Optical Lattice Clock with Spin-1/2 Ytterbium Atoms

Nathan D. Lemke

103

106

109

1012

1015

1018

1100 2010 AD 1500 1250 1750 num

ber

of

seco

nd

s t

o g

ain

/lo

se o

ne

seco

nd

Water clock Huygen’s pendulum Harrison’s chronometer

Shortt clock

Quartz crystal

Cesium beam

Cesium fountain

Optical lattice

Single ion (Al+)

one second per day

one second per year

one second per million years

one second per thousand years

one second per billion years

roughly reproduced from ScienceNews 180(9)

2011

Clocks, past & present

Yb Yb

Yb

Yb

Yb

Yb Yb

Yb

Yb

Yb

Yb

Yb Yb

578 nm

laser

Fast feedback Slow feedback

Why atoms?

• Identical

• Ageless

• High Q

• Easily isolated

from environment

fs-laser comb

Optical Atomic Clocks

reference cavity atomic system

Ca, Sr, Hg..., Sr+, Yb+, Ca+, Al+, Hg+...

Very high stability

Potential for high accuracy

Sr lattice ~ 1.5e-16

Al + ion ~ 9e-18

Will enable

Tests of relativity

Searches for variation of constants

Other science: Synchrotron, radio telescopes, ultralow-noise microwaves

Technology: communications, navigation

Rosenband et al., Science 319, 1808 (2008)

(graph reproduced)

Heavner et al., Metrologia 42, 411

(2005)

Yb, current projected stability

Optical Atomic Clocks Yb

Yb Yb

Yb

Yb

Yb Yb

Yb

Yb

Yb

Yb

Yb Yb

578 nm

laser

reference cavity

Key features of lattice clocks

Long interaction times narrow lines Large numbers (~104) high S/N

3P0

1S0

Doppler- & recoil-free Stark-free

λmagic

Choosing the atom

Benefits of I = 1/2

Simple sub-structure (mF = ± 1/2)

Straightforward optical pumping

No tensor shift

Fermion no collisions?

Choosing the isotope I = 0 (e.g. 88Sr, 174Yb, 202Hg)

I ≠ 0 (e.g. 87Sr, 171Yb, 199Hg)

Boyd, et al, PRA

76, 022510 (2007) Barber, et al, PRL

96, 083002 (2006)

Ytterbium Energy Levels

1S0

1P1

λ = 399 nm

Δν = 28 MHz

3P1

λ = 556 nm

Δν = 180 kHz

3P0

λ = 578 nm

Δν =10 mHz

λmagic = 759 nm

Spectroscopy and Detection

1P1

3P1

3P0

1S0

3D1

λ = 1388 nm

repump

Ground state

Background Excited

state

time 5 ms

Clock pulse

λmagic = 759 nm

171Yb Spectra

Sideband fit

Blatt, et al, PRA 80,

052703 (2009)

Temperature

~15 μK

Ex

cita

tion

fr

acti

on

171Yb Spectra

Lemke, et al, PRL

103, 063001 (2009)

π π

mF =1/2 mF = ‒1/2

mF =1/2

mF = ‒1/2

1S0

3P0

Optical cavity design

Legero, et al, JOSA B

27, 914 (2010)

f

f

L

L

L~30 cm

Thermal noise, vibration isolation,

high vacuum, stable temperature…

Coherence measurement Noise levels for 1 cavity

Jiang, et al, Nature

Photon. 5, 158 (2011)

Narrow lines

900 ms probe time

400 ms trap lifetime (1/e)

Δν = 1 Hz Q = 5 × 1014

Jiang, et al, Nature

Photon. 5, 158 (2011)

Open loop

In-loop Interleave

Dick limit

Blackbody -25.0 2.5

Density-dependent -16.1 0.8

Lattice scalar 0.4 1.0

Lattice hyper-polarizability 3.3 0.7

Lattice multi-polar (M1/E2) 0 1.0

Linear Zeeman 0.4 0.4

Quadratic Zeeman -1.7 0.1

Probe light 0.05 0.2

AOM phase chirp 0 0.1

Others 0 0.1

Total -38.7 3.4

Systematic uncertainty

Effect Shift (10-16) unc. (10-16)

Lemke, et al, PRL

103, 063001 (2009)

