Cold Atoms and Stable Lasers:
The Clocks of the Future Today
Leo Hollberg
National Institute of Standards and Technology (NIST) , Boulder CO
Optical Frequency Reference
Ca Oven
I(f)
0
fr
µ-wave out
f
fn = nfr
Optical Synthesizer
optical out
Optical Frequency Measurements Group
Time and Frequency Division, NIST, Boulder
Cold Ca & Yb
Optical Clocks
Chris Oates
Chad Hoyt
Zeb Barber (CU)
Guido Wilpers (→ PTB)
Anne Curtis (CU → London)
Fs Frequency Combs
Scott Diddams
Chip Scale Atomic Devices
John Kitching
Albrecht Bartels → Konstance
Kyoungsik Kim (CU)
Tara Fortier (LANL)
Eugene Ivanov (UWA)
L-S Ma, Z. Bi, (ECNU-BIPM)
L.Robertson (BIPM)
Tanya Ramond → Ball Aero.
Svenja Knappe
Peter Schwindt
Hugh Robinson
Vishal Shah (CU)
Ying-Ju Wang (CU)
Vlady Gerginov (Notre Dame)
Diode laser and length metrology
Richard Fox
Mercury Standard
Jim Bergquist, Windell Oskay, S Bize → SYRTE, W Itano, D Wineland, and others
Cs fountain and NIST time scale
Steve Jefferts, Liz Donley, Tom Heavner, Tom Parker
•$$ NIST, DARPA-MTO, ONR-CU-MURI, NASA-microgravity physics, LANL
Types of Clocks
Ruler Clock
• require predictable vs. time and measurable
L
∆ t = 2L / c
Resonator
Decay
A=a0e -(t/τ)
e+
α
U
e-
t
Stable Oscillator
quartz
t
Atomic Energy Levels
E2
∆E ≡ h ν
E1
∆t=n/ν
Generic Atomic Clock
Feedback System
Locks LO to
atomic resonance
Detector
∆ν
Atoms
υ
Ca
Local Oscillator
High-Q resonator
Microwave Synthesizer
Quartz
Fabry Perot cavity
Laser
Counter
456 986 240 494 158
Atomic Beam Clock
Ramsey Method
Cs
dB/dx
dB/dx
Local Oscillator
Signal
l
# of Atoms
L
∆ν ≈ v / l
∆ν ≈ v / 2L
NIST F1, Cs atomic fountain clock
Primary frequency Standard of U.S.
S. Jefferts, L. Donley, T. Heavner
CSAC Design: All optical excitation of atomic microwave
clock transition (Coherent Population Trapping)
Photodiode
Cell
3.2 mm
Optics
1.5 mm
1.5 mm
Laser
Volume: 7.2 mm3
Cell interior volume: 0.6 mm3
John Kitching, Svenja Knappe …
1 mm
Current Microwave-Based Standards and Distribution
NIST-F1
Rb and/or Cs
GPS
Hydrogen
Masers
and
Cesium
Clocks
NIST
Measurement
System
∆f/f ~ 1x10-15
for standards
and distribution
Communications
satellites
Radio
broadcasts
Approaching the limit for standards and distribution systems.
Attributes of Clocks / Frequency Standards
Accuracy:
Same average frequency fclock = fatom
Reproducibility:
Different clocks give same frequency.
Stability:
Frequency does not change with time.
∆f rms (τ )
fo
Quartz
Freq.
