Single-atom Optical Clocks— and Fundamental Constants Hg+ clock Brent Young Rob Rafac Sebastien Bize Windell Oskay Luca Lorini Anders Brusch Sarah Bickman 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 Al+ clock Till Rosenband David B. Hume C.-W. Chou P. O. Schmidt Jim Bergquist Till Rosenband Wayne Itano Dave Wineland NIST- F1 Steve Jefferts Tom Heavner Elizabeth Donley Tom Parker JILA Jun Ye Jan Hall et al…

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

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

Optical Clock Laser Oscillator Single Ion/ Neutral Atoms Femtosecond comb 14:46:32 State detector Frequency feedback 1121 THz Drive atomic resonance Count optical cycles Clock frequency: Clock shift: anything that shifts (E 2 -E 1 )

Why Use Optical Transitions? Quantum Limit: Δ /  (2  0 ) -1 (NT R  ) -1/2 0 = transition frequency of reference (usually atom or molecule) N = # of atoms T R = interrogation time  = averaging time Examples: Cs fountains: 0 = 9.2 GHz, N  10 6, T R  1 s Δ /  4   -1/2 Single Atom: 0 = Hz, N  1, T R  30 ms Δ /  1   -1/2

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

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

Ground stateExcited state Time (ms) Counts/ms Quantum Jump Spectroscopy 9 The mercury ion acts as a *noiseless* optical amplifier One absorption event can prevent millions of scattering events

Isolated Cavities

Resonances near 0.3 Hz Servo table height by heating legs Two independent cavity systems

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

Mounted Spherical Cavity Orientation insensitive

“Magic” Mounting Angle of Spherical Cavity Captured cavity: Changing stress from mount points shifts cavity frequency –1°C  1  m  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

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

Vibration-broadened laser power-spectrum (predicted) Cylinder Sphere Linear scale Laser power spectrum at 250 THz [dB]

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

11 Can operate in tight-confinement (Lamb-Dicke) regime ⇒ First-order doppler free. 2nd-order doppler shift (time dilation) due to micromotion will limit accuracy 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 Trapped ions in an rf trap ~ rf

12 Cryogenic ion trap system Magnetic Shield

Cryogenic ion trap system 12 Magnetic Shield Cryostat Wall

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

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

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

13

0.8 mm 14 Trap material: molybdenum

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

Some facts about Al + 8 mHz linewidth clock transition Small quadratic ZS (6x /Gauss 2 ) Negligible electric-quadrupole shift (J=0) Smallest known blackbody shift (8x at 300K) Linear ZS 4 kHz/Gauss (easily compensated) Light mass (2 nd order Doppler shifts) No accessible strong transition for cooling & state detection 1S01S0 167 nm 1P11P1 3P03P0 267 nm 1121 THz I = 5/2

Clock state transfer to Be + 1.Cool to motional quantum ground state with Be + 2.Depending on clock state, add vibrational energy via Al + 3.Detect vibrational energy via Be + (simplified)

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 +

Quantum Logic Spectroscopy 3 P 1  =300  s 1S01S nm Clock transition nm Clock laser pulse Transition occurred? 1 S 0, n = 0 3 P 1 blue side- band pulse yes 3 P 0, n = 0 no 3 P 1 blue side- band pulse 3 P 1, n = 1 27 Al + n = 1 n = 0 P.O. Schmidt, et al. Science 309, 749 (2005) T. Rosenband, et al. PRL 98, (2007) D.B. Hume, et al. PRL 99, (2007) 3 P 0, n = 0 1 S 0, n = 0 3P03P0

Single phonon detection 9 Be + Red side- band pulse 2 S 1/2 F=2 n = 0 2 S 1/2 F=1 n = 0 Detection pulse ~ 4-10 in 200  s ~ 1 in 200  s 27 Al + 3 P 0 n = 0 27 Al + 1 S 0 n = 1 9 Be + 2 S 1/2 F=2 n = 0 9 Be + 2 S 1/2 F=2 n = 1 2 P 3/2 F=3 2 S 1/2 F=2 313 nm Cooling / detection Red sideband pulse  1.2 GHz Photon counter 2 S 1/2 F=1 n = 1 n = 0

High quality transition C.-W. Chou

fiber f b,Al m f rep + f ceo 1070 nm laser ×2 f b,Hg Hg + n f rep + f ceo 199 Hg + 27 Al + 9 Be nm laser Al+/Hg+ Comparison fs-comb locked to Hg+ measure beat with Al+

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

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

Al+/Hg+ Comparison ν Al+ /ν Hg+ = ± 55 x

Al + /Hg + Stability 3.6 x In 3 hours! Averaging time [s] Frequency ratio uncertainty

Al+/Hg+ Comparison

Transition Frequencies 14 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, (2004) Express transition frequencies as:

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

Constraint on  Cs /  B  /  x = (-3.1 +/- 3.9) x / year Hg + vs. Cs T. Fortier et al. PRL 98, Hg + vs. Al + Science  Cs  B 

…..[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

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

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