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Advances in Precision Tests and Experimental Gravitation in Space, Firenze, 28.9.2006 Optical clocks with trapped ions and search for temporal variations of fundamental constants E. Peik, T. Schneider + , Chr. Tamm B. Lipphardt, H. Schnatz, St.


  1. Advances in Precision Tests and Experimental Gravitation in Space, Firenze, 28.9.2006 Optical clocks with trapped ions and search for temporal variations of fundamental constants E. Peik, T. Schneider + , Chr. Tamm B. Lipphardt, H. Schnatz, St. Weyers, R. Wynands S. G. Karshenboim* * D. I. Mendeleev Inst. for Metrology, St. Petersburg Max-Planck-Institut für Quantenoptik, Garching + present address: ENS, Paris Physikalisch-Technische Bundesanstalt Time and Frequency Division Braunschweig, Germany

  2. ������������������ ������� ��������� �������������� �� ������������ ������������������ ~ Quadrupole Electrodes ���� � ���� • �� ��!��"� ���#��� ��� ���� � ��� ���� ���#�� $ ���� ���� ����������� �� � $ ���%�� ���&�������������� $ ���������&���� ��%��'�����������

  3. ������� ��������� ������������� �������������� ������������������ (��� ��� ����������� �� �������� )���*+ �*, - �������� �� .����!�� ��� */0� 12���� ��������� .% � )3���-4��� � )��54�3��-4��� � )6�74�8�9���:-4 �� � )3;�4�3��-4���� � )6���:4������:4:::-4�5� �� )8�9���:-4�<� �� )3���-4�::: 6������ ���� �#�������� ���������� #���������� ����% ����� #�������� ����#� �������������� #�������� �� ��& 199 Hg + S 1/2 - D 5/2 : 1 064 721 609 899 144.94(97) Hz NIST 171 Yb + S 1/2 - D 3/2 : 688 358 979 309 307.5(2.2) Hz PTB 88 Sr + S 1/2 - D 5/2 : 444 779 044 095 484.2(1.7) Hz NPL ��������������� ��� �������� ���=��������� ��������������� �#���� ������ > ������ ������� #�������� �� ���:

  4. Yb + single-ion optical frequency standard 171 Yb + level scheme Measurement cycle 40 ms 40 - 120 ms

  5. .�%���������������������������#��������������� ���������������?,,��.@ ��������� =�������� ���������> �������������������������� �� τ )�����-A*� � τ )�����-AB+� � τ (pulse) = 90 ms ≈ 2 ⋅τ (Yb + ) *�".@���������� B+�.@���������� 10 Hz linewidth Quantum jump probability 0.6 0.4 0.2 ;� �����2�������� ���� B+� ������������������ 0.0 -200 -100 0 100 200 Detuning at 436 nm (Hz)

  6. ������������ ���������������������������� *0* �� � ���� ������ ������ ����������� ���������� ������� ����� �� �����C� ��#�������� ��##������ �#�+:D?)ED-�.@4� �� ������� ������ �����������C���%��� ��� ������� ����� #������� ����"�: ? 2 *+ �*? �:����������4�1:����"4����:��� 4� ����:�;�C:�����:� �� 4�DB+,+*�)D++�-

  7. Absolute frequency measurement Observed Allan deviations Cs fountain Yb + trap Hz & quartz LO Cs Fountain τ servo ~10 s -13 10 69 688 THz 5 MHz (436 nm) Clock Reference + H Maser cavity laser Measured Yb + frequency -14 10 6,9 344 THz 100 MHz τ ) Maser (871 nm) σ y ( 2, τ τ τ ~20 m ~8 m σ σ σ Femtosecond -15 Yb + fiber laser 10 0,69 comb generator s 1 10 100 1000 10000 100000 integration time ν Yb+

  8. Results of absolute frequency measurements 2000-2006 171 Yb + S 1/2 - D 3/2 : 688 358 979 309 307.5(2.2) Hz Main contributions to the uncertainty budget of the measurements in 2005 and 2006: u A =0.40 Hz (continuous measurements up to 36 h) u B (Cs)=1.82 Hz (pulse area related shift) u B (Yb + )=1.05 Hz (quadrupole shift, blackbody AC Stark shift)