Hydrogen maser 1
Cs
fatom
Hydrogen maser 2
Time
Highest Accuracy Atomic Clocks
optical
optical
Advantages of Optical Clocks
Frequency uncertainty ~
fo
∆f 1
1
⋅
⋅
f0
τ
N
f 0 optical
1015
≈ 10 ≈ 10 5
f 0 microwave 10
Laser-cooled Trapped Ions
• Narrow linewidth
• Long observation times
• Possibility of entanglement
Hg+, Al+, B+, Yb+ , Sr+ , In+ …
∆f
Atomic Resonance
τ
= observation time
N = number of atoms
Laser-cooled Neutral atoms
• Large number of atoms
106 or more
• High signal/noise
• Possibility of lattices
Ca, Sr, Yb, Mg, H …
One atomic clock is always “perfect”
Two similar clocks -- hard to detect systematic errors
Different types of clocks can determine most accurate and stable
Oscillator Stability
Quantum Limited Instability
Allan Deviation -- Instability
σ(τ)
σ (τ ) ~
10
-13
10
-14
10
-15
10
1
fo N
τ
H-maser
Ca
Cs
GPS
Hg+
-16
Ca
10
∆f
1 day
-17
10
-2
10
0
2
10
10
Averaging Time (s)
4
1 month
10
6
Alkaline-earth atoms make good optical atomic clocks, Ca example
(1) Singlet-triplet structure leads to narrow transitions in
the optical domain
(2) Strong 1S0 → 1P1 transitions good for laser cooling
1P (4s4p)
1
m=0
657 nm clock
∆ν = 400 Hz
1S (4s2)
0
m=0
3P (4s4p)
1
Ca magneto-optic trap features
KNbO3
846 nm ECDL
+ MOPA
40 mW
AOM
AOM
Probe Beams
∆ = - 10 MHz
Vacuum System
Trapping Beams
∆ = - 35 MHz
Ca Oven
13 cm
dB/dz = 60 G/cm
~107 atoms
T = 2 mK
AOM
Slowing Beam
∆ = - 260 MHz
1P
1
The Ca Optical Standard
3P
1
423 nm
cooling
657 nm
clock
1S
0
Diode Laser
400 Hz wide Ramsey fringes
Isolator
AOM
Servo
EOM
synthesizer
Atom error
signal
C. Oates
G. Wilpers
C. Oates, et al. Opt. Lett. 25, 1603 (2000)
Residual Doppler effect
R2
R1
θ
Freely expanding
atoms
α
g
Atomic velocity
G G G
G
r⊥ (t i ) 2
1 G 2
Φ ( r (t i )) = k ⋅ ( r0 + v 0 ⋅ t i + g ⋅ t i ) + k
2R
2
Wavefront curvature
Gravitation
Beam direction
Trebst et al: IEEE Trans. IM-50 (2001) 535
Neutral Atom Lattice Clock Example
3P
0
1S
0
Optical Clock
Transition
Lattice field
3P
1
87Sr, 171Yb, 43Ca
423 nm
cooling
1S
0
Candidates:
657 nm
clock
Advantages: No motion → Lamb Dicke limit,
Long observation time, Collisions minimized
Generic Atomic Clock
Feedback System
Locks LO to
atomic resonance
Detector
∆ν
Atoms
υ
Ca
Local Oscillator
High-Q resonator
Microwave Synthesizer
Quartz
Fabry Perot cavity
Laser
Counter
456 986 240 494 158
Vastly Simplified and Improved Synthesis Chain
ν10He-Ne
2
1.15 µm
ν10 = 520.206 837
ν10
X2
XTAL
(127I2)
NBS Laser Frequency
Femtosecond-Laser-Based
Synthesis Chain
Synthesizers/Dividers
ν10 = 2ν9 + ν10Β
CHARTREUSE
ν9 = 260.103 264
Ne (20Ne)
ν9 = ν8 + ν’CO 2+ ν’’CO
+ ν9Β
2
SA
13C16O
XTAL
Pump
nm
ν7 = ν6 + ν’CO 532
+ ν’’CO
+ ν7Β
2
2
9 µm R(20)
(1979)
C O 9 µm R(22)
Albrecht
ν8 = 196.780 372 Bartels, Scott Diddams, Tanya Ramond
16
He-Ne (1.52 µm)
ν8 = ν7 + νCO + ν8Β
2
XTAL
2
ν = 48.862 075
SA
CO (6.1 µm)
ν7 = 147.915 857
Xe (2.03 µm)
CO2 9 µm P(36)
CO 10 µm P(8)
Ti:Sapphire
Gain
He-Ne CH P(7) (3.39 µm)
SA
2
ν6 = 88.376 181 627
4
ν6 = 3 ν5 − 0.049 + ν6Β
K
SA
ν5 = 29.442 483 315
CO2 ν R(30) (10.2 µm)
ν5 = ν4 − 3 ν2 − 0.020 + ν5Β
K
SA
ν4 = 32.134 266 891
ν R(10) (9.3 µm)
ν3 =3 ν3 − 0.020 + ν4Β
K
SA
ν3 = 10.718 068 6
H2O (28 µm)
ν3 =12 ν2 + 0.029 + ν3Β
K
SA
ν2 = 0.890 760 550
HCN (337 µm)
ν2 =12 ν1 + ν2Β
K
SA
SA
ν1 = 0.074 232 545 83
SPECTRUM ANALYZER
DIODE
KLYSTRON
ν1 =7 ν0 + ν1Β
KLYSTRON
SA
ν0 = 0.010 600 363 69
COUNTER
KLYSTRON
all frequencies in THz
K. M. Evenson
D. A. Jennings
J. S. Wells
C. R. Pollock
F. R. Petersen
R. E. Drullinger
E. C. Beaty
J. L. Hall
H. P. Layer
B. L. Danielson
G. W. Day
R. L. Barger
Cs FREQ
STANDARD
Required many labs filled with
lasers, microwave synthesizers,
and electronics.
