Single-atom Optical Clocks— and Fundamental Constants

1. Single-atom Optical Clocks—and Fundamental Constants Jim Bergquist Till Rosenband Wayne Itano Dave Wineland Al+ clock Till Rosenband David B. Hume C.-W. Chou P. O. Schmidt Hg+ clock Brent Young Rob Rafac Sebastien Bize Windell Oskay Luca Lorini Anders Brusch Sarah Bickman NIST- F1 Steve Jefferts Tom Heavner Elizabeth Donley Tom Parker JILA Jun Ye Jan Hall et al… fs-comb (Ti:Sapphire) Tara M. Fortier Jason E. Stalnaker Thomas Udem Scott A. Diddams Leo Hollberg fs-comb (fiber) Ian Coddington William C. Swann Nate R. Newbury

2. ~ ~ ~ ~ What is a clock? An Oscillator (Generates periodic events) A Counter (Count and display events / tell time) Period Frequency

3. What Makes a Clock a Time Standard? Requirements: Stability: Δti = Δtj or /t  0 Accuracy: Δt the same for all clocks   0 Added Ingredient Stable, “unperturbed” reference

4. Frequency feedback Optical Clock Femtosecond comb 1121 THz Count optical cycles Laser Oscillator Drive atomicresonance 14:46:32 State detector Clock frequency: Single Ion/ Neutral Atoms Clock shift: anything that shifts (E2-E1)

5. Examples: Cs fountains: 0 = 9.2 GHz, N  106, TR  1 s Δ/  410-14 -1/2 Why Use Optical Transitions? Quantum Limit: Δ/  (20)-1(NTR)-1/2 0 = transition frequency of reference (usually atom or molecule) N = # of atoms TR = interrogation time  = averaging time Single Atom: 0 = 1015 Hz, N  1, TR  30 ms Δ/  110-15 -1/2

6. Electron Shelving H.G. Dehmelt, Bull. Amer. Phys. Soc. 20, 60 (1975) • Gives method to detect weak transition in single atom 1 << 2 1 1 2 2 The absorption of one photon on the weakly allowed transition to level 2 0 shuts off the scattering of many photons on the strongly allowed transition to level 1

7. 199Hg+ Energy Levels • Atomic line • State detection by electron shelving. 3

8. Quantum Jump Spectroscopy The mercury ion acts as a *noiseless* optical amplifier One absorption event can prevent millions of scattering events Excited state Ground state 80 60 40 Counts/ms 20 0 0 200 400 600 800 Time (ms) 9

9. Isolated Cavities

10. Isolated Cavities • Resonancesnear 0.3 Hz • Servo table heightby heating legs • Two independentcavity systems

11. Beatnote between laser sources stabilized to independent cavities 0.22 Hz Relative beatnote power (arb.) frequency (Hz) 15

12. Mounted Spherical Cavity Orientation insensitive

13. “Magic” Mounting Angle of Spherical Cavity • Captured cavity: • Changing stress from mount points shifts cavity frequency • 1°C  1 mm  0.02 lb  300 kHz • Vertical mount points: • Squeeze makes cavity longer • Mount near optical axis: • Squeeze makes cavity shorter • At 37 degrees: zero sensitivity • Symmetry  vibration insensitivity No movement

14. NPL, 2008 SYRTE, 2009 3-D Vibration sensitivity v-block mounted cylindrical cavity Spherical cavity(measured)

15. Vibration-broadened laser power-spectrum (predicted) CylinderSphere Linear scale Laser power spectrum at 250 THz [dB]

16. ~ Trapped ions in an rf trap • No static E or B fields; Trap acts on total charge of ion, not internal structure • Trap ion at trap center where trapping fields approach zero rf • Motion in trap: Micromotion at trap frequency, slow harmonic “secular” motion 21 10

17. ~ Trapped ions in an rf trap • No static E or B fields; Trap acts on total charge of ion, not internal structure • Trap ion at trap center where trapping fields approach zero rf • Can operate in tight-confinement (Lamb-Dicke) regime ⇒ First-order doppler free. 2nd-order doppler shift (time dilation) due to micromotion will limit accuracy 11

18. Cryogenic ion trap system Magnetic Shield 12

19. Cryogenic ion trap system Magnetic Shield Cryostat Wall 12

20. Cryogenic ion trap system Magnetic Shield Cryostat Wall 77 K Shield 12

21. Cryogenic ion trap system Magnetic Shield Cryostat Wall 77 K Shield 4 K Copper Shield around trap 12

22. Liquid Nitrogen Magnetic Shield Cryostat Wall 77 K Shield Liquid Helium • Long storage times • Environmental isolation - Low collision rate - Low blackbody Helical Resonator 4 K Copper Shield around trap 13

23. 13

24. 0.8 mm Trap material: molybdenum 14

25. Spectroscopy of 199Hg+ • Accessible strong transition for laser-cooling, state preparation/detection • Large mass ↔ small 2nd order Doppler shift • static quadrupole shift can be minimized • small blackbody shift • 1.8 Hz linewidth clock transition

