single-atom optical clocks— and fundamental constants

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.

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)