Femtosecond lasers:
the gears of optical atomic clocks
Scott A. Diddams
Time & Frequency Division
National Institute of Standards and Technology
Boulder, Colorado 80305
NIST, Time & Frequency Division:
• Optical Frequency Measurements
Leo Hollberg
Anne Curtis (grad student)
Chris Oates
Tanya Ramond (post-doc)
Isabell Thomann (grad student)
Kristan Corwin (post-doc)
Nate Newbury
• Ion Storage
Jim Bergquist
Sebastian Bize (post-doc)
Bob Drullinger
Wayne Itano
Windell Oskay (post-doc)
Dave Wineland
• Atomic Standards
Steve Jefferts
Tom Heavner
Tom Parker
Guest Researchers:
Albrecht Bartels (U. Aachen)
Eugene Ivanov (U. West. Aust.)
Long-Sheng Ma (U. Colorado & BIPM)
Lennart Robertsson (BIPM)
Utako Tanaka (CRL, Japan)
Carol Tanner (Notre Dame U.)
Thomas Udem (MPQ)
Karl Weber (U. Melbourne)
Tim Birks (U. of Bath)
Robert Windeler (OFS)
What Makes a Clock?
Oscillator
+
Earth Rotation
Pendulum
Quartz Crystal
ATOMIC CLOCKS
Microwave Transition + Oscillator
Optical Transition + Laser
Counting Mechanism
Sundial
Clock Gears/Hands
Electronic Counter
Electronic Counter
Frequency Chain
Improvement of Cs microwave standards over 50 years
Optical Clocks
Why are they interesting?
• Optical standards have superior stability:
e.g. Ca optical standard
∆f
1
σ (τ ) ~
<2x10-16 at 1 s
fo N τ
• Optical standards have the potential for greatly
improved accuracy: e.g. approaching 1x10-18 for
single trapped ions
Oscillator Stability
Allan Deviation -- Instability
σ(τ)
Quantum Limited Instability
10
-13
Ca
10
-14
10
-15
10
H-maser
σ (τ ) ~
1
fo N
τ
Cs
Hg+
-16
Ca
10
∆f
1 day
-17
10
-2
10
0
2
10
10
Averaging Time (s)
4
1 month
10
6
Single Hg+ Ion Optical Standard
2P
F=1
F=0
1/2
199Hg+
F=3
F=2
2D
5/2
Observe
fluorescence
(λ = 194 nm)
Tprobe = 20 ms
“Clock”
Transition
(λ=282 nm)
2S
F=1
1/2
F=0
“clock” transition @
fo ≈ 1.06x1015 Hz
Q=1.6×1014 !!
J. Bergquist, et al. (NIST)
~ 6.5 Hz
Tprobe = 120 ms
Single Hg+ ion
Femtosecond-Laser-Based
Optical Synthesizer
• What is it? A device that phase-coherently
connects optical and RF/microwave domains.
µ-wave in
Optical Synthesizer
µ-wave out
optical in
m
×
n
optical out
Femtosecond-Laser-Based Synthesizer
PZT Control of frep
Pump Power Control of fo
Output
650 mW
frep= 1 GHz
AOM
0
+1
-20
Ti:Sapphire
Gain
Microstructure
Fiber
input
output
-30
Relative Power (dB)
5-8 W of
532 nm
-40
-50
-60
S.A. Diddams, et al.
Proc. SPIE vol. 4269 (200)
600
800
Wavelength (nm)
1000
1200
Optical Clock with a
Femtosecond Synthesizer
PLL 1
fo
fn=fo+nfr
fr÷100
f2n=fo+2nfr
x2
I(f)
Femtosecond Laser +
Microstructure Fiber
fm
PLL 2
fr÷100
fb
fr
f
Optical Standard (fHg )
Clock Output
fr = fHg ÷ m
(m~106)
S. Diddams, et al. Science 293, 825 (2001)
fHg/2 - 532 360 804 000 000 (Hz)
Comparison of Hg+ Optical Clock to a H-maser
949,700
949,600
949,500
5 s gate time
Scatter: 37 Hz
949,400
0
500
1000
1500 2000
Time (s)
2500
3000
8
6
Allan Deviation
4
2
-14
10 8
6
−1/2
τ
4
2
10
-15
1
10
100
Averaging Time (s)
1000
Instability limited
by H-maser
fHg-1 064 721 609 899 143.4 (Hz)
Comparison of Hg+ (optical) to Cs (microwave)
30
20
Weighted Average of all Data:
...899 143.4 (1.0) Hz
Original Measurement: ...899 142.6(2.5)
PRL 86, 4996 (2001)
10
0
-10
-20
-30
Aug 00 Feb 01 Aug 01 Feb 02 Aug 02
Measurement Date
Hg+ -- Cs comparison limits
possible variation of α
 me  6.03
ν Cs
α
∝ g Cs 
m 
ν Hg
 p
Dzuba, Flambaum, Webb
PRA 59, 230 (1999)
Present data constrains possible variations of
 ν Cs

