Cold Atoms and Stable Lasers: The Clocks of the Future Today

Leo Hollberg National Institute of Standards and Technology (NIST) , Boulder CO

Optical Synthesizer

Optical Frequency Reference

µ-wave out

optical out

fr

0

I(f)

f

Ca Oven

fn = nfr

Optical Frequency Measurements GroupTime and Frequency Division, NIST, Boulder

Cold Ca & YbOptical Clocks

Chris OatesChad Hoyt

Zeb Barber (CU) Guido Wilpers (→ PTB)

Anne Curtis (CU → London)

Fs Frequency CombsScott Diddams

Albrecht Bartels → KonstanceKyoungsik Kim (CU)Tara Fortier (LANL)

Eugene Ivanov (UWA)L-S Ma, Z. Bi, (ECNU-BIPM)

L.Robertson (BIPM)Tanya Ramond → Ball Aero.

•$$ NIST, DARPA-MTO, ONR-CU-MURI, NASA-microgravity physics, LANL

Mercury StandardJim Bergquist, Windell Oskay, S Bize → SYRTE, W Itano, D Wineland, and others

Cs fountain and NIST time scaleSteve Jefferts, Liz Donley, Tom Heavner, Tom Parker

Chip Scale Atomic DevicesJohn KitchingSvenja KnappePeter SchwindtHugh Robinson

Vishal Shah (CU)Ying-Ju Wang (CU)

Vlady Gerginov (Notre Dame)

Diode laser and length metrology Richard Fox

Types of Clocks

Ruler Clock

Decay

Stable Oscillator

Atomic Energy Levels

∆E ≡ h ν ∆ t = n / νE1

E2

• require predictable vs. time and measurable

L

Resonator ∆ t = 2L / c

A=a0e -(t/τ)

quartz

e+α

Ue-

t

t

∆ν

Ca

Detector

Local Oscillator

High-Q resonatorQuartz

Fabry Perot cavity

Feedback SystemLocks LO to

atomic resonance

Microwave SynthesizerLaser

456 986 240 494 158

Counter

υ

Generic Atomic Clock

Atoms

Atomic Beam Clock

Ramsey Method

Cs

Signal

# of Atoms

dB/dxdB/dx

Local Oscillator

L

l

∆ν ≈ v / l ∆ν ≈ v / 2L

NIST F1, Cs atomic fountain clockPrimary frequency Standard of U.S.

S. Jefferts, L. Donley, T. Heavner

CSAC Design: All optical excitation of atomic microwave clock transition (Coherent Population Trapping)

1.5 mm

3.2 mm

1.5 mm

Laser

Optics

Cell

Photodiode

1 mmVolume: 7.2 mm3

Cell interior volume: 0.6 mm3

John Kitching, Svenja Knappe …

Current Microwave-Based Standards and Distribution

Approaching the limit for standards and distribution systems.

NISTMeasurementSystemHydrogen

Masersand

CesiumClocks

HydrogenMasers

andCesiumClocks

NIST-F1NIST-F1

GPS

Communications satellites

Radiobroadcasts

∆f/f ~ 1x10-15

for standards and distribution

Rb and/or Cs

Attributes of Clocks / Frequency Standards

Accuracy: Same average frequency fclock = fatom

Reproducibility: Different clocks give same frequency.

Stability: Frequency does not change with time.

fatom

Time

Freq. Quartz

Hydrogen maser 1

Hydrogen maser 2

Cs

o

rms

ff )(τ∆

opticaloptical

Highest Accuracy Atomic Clocks

Advantages of Optical Clocks

0

1 1ff Nτ

∆⋅ ⋅Frequency uncertainty ~

τ = observation time

N = number of atoms

510

15

0

0 101010

≈≈microwave

opticalf

f

Laser-cooled Trapped Ions Laser-cooled Neutral atoms

• Narrow linewidth• Long observation times• Possibility of entanglement

• Large number of atoms 106 or more

• High signal/noise• Possibility of lattices

Hg+, Al+, B+, Yb+ , Sr+ , In+ … Ca, Sr, Yb, Mg, H …

∆f

fo

Atomic Resonance

One atomic clock is always “perfect”Two similar clocks -- hard to detect systematic errors Different types of clocks can determine most accurate and stable

