Optical Clocks With Trapped Ions Ekkehard Peik - - PowerPoint PPT Presentation

Physikalisch-Technische Bundesanstalt Time and Frequency Department Braunschweig, Germany

Optical Clocks With Trapped Ions

Ekkehard Peik

Time and Matter 2007, Bled, 26.-31.8.2007

Outline

• Optical Clocks: Motivation
• Single-Ion Optical Clock with 171Yb+
• Search for Variations of Fundamental Constants
• Possible Nuclear Optical Clock with 229Th

Improvement in the Accuracy of Clocks

from: C. Audoin, B. Guinot: The Measurement of Time

ν ≅ 1/s ν ≅ 104/s ν ≅ 1010/s

Stability of atomic frequency standards microwave optical frequency ν0 increases by 5 orders of magnitude

Accuracy; systematic frequency shifts some shifts are prop. to the frequency:

• 2. order Doppler: δν ~ T ν

some shifts have absolute order of magnitude and are relatively less important in the optical range: relative shift for: Cs 9.19 GHz Yb+ 688 THz

• quadrat. Zeeman shift at 1 μT 4.7 ×10-12

7.6 ×10-17 blackbody AC Stark shift at 300 K

• 1.7 ×10-14
• 5.8 ×10-16

Optical Frequency Standard Atomic Reference „forbidden“ transition of atoms in a laser-cooled sample Laser locked to atomic resonance, short-term stabilized to passive Fabry-Perot cavity Frequency-Comb Generator „optical clockwork“, femtosecond laser provides countable radiofrequency output

Reference Systems for Optical Clocks laser-cooled ensembles

• f neutral atoms:

Sr, Ca, Yb, ... single trapped laser-cooled ions: Hg+, Sr+, Yb+, In+, Al+,... „simple“ atoms: H, He, ... molecules: I2, CH4, OsO4... nuclei:

229Th, ...

Optical Frequency Standards with a Laser-Cooled Ion in a Paul Trap

5 Yb+ ions miniature Paul trap

~

Quadrupole Electrodes

• Lamb-Dicke confinement with

small trap shifts

• unlimited interaction time
• single ion: no collisions
• stability: use high-Q transition

Projection Noise Limited State Detection via Electron Shelving

Cooling transition (dipole allowed) "forbidden" transition Time (s) P h

• t
• n

C

• u

n t R a t e

Single-ion fluorescence (In+): Observation of a „Quantum Jump“

Yb+ single-ion optical frequency standard

171Yb+ level scheme

Measurement cycle

40 ms 40 - 120 ms

High resolution spectroscopy of the quadrupole transition at 688 THz

Close to the resolution limit τ(pulse) = 90 ms ≈ 2⋅τ(Yb+) 10 Hz linewidth „standard operation“ τ(pulse)=30 ms 30 Hz linewidth Pi-Pulse τ(pulse)=1 ms 1 kHz linewidth

Frequency comparison between two trapped 171Yb+ions

• T. Schneider, E. Peik, Chr. Tamm,
• Phys. Rev. Lett. 94, 230801 (2005)

6x10-16

For nominally unperturbed conditions in both traps we observe a frequency difference of 0.26(42) Hz, comparable to the best relative agreement between cesium fountain clocks.

Setup for absolute optical frequency measurements

Clock laser H Maser Femtosecond frequency comb generator

Cs fountain Yb trap

+

5 MHz 100 MHz 344 THz (871 nm) 200 fib li k 688 THz (435.5 nm)

ν in units of

SI Hertz

Yb+

Reference cavity

Laser frequency servo, time constant: 10...30 s

Σ

Day of Measurement (MJD)

51500 52000 52500 53000 53500 54000

fYb-688 358 979 309 307.6 Hz

• 20
• 10

10 20

Main contributions to the uncertainty budget

• f the measurements in 2005 and 2006:

uA=0.40 Hz (continuous measurements up to 36 h) uB(Cs)=0.83 Hz uB(Yb+)=1.05 Hz (quadrupole shift, blackbody AC Stark shift)

Results of absolute frequency measurements 2000-2006

171Yb+ S1/2 - D3/2:

688 358 979 309 307.5(1.4) Hz

Search for Temporal Variations

• f

Fundamental Constants

Evidence for a varying fine structure constant

• n a cosmological time scale ?

Analysis of absorption spectra in the light from quasars,

• J. Webb, M. Murphy, V. Flambaum et al., Univ. New South Wales, Sydney

Many Multiplet Method: transition frequencies in MgI, MgII, FeII, CrII etc. have different dependence on α because of relativistic contributions.