  9. Present uncertainty budget of Yb + 688 THz systematics: 1 Hz stray-field induced quadrupole shift 0.1 Hz line-shape asymmetry, servo error 0.3 Hz AC Stark shift (blackbody anisotropy, deviation from 300 K) 0.03 Hz Stark shift from trap 0.01 Hz Relativistic Doppler shift can be reduced significantly improved thermal design, via averaging schemes cryogenic cooling, precise polarizabilities

  10. Search for α -variation in optical electronic transition frequencies. Method of Analysis: electronic transition frequency can be expressed as Rydberg frequency in SI hertz numerical constant (function of quantum numbers) dimensionless function of α ; describes relativistic level shifts Relative temporal derivative of the frequency: common shift of all specific for the can be calculated with transition frequencies transition under study relativistic Hartree-Fock (Dzuba, Flambaum)

  11. Frequency comparisons of single-ion optical clocks (via Cs fountains) Yb + , S - D at 688 THz, PTB Hg + , S - D at 1064 THz, NIST Boulder, S. Bize et al., PRL 90 , 150802 (2003) W. Oskay et al., PRL 97 , 020801 (2006) A(Hg)=-3.19 A(Yb)=0.88 New limits for the present temporal variations of fine structure constant and Rydberg frequency:

  12. Measured frequency drifts versus sensitivity factor A 10 d ln f /dt [10-15yr-1] Hg+ Yb+ H-data point: 1S - 2S vs. Cs 0 MPQ/SYRTE group H M. Fischer et al., Phys. Rev. Lett. 92 , 230802 (2004) -10 -4 -3 -2 -1 0 1 2 A From a weighted linear regression: slope: Consistent with „constancy of constants“. intercept: E. Peik et al., Phys. Rev. Lett. 93 , 170801 (2004)

  13. ��������������������� !����� ������� #�������� ����� ������ ���� ���� ��#�������� �� �&� �C��� ����������� ������������� #�� ����� ����"� $ 3���&�.% � C�:�<� � &�F ∆ <AB:DF $ ��5G3��&��� � �������� C�:�����������&� | ∆ <A?:D | 2 P 1/2 Level scheme of 171 Yb + ( τ ~ 50 ms) 2 D 3/2 cooling ( τ ~ 10 a) 436 nm 2 F 7/2 and (quadrupole) detection 467 nm (octupole) F=1 2 S 1/2 12.6 GHz F=0 Precision data from more diverse systems: • molecular rotational and vibrational lines m e /m p • nuclear transitions (e.g. Th-229 optical transition) strong interaction

  14. The Thorium Isomer at 3.5 eV: An Optical Mössbauer Transition The lowest-lying known excited state of a nucleus is an isomer of Th-229 at about 3.5 eV. This nucleus can be excited by the absorption of ultraviolet light. Measurements of ∆ E 229m Th Isomer _ + ∆ E [eV] Year 3 2 [631] Method γ -Spectr. 1976 <100 -1 (4) 1990 “ ∆ E=3.5 eV 1990 d-Scatt. <5 γ -Spectr* 1994 3.5 (1.0) M1 transition τ =10 4 s 3.4 (1.8) 2003 “ _ + 5 *R. Helmer and C. Reich, Idaho [633] 2 “ V. Barci et al., Nice 229 Th Ground State

  15. Detection of the Nuclear Excitation in Nuclear-Electronic Double-Resonance with a Single Ion: Observation of Quantum Jumps Nucleus in the ground state; Laser excitation of the nucleus; laser-induced fluorescence change of hyperfine structure detected in from the shell. intensity or polarisation of fluorescence. Possibility for a single-ion frequency standard with a nuclear excitation as the reference transition. • Th 3+ has suitable level scheme for laser cooling • promises a further reduction of systematic line shifts • constitutes a precision oscillator of the strong interaction E. Peik, Chr. Tamm, Europhys. Lett. 61 , 181 (2003)

  16. Scaling of the 229 Th transition frequency ω in terms of α and quark masses: V. Flambaum: Phys. Rev. Lett. 97 , 092502 (2006) 10 5 enhancement in sensitivity to variations results from the near perfect cancellation of two O(MeV) contributions to the nuclear level energies. Comparing the Th nuclear frequency to present atomic clocks will allow to look for temporal variations at the level 10 -20 per year.

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