26. Some facts about Al+ 1P1 • 8 mHz linewidth clock transition • Small quadratic ZS (6x10-16 /Gauss2) • Negligible electric-quadrupole shift (J=0) • Smallest known blackbody shift (8x10-18 at 300K) • Linear ZS 4 kHz/Gauss (easily compensated) • Light mass (2nd order Doppler shifts) • No accessible strong transition forcooling & state detection 3P0 167 nm 267 nm1121 THz 1S0 I = 5/2

27. Clock state transfer to Be+ (simplified) • Cool to motional quantum ground state with Be+ • Depending on clock state, add vibrational energy via Al+ • Detect vibrational energy via Be+

28. Using two ions • Clock ion (Al+) for very accurate spectroscopy • Logic ion (Be+) for cooling and readout • Coulomb-force couples the motion of the ions • Cooling Be+ leads to cooling of Al+ Ion motion is quantized (n=0, 1, …) Transfer information Al+_ Motion _ Be+

29. Quantum Logic Spectroscopy P.O. Schmidt, et al. Science309, 749 (2005) 27Al+ 1S0, n = 0 T. Rosenband, et al. PRL 98, 220801 (2007) n = 1n = 0 3P1t=300ms Clock laserpulse D.B. Hume, et al. PRL 99, 120502 (2007) n = 1n = 0 3P0 Transition occurred? no 267.0 nm Clock transition 267.5 nm yes n = 1n = 0 1S0 3P0, n = 0 1S0, n = 0 3P1 blue side-band pulse 3P1 blue side-band pulse 3P1, n = 1 3P0, n = 0

30. 27Al+3P0n = 0 27Al+1S0n = 1 9Be+ 2S1/2 F=2n = 1 9Be+2S1/2 F=2n = 0 Red side-band pulse Red side-band pulse 2S1/2 F=1n = 0 2S1/2 F=2n = 0 Detection pulse Detection pulse ~ 1 in 200 ms ~ 4-10 in 200 ms Single phonon detection 9Be+ Photoncounter 2P3/2 F=3 n = 1n = 0 313 nm Cooling / detection 2S1/2 F=1 Red sideband pulse Dn = 1.2 GHz n = 1n = 0 2S1/2 F=2

31. High quality transition C.-W. Chou

32. 1126 nmlaser Al+/Hg+ Comparison fs-comb locked to Hg+ measure beat with Al+ 1070 nm laser fiber ×2 ×2 fiber ×2 ×2 9Be+ fb,Al Hg+ 199Hg+ fb,Hg 27Al+ m frep+ fceo n frep+ fceo

33. Femtosecond Ti:Sapphire Laser Pulsed output Pump laser Pulse duration: Repetition rate: 23

34. Counting optical frequencies Laser frequency (563 nm): Interclock comparisons: • Other optical standards (Al+, Ca, Yb, Sr, etc.) Difference frequency: • Microwave standards Difference frequency: Problem: Fastest electronic counters: Solution: Femtosecond laser frequency comb 33

35. Al+/Hg+ Comparison νAl+/νHg+ = 1.052 871 833 148 990 438 ± 55 x 10-17 10-16

36. Al+/Hg+ Stability Frequency ratio uncertainty 3.6 x 10-17In 3 hours! Averaging time [s]

37. Al+/Hg+ Comparison 10-16

38. Transition Frequencies Express transition frequencies as: V. A. Dzuba, V. V. Flambaum, and J.K. Webb,PRA 59, 230 (1999) E. J. Angstmann, V. A. Dzuba, and V. V. Flambaum PRA 70, 014102 (2004) 14

39. Historical Record of νHg • 28 Measurements • Aug. 2000 - Mar. 2004: (23)with realistic assumption uncertainty in quadrupole shift < 1 Hz. • Oct. 2004 - Jan 2005: (3)Uncertainty due to measurement statistics and Hg+ systematics are approximately equal • July 2005 - present: (2) Uncertainty dominated by measurement statistics • Fit to a line: (∂ν/∂t)ν=(0.36 ± 0.39)×10-15/yr implies- (∂α/∂t)/α = (6.2 ± 6.5) × 10-17/yr if ∂(lnμ/μB)/∂t = 0

41. Constraint on mCs/mB . m / m x 10-16 = (-3.1 +/- 3.9) x 10-16 / year Hg+ vs. Al+ Science m = mCs/mB Hg+ vs. Cs T. Fortier et al. PRL 98, 070801

42. …..[the Hg+ ion] clock is so powerful yet so exquisitely fine-tuned that it virtually echoes the ionic heartbeat of the universe itself. And so precise that it is accurate to within seconds per month. Direct-mail copy writers

43. Outlook • Keep measuring Al+/Hg+ • Compare with other standards • Variation of fundamental constants? • Solid state lasers • Second Al+ and Hg+ clock? • More Al ions • More Hg ions

44. “…the most important unit of time?” “A Lifetime.” Howard Bell (~1980)