Relationship Between Pulse Duration and Spectral Bandwidth
10 fs
time
Ultrashort optical pulse, plus nonlinear fiber →
Broad Spectum
Repetitive pulse train → Frequency Comb → “ruler for frequency/time”
Power
Wavelength
•Initial efforts/ideas: J. Eckstein, A. Ferguson & T. Hänsch (1978), V. P. Chebotayev (1988)
**
0
The frequency of a mode is simply
Where N is and integer ~ 10
6
FN = N * frep – f0
f0
0
Frequency
fr=1/ τr.t.
frep ~ 1000 MHz
Self-Referenced Optical Frequency Sythesizer
fo
I(f)
0
frep
f
fn = n frep + fo
x2
f2n = 2nfrep + fo
fo
• fo is generated from a heterodyne beat between the second
harmonic of the nth mode and the 2nth mode.
• Once frep and fo are referenced to a Cs clock, all the
frequency modes of the fs comb are known absolutely
Jones, et al. Science 288, 635 (2000)
RF to Optical Clockwork with a Femtosecond Laser Comb
Femtosecond Laser Comb
50,000:1 Reduction Gear
(not to scale!)
Cs
~9 GHz
Hg+, Ca
~500 THz
Electric Field from a Femtosecond Mode-locked Laser
Time domain
∆φ
E(t)
2∆φ
t
Carrier-envelope
phase slip from pulse
to pulse because:
vg ≠ vp
τr.t = 1/fr
Frequency domain
I(f)
fo
Modes are offset from
harmonics of fr by:
fr
fo = fr ∆φ/2π
0
fn = nfr + fo
= fr (n + ∆φ/2π)
Original ideas: Hänsch, Wineland, Udem
f
Enthusiasm for
Optical atomic clocks
Testing the Femtosecond Synthesizer
A. Bartels, T. Ramond, L.-S. Ma, L. Robertsson, M. Zucco, S. Diddams
S. Diddams, et al. Opt. Lett 27, 58 (2002)
fr1 fo1
fs Comb #1
Diode Laser
456 THz
PMT
fs Comb #2
fr2 fo2
X-Correlation
(tests optical envelope)
Jitter: 400 as (1-100 Hz)
Stability: <2×10-15 τ-1
Reproducibility : < 1 × 10-18
RF Mixing
(tests microwave output)
Stability: ~2×10-15 τ-1
Reproducibility: <1 × 10-16
Optical Heterodyne
(tests comb teeth)
Stability: <2 × 10-16 τ-1
Reproducibility: <1 × 10-19
Optical output is very stable,
but photodetection electronics
adds Noise!
Ultra-low phase noise microwaves
Divided down 500 THz optical frequency reference to 10 GHz
sapphire
resonator
-80
Microwave synthesizer
L(f) [dBc/Hz]
-100
Femtosecond-laser-based
synthesizer
-120
-140
-160
Hg+ optical cavity
-180
Ca standard optical
(projected)
-200
10
0
10
1
10
2
3
10
10
Frequency (Hz)
4
10
5
10
6
Broadband Femtosecond Laser with <10 Hz Linewidth
at optical frequency, ~500 THz
Measurement
limited linwidth
of 10 Hz
10 Hz RBW, 20 averages
82% of power in central peak
-80
Power (dBm)
-70
-80
-90
-100
fs Comb #1
Diode Laser
456 THz
fs Comb #2
Power (dBm)
-110
-90
-200
0
Frequency Offs et (Hz)
200
-100
-110
-120
-10,000
Optical Heterodyne
-5,000
0
5,000
Frequency Offset (Hz)
10,000
Applications of Optical Frequency Standards ?
•Advanced communication systems (security, autonomous synchronization)
•Advanced Navigation (position determination and control)
•Precise timing (moving into the fs range)
•Tests of fundamental physics (special and general relativity, time variation of
fundamental constants)
•Sensors (strain, gravity, length metrology ……)
•Ultrahigh speed data, multi-channel parallel broadcast, or receivers,
coherent communications
A Cosmological Test of the Stability of α
∆α
α = 1×10
10
∆t
−5
10 yr
≈ 10 −15 yr -1
An accessible level for
atomic clocks!
Ca and Hg+ optical frequencies compared to Cs
(difference from respective mean values vs. date)
150
Frequency Offset (Hz)
100
50
0
-50
-100
-150
1/1/1996
1/1/1998
1/1/2000
Measurement Date
1/1/2002
1/1/2004
Frequency references, precise timing and
Clocks of 21st Century are OPTICAL
•
•
•
•
•
2000 begins Optical/Laser era in atomic clocks and precision timing
Already providing lowest phase-noise and timing jitter
– (fs jitter will soon be common place)
Very Cold (cm/s) atoms/ions provide the best stability and will provide
the best accuracy
– Requires super quality cw lasers and optical cavities
– Fs laser based optical frequency combs enabling and nearly pefect
Not clear which atoms will give best performance and depends on use
Some applications are beginning to appear:
– New tool for science, precise timing, length metrology,
communications, navigation, optical radar, chemistry, biology,
fundamental physics …