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