Femtosecond lasers: the gears of optical atomic clocks

Scott A. DiddamsTime & Frequency Division

National Institute of Standards and TechnologyBoulder, Colorado 80305

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)

NIST, Time & Frequency Division:

• Optical Frequency MeasurementsLeo HollbergAnne Curtis (grad student)Chris OatesTanya Ramond (post-doc)Isabell Thomann (grad student)Kristan Corwin (post-doc)Nate Newbury

• Ion StorageJim Bergquist Sebastian Bize (post-doc)Bob DrullingerWayne ItanoWindell Oskay (post-doc)Dave Wineland

• Atomic StandardsSteve JeffertsTom HeavnerTom Parker

What Makes a Clock?

Earth Rotation SundialPendulum Clock Gears/HandsQuartz Crystal Electronic Counter

Oscillator + Counting Mechanism

ATOMIC CLOCKSMicrowave Transition + Oscillator Electronic CounterOptical Transition + Laser Frequency Chain

Improvement of Cs microwave standards over 50 years

Optical ClocksWhy are they interesting?

• Optical standards have superior stability:e.g. Ca optical standard<2x10-16 at 1 s

• Optical standards have the potential for greatly improved accuracy: e.g. approaching 1x10-18 for single trapped ions

ττσ 1~)(

Nff

o

∆

10-17

10-16

10-15

10-14

10-13

Alla

n D

evia

tion

-- In

stab

ility

10-2 100 102 104 106

Averaging Time (s)

H-maser

Cs

Hg+

Ca

1 day 1 monthCa

ττσ 1~)(

yInstabilit Limited Quantum

Nff

o

∆

Oscillator Stabilityσ(

τ)

Single Hg+ Ion Optical Standard

Tprobe = 20 ms

Tprobe = 120 ms

~ 6.5 Hz

2S1/2

2D5/2

2P1/2

Observefluorescence(λ = 194 nm)

“clock” transition @fo ≈ 1.06x1015 Hz

199Hg+

F = 1

F = 0

F=2F=3

“Clock”Transition(λ=282 nm)

F=0F=1

Q=1.6×1014 !!

J. Bergquist, et al. (NIST)

Single Hg+ ion

Femtosecond-Laser-BasedOptical Synthesizer

• What is it? A device that phase-coherently connects optical and RF/microwave domains.

Optical Synthesizer

nm×

µ-wave in

optical in

µ-wave out

optical out

Femtosecond-Laser-Based SynthesizerPump Power Control of fo

Ti:SapphireGain

Output650 mW

frep= 1 GHz

PZT Control of frep

AOM5-8 W of532 nm

-60

-50

-40

-30

-20

Rela

tive

Powe

r (dB

)

12001000800600Wavelength (nm)

input output

MicrostructureFiber

S.A. Diddams, et al.Proc. SPIE vol. 4269 (200)

+1

0

Optical Clock with aFemtosecond Synthesizer

fm

PLL 2 fbOptical Standard (fHg )

frClock Output

fr = fHg ÷ m(m~106)

Femtosecond Laser +Microstructure Fiber

I(f)

f

fox2 f2n=fo+2nfrfn=fo+nfr

PLL 1

fr÷100

fr÷100

S. Diddams, et al. Science 293, 825 (2001)

Comparison of Hg+ Optical Clock to a H-maser

949,700

949,600

949,500

949,400

f Hg/

2 - 5

32 3

60 8

04 0

00 0

00 (H

z)

300025002000150010005000Time (s)

5 s gate timeScatter: 37 Hz

10-15

2

4

6810-14

2

4

68

Alla

n D

evia

tion

1 10 100 1000Averaging Time (s)

τ−1/2

Instability limitedby H-maser

Comparison of Hg+ (optical) to Cs (microwave)

-30

-20

-10

0

10

20

30f H

g-1

064

721

609

899

143.

4 (H

z)

Aug 00 Feb 01 Aug 01 Feb 02 Aug 02Measurement Date

Weighted Average of all Data:...899 143.4 (1.0) Hz Original Measurement: ...899 142.6(2.5) PRL 86, 4996 (2001)

Hg+ -- Cs comparison limits possible variation of α

constant assumed are and if yr101.1

or

yr107 to

of s variationpossible constrains dataPresent

1-15

1-15

03.6

×≤

×≤

∝

−

−

p

eCs

Hg

Cs

p

eCs

Hg

Cs

mmg

mmg

αα

νν

ανν

&

Dzuba, Flambaum, WebbPRA 59, 230 (1999)

S. Bize, et al. (submitted to Phys. Rev. Letters)

Hg-Ca Optical Comparison

fm

PLL 2 fbOptical Standard (fHg )

Femtosecond Laser +Microstructure Fiber

I(f)

f

fo

Self-Referencing

PLL 1

fCa

1.2

1.0

0.8

0.6

0.4

0.2Beat

am

plitu

de (a

.u.)