ν
 Hg
or

 to ≤ 7 × 10 −15 yr -1


 me 
α&
−15
-1
 are assumed constant
≤ 1.1× 10 yr if g Cs and 
m 
α
 p
S. Bize, et al. (submitted to Phys. Rev. Letters)
Hg-Ca Optical Comparison
PLL 1
fo
Self-Referencing
fCa
I(f)
Femtosecond Laser +
Microstructure Fiber
fm
PLL 2
fb
f
Optical Standard (fHg )
Hg+
Standard
180 m
fiber
Beat Amplitude (a.u.)
“Beat” between Hg+ and Ca across 76 THz
Millions of Narrow Linewidth Oscillators
Femtosecond
laser
Ca
Standard
0.8
0.6
a)
180 m fiber noise
-40,000
0.4
0
40,000
Frequency (Hz)
0.2
0.0
-10,000
Beat amplitude (a.u.)
10 m
fiber
1.0
1.2
-5,000
0
Frequency (Hz)
5,000
10,000
10 m fiber noise
b)
1.0
0.8
0.6
Hg-Ca beat
0.4
0.2
-1,000
-500
0
Frequency (Hz)
500
1,000
Testing the Femtosecond Synthesizer
fr1 fo1
fs Comb #1
Diode Laser
456 THz
X-Correlation
PMT
(tests envelope)
Jitter: 400 as (1-100 Hz)
Stability: <2ä10-15 τ-1
fs Comb #2
fr2 fo2
RF Mixing
(tests microwave output)
Stability: ~2ä10-14 τ-1
Optical Heterodyne
(tests comb teeth)
Stability: <6ä10-16 τ-1
Accuracy: <4ä10-17
Allan Deviation
Stability of Microwave and Optical Signals
10
-13
10
-14
Nonlinear X-Correlation
Photodection +
Microwave RF Mixing
2x10
10
-14 −1
τ
-15
2x10
10
-16
10
-17
-15 −1
τ
(Measurement Limited)
0.1
1
10
Averaging Time (s)
100
Comparison of Various Oscillators/Synthesizers
Phase noise for 1 GHz carrier
-80
L(f) [dBc/Hz]
-100
a
f
-120
a.
b.
c.
d.
e.
f.
g.
b
g
-140
-160
e
-180
c
d
-200
0
10
10
1
2
10
10
3
Frequency [Hz]
4
10
10
5
Premium quartz oscillator
Low noise synthesizer
Sapphire oscillator
Ca optical (projected)
Hg+ optical cavity
fs synthesizer: optical pulse train
fs synthesizer: microwave output
Potential Limitations to RF Stability
shot
•Shot Noise: σ y ( τ ) =
1
2πnf rτ
6 eiR∆f
Prf
σ yshot (τ ) = 1× 10 −15τ -1 for i = 4 mA, Prf = −10dBm, ∆f = 150 kHz
•Excess Phase Noise in Photodetection
→ AM-PM conversion exists. For example, timing jitter
of 1-10 ps/mW in various photodetectors.
→ Saturation with high peak power??
•Excess noise from Laser or Microstructure Fiber
Amplification of Fundamental Noise in
Microstructured Fibers
-20
RIN (dBc/Hz)
-60
λL
(b)
-120
Power (dB)
-40
(a)
K. Corwin, N. Newbury, J. Dudley,
S. Coen, K. Weber, S. Diddams,
R. Windeler (to appear in PRL)
λR
-140
600
800
1000
Wavlength (nm)
1200
1400
RIN (dBc/Hz)
600
400
-100 (b)
-120
0.0
0.2
0.4
0.6
0.8
Pulse Energy (nJ)
1.0
Width (nm)
(a)
Experiment
Theory
A New, Simpler Tool:
1 GHz Ti:sapphire Octave-Spanning Oscillator
A. Bartels and H. Kurz, Opt. Lett. 27, 1839 (2002)
M3
OC
532 nm
pump
L
M1
Ti:Sa
• High repetition rate—
800 mW total power
• Compact, 5-element
ring design
M2
KEY ELEMENT: 1000mm ROC convex mirror (M3)
increased self-amplitude modulation Æ shorter pulses Æ enhanced
self-phase modulation
Output spectrum of laser
102
Power Per 1 GHz Mode (µW)
101
100
10-1
10-2
10-3
10-4
10-5
10-6
600
800
1000
1200
1400
Wavelength (nm)
Frequency triple 960nm and double 640nm to obtain
320nm heterodyne (fo)
3fn – 2fm = 3(nfr + fo) – 2(mfr + fo) = fo
Detection of fo without microstructure fiber
Ti:Sa
laser
640 nm
U. Morgner, et al. Phys. Rev. Lett. 86, 5462 (2001).
T. Ramond, et al. Opt. Lett. 27, 1842 (2002).
2f
BBO
320 nm
960 nm
LiIO3
960 nm
3f
480 nm
Single Mode
Fiber
BBO
320 nm
fo
PMT
No critical alignment of nonlinear elements
Can be phase-locked nearly indefinitely….
Ramond et al. Optics Letters 27, 1842
Long-term Phase Locking of Broadband Laser
Control of femtosecond laser: <6ä10-18 @ 10 s
ïcan count >1019 optical cycles without missing a single one!
(mHz)
f0 - 100 MHz
5
a)
Offset Frequency
0
b)
(mHz)
100
Beat with Stabilized
Laser Diode
50
0
(mHz)
0.6
300
c)
0.4
200
0.2
100
0.0
0
-0.2
-100
0
2
4
6
8
10
12
Time (h)
14
16
18
20
fLD Drift (kHz)
fR - 998,092,449.54 Hz
fb - 600 MHz
-5
Repetition
Rate
Summary + Outlook
•Femtosecond lasers combined with cold atom standards
will be the basis of future atomic clocks
(stability ~1µ10-16 @1s, accuracy < 1µ10-17 )
•Emerging applications and uses:
--secure communications
--ultra low noise microwaves (RADAR)
--length metrology
--time/frequency transfer over fiber networks
--remote sensing
--extreme nonlinear optics
•Smaller, more compact, more robust
--novel solid state femtosecond lasers
--broader spectra, different wavelength regimes