1 / 57

Polarizabilities, Atomic Clocks, and Magic Wavelengths

DAMOP 2008 focus session: Atomic polarization and dispersion. Polarizabilities, Atomic Clocks, and Magic Wavelengths. May 29, 2008. Marianna Safronova Bindiya arora. Charles W. clark NIST, Gaithersburg. Outline. Motivation Method Applications

doane
Download Presentation

Polarizabilities, Atomic Clocks, and Magic Wavelengths

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. DAMOP 2008 focus session: Atomic polarization and dispersion Polarizabilities, Atomic Clocks, and Magic Wavelengths May 29, 2008 Marianna Safronova Bindiya arora Charles W. clark NIST, Gaithersburg

  2. Outline • Motivation • Method • Applications • Frequency-dependent polarizabilities of alkali atoms • and magic frequencies • Atomic clocks: blackbody radiation shifts • Future studies

  3. Motivation: 1Optically trapped atoms Atom in state B sees potential UB Atom in state A sees potential UA State-insensitive cooling and trapping for quantum information processing

  4. Motivation: 2 Atomic clocks: Next Generation Microwave Transitions Optical Transitions http://tf.nist.gov/cesium/fountain.htm, NIST Yb atomic clock

  5. Motivation: 3 Parity violation studies with heavy atoms & search for Electron electric-dipole moment http://CPEPweb.org, http://public.web.cern.ch/, Cs experiment, University of Colorado

  6. Motivation • Development of the high-precision methodologies • Benchmark tests of theory and experiment • Cross-checks of various experiments • Data for astrophysics • Long-range interactions • Determination of nuclear magnetic and anapole moments • Variation of fundamental constants with time

  7. Atomic polarizabilities

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

  9. How to accurately calculate various matrix elements ? Very precise calculation of atomic properties We also need to evaluate uncertainties of theoretical values!

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

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

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

  13. Actual implementation: codes that write formulas The derivation gets really complicated if you add triples! Solution: develop analytical codes that do all the work for you! Input: ASCII input of terms of the type Output: final simplified formula in LATEX to be used in the all-order equation

  14. Problem with all-order extensions: TOO MANY TERMS The complexity of the equations increases. Same issue with third-order MBPT for two-particle systems (hundreds of terms) . What to do with large number of terms? Solution: automated code generation !

  15. 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!

  16. Results for alkali-metal atoms 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)

  17. 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

  18. Polarizabilities: Applications • Optimizing the Rydberg gate • Identification of wavelengths at which two different alkali atoms have the same oscillation frequency for simultaneous optical trapping of two different alkali species. • Detection of inconsistencies in Cs lifetime and Stark shift experiments • Benchmark determination of some K and Rb properties • Calculation of “magic frequencies” for state-insensitive cooling and trapping • Atomic clocks: problem of the BBR shift • …

  19. Polarizabilities: Applications • Optimizing the Rydberg gate • Identification of wavelengths at which two different alkali atoms have the same oscillation frequency for simultaneous optical trapping of two different alkali species. • Detection of inconsistencies in Cs lifetime and Stark shift experiments • Benchmark determination of some K and Rb properties • Calculation of “magic frequencies” for state-insensitive cooling and trapping • Atomic clocks: problem of the BBR shift • …

  20. ApplicationsFrequency-dependent polarizabilities of alkali atoms from ultraviolet through infrared spectral regions Goal: First-principles calculations of the frequency-dependent polarizabilities of ground and excited states of alkali-metal atoms Determination of magic wavelengths

  21. Magic wavelengths Excited states: determination of magic frequencies in alkali-metal atoms for state-insensitive cooling and trapping, i.e. When does the ground state and excited np state has the same ac Stark shift? Bindiya Arora, M.S. Safronova, and Charles W. Clark, Phys. Rev. A 76, 052509 (2007) Na, K, Rb, and Cs

  22. 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

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

  24. What do we need?

  25. What do we need? Lots and lots of matrix elements!

  26. 56 matrix elements in What do we need? Lots and lots of matrix elements! Cs

  27. What do we need? Lots and lots of matrix elements! All-order “database”: over 700 matrix elements for alkali-metal atoms and other monovalent systems

  28. Theory (This work) Experiment* w=0 (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 !

  29. MJ = ±3/2 MJ = ±1/2 Frequency-dependent polarizabilities of Naatom in the ground and 3p3/2 states. The arrows show the magic wavelengths

  30. Magic wavelengths for the 3p1/2 - 3s and 3p3/2 - 3s transition of Na.

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

  32. 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.