-1,000 -500 0 500 1,000Frequency (Hz)

1.0

0.8

0.6

0.4

0.2

0.0

Beat

Am

plitu

de (a

.u.)

-10,000 -5,000 0 5,000 10,000Frequency (Hz)

40,0000-40,000Frequency (Hz)

a)

b)

“Beat” between Hg+ and Ca across 76 THzMillions of Narrow Linewidth Oscillators

Femtosecondlaser

Hg+Standard

CaStandard

180 mfiber

10 mfiber

10 m fiber noise

180 m fiber noise

Hg-Ca beat

Testing the Femtosecond Synthesizer

Diode Laser456 THz

fs Comb #1

fs Comb #2

fr1 fo1

fr2 fo2

Optical Heterodyne(tests comb teeth)

Stability: <6ä10-16 τ-1

Accuracy: <4ä10-17

PMT

X-Correlation(tests envelope)Jitter: 400 as (1-100 Hz)Stability: <2ä10-15 τ-1

RF Mixing(tests microwave output)

Stability: ~2ä10-14 τ-1

Stability of Microwave and Optical Signals

10-17

10-16

10-15

10-14

10-13

Alla

n D

evia

tion

0.1 1 10 100Averaging Time (s)

Nonlinear X-Correlation Photodection +

Microwave RF Mixing

2x10-14 τ−1

2x10-15 τ−1

(Measurement Limited)

-200

-180

-160

-140

-120

-100

-80

100 101 102 103 104 105

Frequency [Hz]

L(f)

[dBc

/Hz]

a

b

cde

f

g

Comparison of Various Oscillators/Synthesizers

Phase noise for 1 GHz carrier

a. Premium quartz oscillatorb. Low noise synthesizerc. Sapphire oscillatord. Ca optical (projected)e. Hg+ optical cavityf. fs synthesizer: optical pulse traing. fs synthesizer: microwave output

Potential Limitations to RF Stability

•Shot Noise:rfr

shoty P

feiR6nf21)( ∆

τπτσ =

kHz 150 10dBm, mA, 4 for 101)( -115 =−==×= − ∆fPi rfshoty ττσ

•Excess noise from Laser or Microstructure Fiber

→ AM-PM conversion exists. For example, timing jitter of 1-10 ps/mW in various photodetectors.

→ Saturation with high peak power??

•Excess Phase Noise in Photodetection

Amplification of Fundamental Noise in Microstructured Fibers

-60

-40

-20 Power (dB

)140012001000800600

Wavlength (nm)

-140

-120

RIN

(dB

c/H

z)

(a)

(b) λL λR

-120

-100

RIN

(d

Bc/

Hz)

1.00.80.60.40.20.0Pulse Energy (nJ)

600

400

Wid

th (n

m)

(a)

(b)

K. Corwin, N. Newbury, J. Dudley,S. Coen, K. Weber, S. Diddams,R. Windeler (to appear in PRL)

ExperimentTheory

• High repetition rate—800 mW total power• Compact, 5-element ring design

532 nmpump

L M1 M2

M3 OC

Ti:Sa

A New, Simpler Tool:1 GHz Ti:sapphire Octave-Spanning Oscillator

A. Bartels and H. Kurz, Opt. Lett. 27, 1839 (2002)

KEY ELEMENT: 1000mm ROC convex mirror (M3) increased self-amplitude modulation shorter pulses enhanced

self-phase modulation

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

Pow

er P

er 1

GH

z M

ode

(µW

)

140012001000800600

Wavelength (nm)

Frequency triple 960nm and double 640nm to obtain 320nm heterodyne (fo)

3fn – 2fm = 3(nfr + fo) – 2(mfr + fo) = fo

Output spectrum of laser

Detection of fo without microstructure fiber

No critical alignment of nonlinear elementsCan be phase-locked nearly indefinitely….

Ramond et al. Optics Letters 27, 1842

Ti:Salaser

BBO640 nm

LiIO3

480 nm960 nm

960 nm

BBO

320 nm

Single ModeFiber

PMT320 nm

2f

3ffo

U. Morgner, et al. Phys. Rev. Lett. 86, 5462 (2001).T. Ramond, et al. Opt. Lett. 27, 1842 (2002).

Long-term Phase Locking of Broadband Laser

-5

0

5

c)

b)

a)

fLD Drift (kH

z)

f R -

998

,092

,449

.54

Hz

(mH

z)

f b - 6

00 M

Hz

(mH

z)

f 0 - 1

00 M

Hz

(mH

z)

0

50

100

0 2 4 6 8 10 12 14 16 18 20-0.20.00.20.40.6

Time (h)

-100

0

100

200

300

Offset Frequency

Beat with StabilizedLaser Diode

RepetitionRate

Control of femtosecond laser: <6ä10-18 @ 10 sïcan count >1019 optical cycles without missing a single one!

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