The future of time

1. The future of time Frequency combs, optical clocks

2. 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

3. 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

4. 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.

5. Quick review of Caesium fountain

6. 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) F=4 9.19263177 GHz H F=3 Energy levels converted in Hz

7. Laser Cooling of Atoms 1 Direction of motion Light Light Atom 3 4 2 Direction of force

8. Sub-Doppler cooling 0.1 µK One dimension, lin  lin,P=/4 Sisyphus effect Better yet: evaporative cooling nK no spatial polarization gradient P Dalibard, Cohen-Tannoudji, J. Opt. Soc. Am. B 6, 2023-45, Nov. 1989

9. Trapping /Cooling /Acceleration • Launching cycle: • 6-beam configuration • (+/- 45o and horizontal) • Trapping a small atomic • cloud in a MOT • Six-beam cooling molasses • Acceleration No laser beam goes into fountain Acceleration distance is short! • Further Cooling in moving molasses • with reduced beam intensity for a time 

10. Operating Principle • Atoms are trapped and cooled to a few mK. • They are launched upward by the lasers through a m -wave cavity. • Gravity pulls the atoms back through the cavity. • The Cs atoms are interrogated by a m -wave field generated by the local oscillator. • The Cs atoms are detected by a probe laser. • The correction signal is sent back to the local oscillator. The entire process is repeated .

11. Louis Marmet about to install the new vacuum chamber for the caesium fountain

12. Dead time can be introduced to avoid spin exchange Phase modulated detection -p/2 +p/2 +p/2 -p/2 Single pulse operation Passage through µ wave cavity-> -Dn +Dn gap Will avoid the need for a super-duper local oscillator Detection time Trapping and launching

13. Phase modulation:phase measurement of the local oscillator Phase modulation y() Frequency modulation White freq. -1 -1/2 Flicker phase Will act like an active atomic clock! And yet will be a passive clock. Flicker freq. 0  Phase tracking is first true realisation of the SI second

14. 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?

15. 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.

16. How to link all those frequencies? laser laser laser Cs laser Ion Trap Frequency chain

17. 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

18. The Optical Frequency Comb

19. fbeat1 fbeat2

20. The comb offset is caused by dispersion

23. fs Optical Frequency Comb Output Mode-locked Ti:sapphire laser From 532 nm pump laser Micro- Structured fibre

24. The probe laser

25. The Ultra-stable 674-nm laser for probing the Sr+ ion

26. The heart of the probe laser

27. to ion trap The diode laser at 674 nm is stabilized by a first INVAR Fabry-Perrot cavity The signal is further stabilized on the ULE cavity.

28. to ion trap 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.

29. Single ion trap

31. 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.

32. NRC Single Strontium Ion Trap Artist Impression of Trap and Excitation Beams View of Chamber and Photomultiplier

33. 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.

34. Frequency Comb Era Frequency Chain Era

36. 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

38. Optical lattice

39. 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.

40. Energy Structure of 87Sr

41. The Sr optical Lattice Clock: How it Works 3S 1 1P1 Dipole Trap ltrap=813.5 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). Pal’chikov, 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).

42. 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 @ 689 nm 1 4- Ramsey pulses at clock transition: large t 5- measure 1S0 state population @ 461 nm 707 nm 1P1 6- repump atoms 7- measure 1S0 state population @ 461 nm 679 nm 3P MOT =461 nm 8- Use fluorescence measurements to calculate populations 2 1 ltrap=813.5 nm 0 Sideband cooling: 689 nm Clock transition: 698 nm 1S0

43. Clock Frequency Measurements • Magic lattice wavelength: 813.5 nm • Cooling: 461 nm • 87Sr: Clock transition: weakly dipole allowed, 1 mHz linewidth 5s21S0 5s5p 3P0 : 698 nm f(5s21S0 5s5p 3P0) = 429228004229952 ± 15 Hz (Katori, Nature, May 2005) • 88Sr: Transition: 7.6 kHz linewidth 5s21S0 5s5p 3P1 : 689 nm f(5s21S0 5s5p 3P1) = 434829121312334 ± 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).

44. Experimental System Strontium source Zeeman Slower Vacuum chamber 2-D shown Ti:Saph 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: 429.22800422995 THz Repumper laser 707 nm

45. 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 @ 461 nm

46. 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.