Absolute Frequency

νYb-171= 518,295,836,590,865.0 ± 0.5 Hz

Absolute Frequency

νYb-171= 518,295,836,590,865.0 ± 0.5 Hz

Park, et al,

arXiv:1112.5939

Outline for the rest

1. Cold collisions of fermions

2. High-accuracy polarizability measurement

“Taking stock of a locked clock’s tick-tock

shocks from knocks and a mock hot-box”

- J. Sherman

Fermionic collisions

Identical & Ultracold No s-wave scattering amplitude

(quantum statistics) Small p-wave scattering amplitude

(threshold at 30 – 45 µK)

Campbell et al,

Science 324, 360

(2009)

DeMarco et al,

PRL 96, 4280 (1999)

Excitation Inhomogeneity

zyx nnn ,,Rabi frequency

depends on atom

temperature

Singlet – triplet basis

Lemke, et al,

PRL 107, 103902 (2011)

Gibble,

PRL 103, 113202 (2009)

Swallows, et al,

Science 25, 1043 (2011)

Identifying p-wave collisions

Lemke, et al, PRL

107, 103902 (2011)

1-D lattice 2-D lattice 1-D lattice

bgg = 0

beg = ‒74 a0 bee

3 = 0.1 beg3

s-wave only

p-wave only

p-wave + smaller s-wave

Canceling the collision shift

Weighted mean: 2.5 2.4 mHz Ludlow, et al, PRA

84, 052724 (2011)

Outline for the rest

1. Cold collisions of fermions

2. High-accuracy polarizability measurement

“Taking stock of a locked clock’s tick-tock

shocks from knocks and a mock hot-box”

- J. Sherman

Blackbody radiation shift

400 K

300 K

200 K

Fused silica

substrate

Conductive &

transparent ITO

2 nm Cr / 33 nm Au

~90% R @ 760 nm

Electrodes

Fused silica

substrate

Set of precision ground fused silica spacers

Length matched ~ 200 nm, < 1 arcsecond wedging

Conductive &

transparent ITO

2 nm Cr / 33 nm Au

~90% R @ 760 nm

Electrodes

Electrodes

Electrodes

Laser frequency (GHz)

Tra

nsm

issio

n

Fringe center uncertainty:

50 MHz

ECDL

760 nm

0 10

Plate separation

Tra

nsm

issio

n

Laser frequency (GHz)

ECDL

760 nm

Plate separation

Tra

nsm

issio

n

Tuning ~17 THz

(1700 fringes)

ECDL

760 nm

1-2 ppm

statistical error

Plate separation

Laser frequency (GHz)

Field Reversal

–

Measurement Results

Sherman, et al, PRL

108, 153002 (2012)

Measurement Results

Sherman, et al, PRL

108, 153002 (2012)

Measurement Uncertainty

a

b

c

Porsev, et al, PRA 74, 020502 (2006)

Porsev, et al, PRA 60, 2981 (1999)

Dzuba, et al, J. Phys B 43, 074011 (2010) a

b

c

Sherman, et al, PRL

108, 153002 (2012)

Dynamic correction

Extracting the BBR shift

Inside an ideal blackbody at 300 K

Δν = –2.465(1) × 10-15

ΔT = 1 K causes clock uncertainty of 3.3 ×10-17

Is this a blackbody?

Systematic table: update

Effect Shift (10-16) unc. (10-16)

Blackbody -25.0 2.5

Density-dependent -16.1 0.8

Lattice scalar 0.4 1.0

Lattice hyper-polarizability 3.3 0.7

Lattice multi-polar (M1/E2) 0 1.0

Linear Zeeman 0.4 0.4

Quadratic Zeeman -1.7 0.1

Probe light 0.05 0.2

AOM phase chirp 0 0.1

Others 0 0.1

Total -38.7 3.4

-24.65 0.3

0.05 0.05

0.4 ?

What’s next for lattice clocks?

• 10-17 level uncertainty (collisions, lattice light shifts…)

• Cryogenic apparatus

• Frequency ratios

• Transportable systems

Acknowledgements

Yb Clock Chris Oates, Andrew Ludlow, Jeff Sherman, Rich Fox, Nathan Hinkley, Kyle Beloy, Nate Phillips

Frequency Comb Tara Fortier, Scott Diddams, et al

Collisions (Theory) Ana Maria Rey, Javier Von Stecher

Al+, Hg+ Clocks Jim Bergquist, Till Rosenband, et al

Sr Lattice Clock Jun Ye and his group

Cs Fountain & Timescale Steve Jefferts, Tom Heavner, Tom Parker