Single-atom Optical Clocks—and Fundamental Constants
Hg+ clockBrent YoungRob Rafac
Sebastien BizeWindell Oskay
Luca LoriniAnders BruschSarah Bickman
fs-comb (Ti:Sapphire)Tara M. Fortier
Jason E. StalnakerThomas Udem
Scott A. DiddamsLeo Hollberg
fs-comb (fiber)Ian Coddington
William C. SwannNate R. Newbury
Al+ clockTill RosenbandDavid B. Hume
C.-W. ChouP. O. Schmidt
Jim BergquistTill Rosenband
Wayne ItanoDave Wineland
NIST- F1Steve JeffertsTom Heavner
Elizabeth DonleyTom Parker
JILAJun Ye
Jan Hallet 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: Δti = Δtj 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
Frequencyfeedback
1121 THz
Drive atomicresonance
Count optical cycles
Clock frequency:
Clock shift: anything that shifts (E2-E1)
Why Use Optical Transitions?
Quantum Limit: Δ/ (20)-1(NTR)-1/2
0 = transition frequency of reference (usually atom or molecule)
N = # of atoms TR = interrogation time = averaging time
Examples:
Cs fountains:0 = 9.2 GHz, N 106, TR 1 s Δ/ 410-14 -1/2
Single Atom: 0 = 1015 Hz, N 1, TR 30 ms
Δ/ 110-15 -1/2
Electron Shelving H.G. Dehmelt, Bull. Amer. Phys. Soc. 20, 60 (1975)
Gives method to detect weak transition in single atom
1 11 << 2
0
2 2
The absorption of one photon on the weakly allowed transition to level 2
shuts off the scattering of many photonson the strongly allowed transition to level 1
199Hg+ Energy Levels
3
• Atomic line • State detection by electron shelving.
Ground stateExcited state
0 200 400 600 800Time (ms)
0
20
40
60
80
Cou
nts/
ms
Quantum Jump Spectroscopy
9
The mercury ion acts asa *noiseless* optical amplifier
One absorption event can preventmillions of scattering events
Isolated Cavities
Isolated Cavities
• Resonancesnear 0.3 Hz
• Servo table heightby heating legs
• Two independentcavity systems
frequency (Hz)
Rela
tive b
eatn
ote
pow
er
(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
-60
-50
-40
-30
-20
-10
0
10
20
0 10 20 30 40 50 60 70
Angle [deg]
Sq
ue
eze
se
ns
itiv
ity
[M
Hz/
lb]
No movement
3-D Vibration sensitivity
v-block mounted cylindrical cavity
Spherical cavity(measured)
NPL, 2008
SYRTE, 2009
Vibration-broadened laser power-spectrum (predicted)
CylinderSphere
Linear scale
Las
er p
ow
er s
pec
tru
m a
t 25
0 T
Hz
[dB
]
• No static E or B fields; Trap acts on total charge of ion,
not internal structure
21
• Trap ion at trap center wheretrapping 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 wheretrapping fields approach zero
Trapped ions in an rf trap
~ rf
12
Cryogenic iontrap system
Magnetic Shield
Cryogenic iontrap system
12
Magnetic Shield
Cryostat Wall
Cryogenic iontrap system
12
Magnetic Shield
Cryostat Wall
77 K Shield
Cryogenic iontrap system
12
Magnetic Shield
Cryostat Wall
77 K Shield
4 K Copper Shieldaround trap
13
Helical Resonator
Magnetic Shield
Cryostat Wall
Liquid Nitrogen
Liquid Helium77 K Shield
4 K Copper Shieldaround trap
• Long storage times
• Environmental isolation- Low collision rate- Low blackbody
13
0.8 mm
14
Trap material: molybdenum
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
Some facts about Al+
• 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
1S0
167 nm
1P1
3P0
267 nm1121 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 ionsClock ion (Al+) for very accurate spectroscopyLogic ion (Be+) for cooling and readoutCoulomb-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
3P1=300s
1S0
267.0 nmClock transition267.5 nm
Clock laserpulse
Transitionoccurred?
1S0, n = 0
3P1 blue side-band pulse
yes
3P0, n = 0
no
3P1 blue side-band pulse
3P1, n = 1
27Al+n = 1n = 0
n = 1n = 0
n = 1n = 0
P.O. Schmidt, et al.Science 309, 749 (2005)
T. Rosenband, et al. PRL 98, 220801 (2007)
D.B. Hume, et al. PRL 99, 120502 (2007)
3P0, n = 0 1S0, n = 0
3P0
Single phonon detection
9Be+
Red side-band pulse
Red side-band pulse
2S1/2 F=2n = 0
2S1/2 F=1n = 0
Detection pulse
Detection pulse
~ 4-10in 200 s
~ 1in 200 s
27Al+ 3P0
n = 0
27Al+ 1S0
n = 1
9Be+ 2S1/2 F=2n = 0
9Be+ 2S1/2 F=2n = 1 2P3/2 F=3
2S1/2 F=2
313 nmCooling /detection
Red sideband pulse 1.2 GHz
Pho
toncounter
2S1/2 F=1
n = 1n = 0
n = 1n = 0
-10 -5 0 5 100
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Frequency offset [Hz] near 1121 THz
Tra
nsiti
on p
rob.
Al+ 1S0 - 3P
0 resonance (20 scans, 250 ms probe time)
3.2 Hz
Q = 3.5 x 1014
High quality transition
C.-W. Chou
fiber
fiber
fb,Al
m frep+ fceo
1070 nmlaser
×2
×2
×2
×2
fb,HgHg+
n frep+ fceo
199Hg+
27Al+
9Be+
1126 nmlaser
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
Dec Jan FebMar Apr May Jun Jul Aug Sep Oct Nov Dec
0.4
0.5
Al/
Hg
10
15 -
1 0
52
87
1 8
33
14
8 9
90
-dot / = (1.433 +/- 1.702) x 10-17 / yr 2 =2.9674
2006 20072007
Al+/Hg+ Comparison
10-16
νAl+/νHg+ = 1.052 871 833 148 990 438 ± 55 x 10-17
Al+/Hg+ Stability
100
101
102
103
104
105
10-17
10-16
10-15
10-14
Al+ vs Hg+, 11874 seconds total
3.9*10-15 * ( / s)-1/2
Al+ vs Hg+ ADEVAl+ vs Hg+ THEO1
3.6 x 10-17
In 3 hours!
Averaging time [s]
Fre
quen
cy r
atio
unc
erta
inty
Dec Jan FebMar Apr May Jun Jul Aug Sep Oct Nov Dec
0.4
0.5
Al/
Hg
10
15 -
1 0
52
87
1 8
33
14
8 9
90
-dot / = (1.433 +/- 1.702) x 10-17 / yr 2 =2.9674
2006 20072007
Al+/Hg+ Comparison
10-16
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, 014102 (2004)
Express transition frequencies as:
-10
0
10
Hg
- 1
064
721
609
899
145.
33 (
Hz)
Jan 01 Jan 02 Jan 03 Jan 04 Jan 05 Jan 06
Measurement Date
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
Constraint on Cs/B
-1.0 -0.5 0.0 0.5 1.0-10
-5
0
5
10
d/d
t ln( C
s/B)
x 1
0-16
d/dt ln() x 10-16
/ x 10-16 = (-3.1 +/- 3.9) x 10-16 / year
Hg+ vs. CsT. Fortier et al.PRL 98, 070801
Hg+ vs. Al+
Science
CsB
…..[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.
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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)