Frequency combs, optical clocks and the future of the unit of time

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• Frequency combs, optical clocks and the future of
  the unit of time

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What is needed to improve the SI second? The best
value is limited by the noise at the optimum
measurement time t. The signal to noise S/N, the
line width Dn and the frequency n0 are the other
parameters. p is equal to ½ for a passive
clock p is equal to 1 for an active clock
Possible strategies 1-Reduce the line width by
cooling the atoms 2-Increse the signal by using
more atoms 3-Increase the frequency change the
atom.
This last solution is easier said than done
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The caesium fountain is an elegant answer to the
future of the SI second. Cooled slow atoms ? Dn
reduced by two orders of magnitude Spin exchange
limits the number of atoms
The frequency is obviously not
negotiable Ion and atom traps in the optical
spectrum are the answer for the future Cooled
atoms or ions in optical or RF trap. Frequencies
in the 400 THz range! Optical lattice clocks has
all the right answers Cooled atoms in a trap

No limit on the number of atoms (?)
Optical
frequencies
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State-of-the-art Time Frequency Standards
Cesium fountain clocks use a large number of
atoms for a limited period of time HIGH
stability 10-14 in 1s, Accuracy
5?10-16. (Accuracy limit reached in 10 minutes)
Ion clocks use atoms trapped for extended periods
of time HIGH accuracy 10-17, Stability 5?10-15
in 1s. (Accuracy limit reached in one month)
Lattice clocks combine the advantages of trapped
ion clocks and cooled neutral atoms clocks large
number of atoms for extended periods of
time HIGH stability 10-17 in 1s AND HIGH
accuracy 10-17.
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Cs Hyperfine Energy Levels
(F,mF) (4,4) . (4,0) . . (4,-3) (4,-
4) (3,-3) . (3,0) . (3, 3)
Cs mass 133 amu Clock transition in the ground
state (4,0)-(3,0)
F4
9.19263177 GHz
H
F3
Energy levels converted in Hz
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Caesium fountains will probably never be better
than 10-16 due to the intrinsic nature of the
caesium atom spin exchange, microwave
frequency. Optical frequency standards have the
advantage of a much higher frequency. Then the
big question
Why not go immediately to optical frequency
sources for the SI second?
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Why not go immediately to optical frequency
sources for the SI second?

• The optical clocks need to be probed by an
  ultra stable laser.
• The drift of these ultra stable lasers has to be
  under control.
• There is a need to link the optical frequencies
  to microwave signals to use them for clock work.
• Can the whole system run continuously?

Until a few years ago the main problem was the
link between the microwave and the optical
frequencies. The frequency comb based on
femtosecond laser has change everything.
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How to link all those frequencies?
laser
laser
laser
Cs
laser
Ion Trap
Frequency chain
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Until a few years ago only two chains in the
world PTB and NRC
Needs about one year and four people to do one
measurement at a new frequency
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The Optical Frequency Comb
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fbeat1
fbeat2
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The comb offset is caused by dispersion
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fs Optical Frequency Comb
Output
Mode-locked Tisapphire laser
From 532 nm pump laser
Micro- Structured fibre
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The probe laser
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The Ultra-stable 674-nm laser for probing the Sr
ion
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The heart of the probe laser
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The diode laser at 674 nm is stabilized by a
first INVAR Fabry-Perrot cavity
The signal is further stabilized on the ULE
cavity.
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The link with the frequency comb guarantee
traceability to the SI second based on
caesium. When caesium will be replaced, the
frequency chain may be used in reverse,
referencing microwaves to the optical SI second
Probe is sent to ion traps or optical lattice.
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Single ion trap
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Holding Single Ions With Time Varying Fields
Rf Trap Axial (z) and Radial( r) confinement is
provided by a rapidly oscillating quadratic
potential created by the electrode configuration.
Solution of the equation of motion shows that the
ion moves within a time-averaged 3-D potential
well.
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NRC Single Strontium Ion Trap
Artist Impression of Trap and Excitation Beams
View of Chamber and Photomultiplier
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Laser Cooling Dramatically reduces The Volume of
Action of the Single Ion

• Imagine the ring electrode of our Trap was
  expanded to 5 km diameter. When laser cooled, our
  Sr ion at 5mK would occupy no more than 1 m3 !
  The electron cloud of the ion would be 1 mm3 in
  size.