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

Oscillator Stabilityσ(

τ)

GPS

Quantum Limited Instability1 ( ) ~

o

ff N

σ ττ

∆

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

m = 01S0 (4s2)

1P1 (4s4p)

657 nm clock∆ν = 400 Hz

3P1 (4s4p)m = 0

Ca magneto-optic trap features

Slowing Beam∆ = - 260 MHz

~107 atoms

846 nm ECDL+ MOPA

KNbO3 40 mW

Trapping Beams∆ = - 35 MHz

Probe Beams∆ = - 10 MHz

T = 2 mK

AOM

AOM

AOM

dB/dz = 60 G/cm

13 cmCa Oven

Vacuum System

657 nm clock

1S0

3P1

423 nmcooling

400 Hz wide Ramsey fringes

Diode Laser

EOMServo

Isolator

AOM synthesizer

Atom error signal

1P1The Ca Optical StandardThe Ca Optical Standard

C. Oates G. Wilpers

C. Oates, et al. Opt. Lett. 25, 1603 (2000)

Residual Doppler effect

Trebst et al: IEEE Trans. IM-50 (2001) 535

R1

Freely expanding atoms

αg

R2

Atomic velocityAtomic velocity

WavefrontWavefront curvaturecurvature

GravitationGravitation

Beam directionBeam direction

Rtrktgtvrktr i

iii 2)()

21())((

22

00⊥+⋅+⋅+⋅=Φ

θ

Neutral Atom Lattice Clock Example

1S0

3P0

Optical Clock Transition

Advantages: No motion → Lamb Dicke limit, Long observation time, Collisions minimized

Candidates:87Sr, 171Yb, 43Ca

657 nm clock

1S0

3P1

423 nmcooling

Lattice field

∆ν

Ca

Detector

Local Oscillator

High-Q resonatorQuartz

Fabry Perot cavity

Feedback SystemLocks LO to

atomic resonance

Microwave SynthesizerLaser

456 986 240 494 158

Counter

υ

Generic Atomic Clock

Atoms

Vastly Simplified and Improved Synthesis Chain

NBS Laser Frequency Synthesis Chain(1979)

K. M. EvensonD. A. Jennings J. S. WellsC. R. PollockF. R. PetersenR. E. DrullingerE. C. BeatyJ. L. HallH. P. LayerB. L. DanielsonG. W. DayR. L. Barger

Required many labs filled with lasers, microwave synthesizers, and electronics.

Cs FREQSTANDARD

COUNTERν0 = 0.010 600 363 69KLYSTRON

ν1 = 0.074 232 545 83KLYSTRON

ν2 = 0.890 760 550HCN (337 µm)

ν3 = 10.718 068 6H2O (28 µm)

ν4 = 32.134 266 891

ν R(10) (9.3 µm)

ν5 = 29.442 483 315

CO2 ν R(30) (10.2 µm)

ν6 = 88.376 181 627He-Ne CH4P(7) (3.39 µm)

ν7 = 147.915 857Xe (2.03 µm)

ν8 = 196.780 372He-Ne (1.52 µm)

ν9 = 260.103 264Ne (20Ne)

He-Ne ν102 1.15 µm

X2XTAL

ν10(127I2)

ν10 = 520.206 837

13C16O2 9 µm R(20)

C16O2 9 µm R(22)XTALXTAL

CO (6.1 µm)ν = 48.862 075

CO2 9 µm P(36)

CO2 10 µm P(8)

