiation shift.

  22. Blackbody radiation shift 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.

  23. 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)

  24. 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

  25. 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)

  26. Example: BBR shift in sr+ Need precise lifetime measurements nf tail contribution issue has been resolved [1] A. A. Madej et al., PRA 70, 012507 (2004); [2] H. S. Margolis et al., Science 306, 19 (2004). 1% Dynamic correction, E2 and M1 corrections negligible Sr+: Dansha Jiang, Bindiya Arora, M. S. Safronova, and Charles W. Clark, J. Phys. B 42 154020 (2010). Ca+: Bindiya Arora, M.S. Safronova, and Charles W. Clark, Phys. Rev. A 76, 064501 (2007)

  27. 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).

  28. Atoms in optical lattices • Cancellations of ac Start shifts: state-insensitive optical cooling and trapping • State-insensitive bichromatic optical trapping schemes • Simultaneous optical trapping of two different alkali-metal species • Determinations of wavelength where atoms will not be trapped • Calculations of relevant atomic properties: dipole matrix elements, • atomic polarizabilities, magic wavelengths, scattering rates, lifetimes, etc. Optimizing the fast Rydberg quantum gate, M.S. Safronova, C. J. Williams, and C. W. Clark, Phys. Rev. A 67, 040303 (2003) . Frequency-dependent polarizabilities of alkali atoms from ultraviolet through infrared spectral regions, M.S. Safronova, Bindiya Arora, and Charles W. Clark, Phys. Rev. A 73, 022505 (2006) 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). Theory and applications of atomic and ionic polarizabilities (review paper), J. Mitroy, M.S. Safronova, and Charles W. Clark, submitted to J. Phys. B (2010) State-insensitive bichromatic optical trapping, Bindiya Arora, M.S. Safronova, and C. W. Clark, submitted to Phys. Rev. A (2010)

  29. 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

  30. α(l) S State P State wavelength Locating magic wavelength

  31. Polarizability of an alkali atom in a statev Valence term (dominant) Core term Compensation term Electric-dipole reduced matrix element Example: Scalar dipole polarizability

  32. Relativistic all-order method Sum over infinite sets ofmany-body perturbation theory(MBPT) terms. Calculate the atomic wave functions and energies Scheme: Calculate various matrix elements Calculate “derived” properties useful for particular problems

  33. Results for alkali-metal atoms:E1 transition matrix elements in 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)

  34. Example: “Best set” Rb matrix elements

  35. Magic wavelengths for the 5p3/2 - 5s transition of Rb.

  36. ac Stark shifts for the transition from 5p3/2F′=3 M′sublevels to 5s FM sublevels in Rb.The electric field intensity is taken to be 1 MW/cm2.

  37. MJ = ±3/2 MJ = ±1/2 Magic wavelength for Cs lmagic Other* a0+ a2 lmagic around 935nm a0- a2 * Kimble et al. PRL 90(13), 133602(2003)

  38. bichromatic optical trapping A combination of trapping and control lasers is used to minimize the variance of the potential experienced by the atom in ground and excited states. atom Trap laser Control laser

  39. Surface plot for the 5s and 5p3/2 |m| = 1/2 state polarizabilities as a function of laser wavelengths l1 and l2 for equal intensities of both lasers.

  40. Magic wavelengths for the the 5s and 5p3/2 | m| = 1/2 states for l1 =800-810nm and l2=2 l1 for various intensities of both lasers. The intensity ratio (e1/e2)2 ranges from 1 to 2.

  41. Other applications • Variation of fundamental constants • Long-range interaction coefficients • Data for astrophysics • Actinide ion studies for chemistry models • Benchmark tests of theory and experiment • Cross-checks of various experiments • Determination of nuclear magnetic moment in Fr • Calculation of isotope shifts • …

  42. MONovalent systems: Very brief summary of what wecalculated with all-order method • 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

  43. how to evaluateuncertainty of theoretical calculations?

  44. 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

  45. 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)

  46. 3D5/2 quadrupole moment in Ca+ Lowest order 2.451

  47. 3D5/2 quadrupole moment in Ca+ Third order 1.610 Lowest order 2.451

  48. 3D5/2 quadrupole moment in Ca+ All order (SD) 1.785 Third order 1.610 Lowest order 2.451

  49. 3D5/2 quadrupole moment in Ca+ All order (SDpT) 1.837 All order (SD) 1.785 Third order 1.610 Lowest order 2.451

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