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Observation of quantum jumps and ultra-narrow
spectra
Through the observation of quantum Jumps in the
fluorescence at 422 nm, we can detect the
absorption of single photons by a single ion.
Linewidths of single Zeeman components as small
as 50 Hz have been observed.
Q of almost 1013
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Summary of Sr Ion S-D Frequency Measurements

• Determined mean fS-D 444 779 044 095 494 50
  Hz

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Optical lattice
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The Optical Lattice Clock
Light interference creates patterns of energy
wells in space these patterns are deep enough to
prevent atoms from falling due to gravitation
To create a useful trap, magical wavelengths have
to be used to cancel Stark shift.
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Energy Structure of 87Sr
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The Sr optical Lattice Clock How it Works
3S
1
1P1
Dipole Trap ltrap813.5 nm
3P
2
1
Magic l 813.5 nm?
0
698 nm (87Sr 1 mHz)
1S0
Clock transition 1S0-3P0
One million atoms trapped for extended periods of
time Potential accuracy 1 mHz (df / f 10-17)
Katori, Proc. 6th Symp. Freq. Standards and
Metrology (2002). Palchikov, et al., J. Opt. B.
5 (2003) S131. Katori et al. PRL 91, 173005
(2003). Courtillot et al., PRA 68, 030501(R),
(2003). Takamoto et al., Nature 435, 321, (2005).
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The Sr Optical Lattice Clock How it Works
Clock Cycle
1- use dipole trap Optical Lattice
2- capture large number of atoms in MOT
3S
3- side band cooling _at_ 689 nm
1
4- Ramsey pulses at clock transition large ?t
5- measure 1S0 state population _at_ 461 nm
707 nm
1P1
6- repump atoms
7- measure 1S0 state population _at_ 461 nm
679 nm
3P
MOT ?461 nm
8- Use fluorescence measurements to
calculate populations
2
1
ltrap813.5 nm
0
Sideband cooling 689 nm
Clock transition 698 nm
1S0
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Clock Frequency Measurements

• Magic lattice wavelength 813.5 nm
• Cooling 461 nm
• 87Sr Clock transition weakly dipole allowed, 1
  mHz linewidth
• 5s2 1S0 ? 5s5p 3P0 698 nm
• f(5s2 1S0 ? 5s5p 3P0) 429 228 004 229 952
  15 Hz
• (Katori, Nature, May 2005)

• 88Sr Transition 7.6 kHz linewidth
• 5s2 1S0 ? 5s5p 3P1 689 nm
• f(5s2 1S0 ? 5s5p 3P1) 434 829 121 312 334
  20 Hz
• (Ye, PRL 94, 153001, 2005)
• Theoretically, it is possible to engineer a 1S0 ?
  3P0 transition with a scalar nature (no
  dependence on laser polarization) using
  three-level coherence (electromagnetically
  induced transparency).

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Experimental System
Strontium source
Zeeman Slower
Vacuum chamber 2-D shown
TiSaph laser and pump
Sideband cooling 689 nm
Ultra-stable optical resonator
MOT Coils
Laser Cooling and detection
Probe laser 698 nm
Repumper laser 679 nm
Clock output 429.228 004 229 95 THz
Repumper laser 707 nm
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Optical Lattice Clock other NMIs
Experimental development of the Sr lattice clock
at the University of Tokyo and two NMIs
JILA/NIST and BNM-SYRTE.
Prototype of an optical lattice clock built
at BNM-SYRTE Fluorescence _at_ 461 nm
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Secondary representations of the second Paving
the way for a new definition of the second
The unperturbed ground-state hyperfine quantum
transition of 87Rb with a frequency of f (87Rb)
6 834 682 610.904 324 Hz and an estimated
relative standard uncertainty of 3 10-15,
The unperturbed optical 5d10 6s 2S1/2 (F 0)
5d9 6s2 2D5/2 (F 2) transition of the 199Hg
ion with a frequency of f (199Hg) 1 064 721
609 899 145 Hz and a relative standard
uncertainty of 3 x 10-15, The unperturbed
optical 5s 2S1/2 4d 2D5/2 transition of the
88Sr ion with a frequency of f (88Sr) 444
779 044 095 484 Hz and a relative uncertainty of
7 x 10-15, The unperturbed optical 6s 2S1/2
(F 0) 5d 2D3/2 (F 2) transition of the
171Yb ion with a frequency of f (171Yb) 688
358 979 309 308 Hz and a relative standard
uncertainty of 9 x 10-15, The unperturbed
optical transition 5s2 1S0 5s5p 3P0 87Sr
neutral atom with a frequency of f (87Sr) 429
228 004 229 877 Hz and a relative standard
uncertainty of 1.5 x 10-14.
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Conclusion

• Optical frequencies are doing pretty well
• When there will be at least one order, maybe two
  orders of magnitude better measurements with
  optical clocks than caesium fountains, the era of
  caesium will be over.
• The SI second will be the central unit for many
  decades to go, if not forever.