SA

SA

SA

SA K

KSA

KSA

SA K

SA

SA

SA

K KLYSTRON

SPECTRUM ANALYZER

DIODE

CHARTREUSE

ν1 =7 ν0 + ν1Β

ν2 =12 ν1 + ν2Β

ν3 =12 ν2 + 0.029 + ν3Β

ν3 =3 ν3 − 0.020 + ν4Β

ν5 = ν4 − 3 ν2 − 0.020 + ν5Β

ν6 = 3 ν5 − 0.049 + ν6Β

ν7 = ν6 + ν’CO + ν’’CO + ν7Β2 2

ν9 = ν8 + ν’CO + ν’’CO + ν9Β2 2

ν8 = ν7 + νCO + ν8Β

ν10 = 2ν9 + ν10Β

all frequencies in THz

Ti:SapphireGain

532 nmPump

Femtosecond-Laser-Based Synthesizers/Dividers

Albrecht Bartels, Scott Diddams, Tanya Ramond

10 fs

Ultrashort optical pulse, plus nonlinear fiber → Broad SpectumRepetitive pulse train → Frequency Comb → “ruler for frequency/time”

Relationship Between Pulse Duration and Spectral Bandwidth

time

Wavelength

Power

•Initial efforts/ideas: J. Eckstein, A. Ferguson & T. Hänsch (1978), V. P. Chebotayev (1988)**

The frequency of a mode is simply FN = N * frep – f0Where N is and integer ~ 10

6

Frequencyfr=1/ τr.t.

f0

frep ~ 1000 MHz

0

0

I(f)

f

fo

0fn = n frep + fo

frep

x2 f2n = 2nfrep + fo

fo

Self-Referenced Optical Frequency Sythesizer

• 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)

Cs ~9 GHz

Hg+, Ca~500 THzFemtosecond Laser Comb

50,000:1 Reduction Gear(not to scale!)

RF to Optical Clockwork with a Femtosecond Laser Comb

Electric Field from a Femtosecond Mode-locked Laser

0 fn = nfr + fo= fr (n + ∆φ/2π)

I(f)

f

fo fr

Frequency domain

2∆φ

τr.t = 1/fr

t

E(t)

Time domain∆φ

Carrier-envelopephase slip from pulseto pulse because:

vg ≠ vp

Modes are offset from harmonics of fr by:

fo = fr ∆φ/2π

Original ideas: Hänsch, Wineland, Udem

Enthusiasm for

Optical atomic clocks

Testing the Femtosecond Synthesizer

Diode Laser456 THz

fs Comb #1

fs Comb #2

fr1 fo1

fr2 fo2

PMT

X-Correlation(tests optical envelope)Jitter: 400 as (1-100 Hz)Stability: <2×10-15 τ-1

Reproducibility : < 1 × 10-18

Optical output is very stable,but photodetection electronics adds Noise!

A. Bartels, T. Ramond, L.-S. Ma, L. Robertsson, M. Zucco, S. Diddams

Optical Heterodyne(tests comb teeth)

Stability: <2 × 10-16 τ-1

Reproducibility: <1 × 10-19

S. Diddams, et al. Opt. Lett 27, 58 (2002)

RF Mixing(tests microwave output)

Stability: ~2×10-15 τ-1

Reproducibility: <1 × 10-16

Ultra-low phase noise microwavesDivided down 500 THz optical frequency reference to 10 GHz

-200

-180

-160

-140

-120

-100

-80

L(f)

[dB

c/H

z]

100 101 102 103 104 105 106

Frequency (Hz)

sapphireresonator

Hg+ optical cavity

Ca standard optical(projected)

Femtosecond-laser-basedsynthesizer

Microwave synthesizer

Broadband Femtosecond Laser with <10 Hz Linewidthat optical frequency, ~500 THz

Diode Laser456 THz

fs Comb #1

fs Comb #2

Optical Heterodyne

-120

-110

-100

-90

-80

Pow

er (d

Bm)

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

10 Hz RBW, 20 averages82% of power in central peak

-110

-100

-90

-80

-70

Pow

er (d

Bm

)

-200 0 200Frequency Offset (Hz)

Measurementlimited linwidth

of 10 Hz

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

1-1510

5

yr 10yr 10

101 −−

≈×

=∆

∆

tα

α

An accessible level foratomic clocks!

Ca and Hg+ optical frequencies compared to Cs (difference from respective mean values vs. date)

-150

-100

-50

0

50

100

150

Freq

uenc

y O

ffset

(Hz)

1/1/1996 1/1/1998 1/1/2000 1/1/2002 1/1/2004Measurement Date

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 …