  33. 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)

  34. ac Stark shifts for the transition from 6p3/2F′=5 M′sublevels to 6s FM sublevels in Cs.The electric field intensity is taken to be 1 MW/cm2.

  35. Applications:atomic clocks

  36. atomic clocksblack-body radiation ( BBR ) shift Motivation: BBR shift gives the larges uncertainties for some of the optical atomic clock schemes, such as with Ca+

  37. Blackbody radiation shift in optical frequency standard with 43Ca+ ion Bindiya Arora, M.S. Safronova, and Charles W. Clark, Phys. Rev. A 76, 064501 (2007)

  38. Motivation For Ca+, the contribution from Blackbody radiation gives the largest uncertainty to the frequency standard at T = 300K • DBBR = 0.39(0.27) Hz [1] [1] C. Champenois et. al. Phys. Lett. A 331, 298 (2004)

  39. Frequency standard Level B Clock transition Level A T = 0 K Transition frequency should be corrected to account for the effect of the black body radiation at T=300K.

  40. Frequency standard Level B Clock transition DBBR Level A T = 300 K Transition frequency should be corrected to account for the effect of the black body radiation at T=300K.

  41. Why Ca+ ion? The clock transition involved is 4s1/2F=4 MF=0→ 3d5/2 F=6 MF=0 4p3/2 Easily produced by non-bulky solid state or diode lasers 854 nm 4p1/2 3d5/2 866 nm Lifetime~1.2 s 393 nm 3d3/2 397 nm E2 729 nm 732 nm 4s1/2

  42. BBR shift of a level • The temperature-dependent electric field created by the blackbody radiation is described by (in a.u.) : • Frequency shift caused by this electric field is: Dynamic polarizability

  43. BBR shift and polarizability BBR shift can be expressed in terms of a scalar static polarizability: Dynamic correction Dynamic correction ~10-3 Hz. At the present level of accuracy the dynamic correction can be neglected. Vector & tensor polarizability average out due to the isotropic nature of field.

  44. BBR shift for a transition Effect on the frequency of clock transition is calculated as the difference between the BBR shifts of individual states. 3d5/2 729 nm 4s1/2

  45. Need BBR shifts Need ground and excited state scalar static polarizability NOTE: Tensor polarizability calculated in this work is also of experimental interest.

  46. Contributions to the 4s1/2 scalar polarizability ( ) 43Ca+(w = 0) Stail 6p1/2 6p3/2 0.01 0.01 0.06 5p3/2 5p1/2 0.01 0.01 4p1/2 4p3/2 24.4 48.4 Total: 76.1 ± 1.1 4s 3.3 Core

  47. Contributions to the 3d5/2 scalar polarizability ( ) 43Ca+ nf7/2 7-12f7/2 nf5/2 6f7/2 1.7 np3/2 tail 0.2 0.5 0.3 0.01 5f7/2 5p3/2 0.01 0.8 4f7/2 4p3/2 2.4 22.8 3d5/2 Total: 32.0 ± 1.1 3.3 Core

  48. Comparison of our results for scalar static polarizabilities for the 4s1/2 and 3d5/2 states of 43Ca+ ion with other available results [1] C. Champenois et. al. Phys. Lett. A 331, 298 (2004) [2] Masatoshi Kajit et. al. Phys. Rev. A 72, 043404, (2005) [3] C.E. Theodosiou et. al. Phys. Rev. A 52, 3677 (1995)

  49. Black body radiation shift Comparison of black body radiation shift (Hz) for the 4s1/2- 3d5/2 transition of 43Ca+ ion at T=300K (E=831.9 V/m). An order of magnitude improvement is achieved with comparison to previous calculations [1] C. Champenois et. al. Phys. Lett. A 331, 298 (2004) [2] Masatoshi Kajit et. al. Phys. Rev. A 72, 043404, (2005)

  50. Black body radiation shift Comparison of black body radiation shift (Hz) for the 4s1/2- 3d5/2 transition of 43Ca+ ion at T=300K (E=831.9 V/m). Sufficient accuracy to establish The uncertainty limits for the Ca+ scheme [1] C. Champenois et. al. Phys. Lett. A 331, 298 (2004) [2] Masatoshi Kajit et. al. Phys. Rev. A 72, 043404, (2005)

More Related