Result: >4σ evidence for α-variation. Linear fit: Measurements from other groups with a different instrument, different selections of quasars and absorption lines are consistent with Δα=0. See e.g., R. Srianand et al., Phys. Rev. Lett. 92, 121302 (2004)

• E. Reinhold et al., Phys. Rev. Lett. 96, 151101 (2006):

3.5σ evidence for a rel. change in me/mp of 2x10-5 over 12 Gyr.

sensitivity factor A

• 6
• 4
• 2

2 4

relative frequency drift rate

• 4
• 2

2

Search for variations of the fine structure constant in atomic clock comparisons

• S. G. Karshenboim

physics/0311080 heavy atoms, j g> j e light atoms heavy atoms, j g< j e relativistic level shift:

∼

calculations by

• V. Dzuba and V. Flambaum

H Ca In+ Sr+ Yb+ Yb+ Hg+ Ba+

New Limits for Temporal Variations of Fundamental Constants

Combining the data from Yb+ with those from the Hg+ frequency standard at NIST,

• W. H. Oskay et al., Phys. Rev. Lett. 97, 020801 (2006), yields

For the fine structure constant: For the Rydberg frequency:

d ln α / dt (10-15 yr-1)

• 1.0
• 0.5

0.0 0.5 1.0

d ln Ry / dt (10-15 yr-1)

• 3
• 2
• 1

1 2 3

Yb+ Hg+

• E. Peik et al., physics/0611088
• Proc. 11th Marcel Grossmann Meeting,

Berlin 2006 NIST group:

• T. Fortier et al., PRL 98, 070801 (2007)

d ln α / dt (10-15 per year)

• 6
• 4
• 2

2 4

2 4 6

Limits for changes of the fine structure constant from laboratory experiments

Early work: 1993: Mg FS / Cs HFS + astro. data: 2.7× 10-13 / yr 1995: H HFS / Hg+ HFS: 3.7× 10-14 / yr * 2003: Rb HFS / Cs HFS * 2004: H / Hg+ 2004: H / Hg+ / Yb+ 2006: Hg+ / Yb+ 2007: Dy 2007: Hg+ / Cs HFS *

* assuming constancy

• f the strong interaction

Th-229: A Nuclear Optical Clock?

[633]

5 _ + 2 3 _ + 2 [631]

ΔE=7.6 eV M1 transition τ=104 s

The Thorium Isomer at 7.6 eV: An Optical Mössbauer Transition The lowest-lying known excited state of a nucleus is an isomer of Th-229. This nucleus can be excited by the absorption of VUV light.

229Th Ground State 229mTh Isomer

1976 1990 1990 1994 2003 2007 Measurements of ΔE ΔE [eV] Year Method <100

• 1 (4)

<5 3.5 (1.0) 3.4 (1.8) 7.6 (0.5) γ-Spectr. “ d-Scatt. γ-Spectr* “ “ *R. Helmer and C. Reich, Idaho “ V. Barci et al., Nice “ B. Beck et al., LLNL

Detection of the Nuclear Excitation in Nuclear-Electronic Double-Resonance with a Single Ion: Observation of Quantum Jumps Nucleus in the ground state; laser-induced fluorescence from the shell. Laser excitation of the nucleus; change of hyperfine structure detected in intensity or polarisation of fluorescence. Possibility for a single-ion frequency standard with a nuclear excitation as the reference transition.

• Th3+ 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)

Scaling of the 229Th transition frequency ω in terms of α and quark masses:

• V. Flambaum: Phys. Rev. Lett. 97, 092502 (2006)

105 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.

See also:

• X. He, Z. Ren, J. Phys. G. 34, 1611 (2007)
• A. C. Hayes, J. L. Friar, nucl-th/0702048

Outlook: Optical Clocks in Space proposals to ESA in the program Cosmic Vision 2015-25

Design study of the SAGAS mission with laser link to a Sr+ optical clock

• P. Wolf et al., LNE-SYRTE, Paris
• on the ground: replacement of H-masers for deep space navigation;

VLBI

• in earth orbit: time and frequency transfer between laboratories;

gravimetry; geodesy

• in the solar system: tests of general relativity; investigation of the

Pioneer anomaly

Ion Traps:

• Chr. Tamm
• I. Sherstov
• B. Stein
• T. Schneider

Cesium Fountain:

• S. Weyers
• R. Wynands

Frequency Comb:

• B. Lipphardt
• H. Schnatz

Thorium:

• K. Zimmermann

Funding: DFG FQXi Acknowledgements