ATOMIC CLOCKS: BASIC PRINCIPLES AND · PDF fileIntroduction to the lectures and to atomic...

Conférence Universitaire de Suisse OccidentaleProgramme doctoral en physique, Printemps 2014 1Vapour cell atomic frequency standards

Lecture 4, Gaetano Mileti, 13.03.2014

ATOMIC CLOCKS: BASIC PRINCIPLES AND APPLICATIONSLecture 4 Vapour cell atomic frequency standards

Gaetano Mileti, C. Affolderbach, Laboratoire Temps – Fréquence (LTF), Université de Neuchâtel

CUSO – Conférence Universitaire de Suisse OccidentaleProgramme doctoral de Physique – Printemps 2014

13.03.2014



PROGRAM OF CUSO LECTURES 2014 (3RD EDITION)

Thursday February 20, lecture # 1G. Mileti, Laboratoire Temps‐Fréquence (LTF), Université de NeuchâtelIntroduction to the lectures and to atomic clocks, Cs thermal beam standards

Thursday February 27, lecture # 2L.‐G. Bernier, Laboratoire de Photonique, Temps et Fréquence, Institut fédéral de métrologie (METAS)Atomic time scale, Allan deviation, time transfer, Hydrogen Masers & its applications

Thursday March 6, lecture # 3S. Schilt and R. Matthey, Laboratoire Temps‐Fréquence (LTF), Université de NeuchâtelFundamentals in laser spectroscopy and laser frequency stabilisations. Examples of applications

Thursday March 13, lecture # 4G. Mileti and C. Affolderbach, Laboratoire Temps‐Fréquence (LTF), Université de NeuchâtelVapour cell standards, chip‐scale atomic clocks, applications in telecommunications and navigation

Thursday March 20, lecture # 5J. Guéna, LNE‐SYRTE (Laboratoire National de Métrologie et d'Essais, SYRTE), Observatoire de ParisAtomic fountains, primary frequency standards

Thursday March 27, lecture # 6T. Südmeyer, LTF‐UniNe and T. Kippenberg, Laboratoire de Photonique et Mesures Quantiques, EPFLIntroduction to optical combs and applications. Examples of recent developments.

Thursday April 3, lecture # 7C. Salomon, Laboratoire Kastler Brossel, Département de Physique Ecole Normale Supérieure, ParisLaser cooling and trapping of atoms. Bose‐Einstein Condensation. The ACES experiment on the ISS

Thursday April 10, lecture # 8S. Bize, LNE‐SYRTE (Laboratoire National de Métrologie et d'Essais, SYRTE), Observatoire de ParisOptical frequency standards and applications



Rubidium clocks:

• Chapter 8 of book J. Vanier and C. Audoin, Adam-Hilger, Bristol (1989)

• Article of J. Camparo, Physics Today, November (2007)

From the lecturer (Rb clocks):

• PhD of G. Mileti thesis, Université de Neuchâtel (1995)

• ESA bulletin, vol. 122 (May), p. 53, (2005)

• Proc. SPIE, vol. 5830, p. 159, (2005)

• Comptes-rendus du Congrès Intern. de Chronométrie, p. 91 (2007)

• Journal and Web site of the Swiss Physical Society, July, (2008)

• Tutorial on Rb clocks joint IFCS EFTF conference, Prague, July, (2013)

ESSENTIAL BIBLIOGRAPHY ON RB CLOCKS



1. Vapour cell standards basic principle

2. Laser-pumped Rubidium clock

3. Coherent Population Trapping

4. Chip-scale atomic clocks

CONTENTS OF LECTURE 4



Heart of the clock: a Rubidium vapour cell

5S1/2

F=1

F=2mF = 0mF = -1mF= -2

mF = 1mF = 2

mF = 0mF = -1

mF = 1

6.8346 GHz

87Rb

Rb partial pressure: 10-5 torr(1011-1012 atoms)

RUBIDIUM VAPOUR CELL

We apply to the atoms in the vapourphase one or more

resonant electromagnetic

fields.



Absorption spectrum of natural rubidiumD2 line (780 nm)with 30 mb of nitrogen

Rb 85 - F= 2

Rb 87 - F= 2

Rb 85 - F= 3

Rb 87 - F= 1

Optical frequency detuning [GHz]0 2 4 6 8

S

P

RUBIDIUM ISOTOPES (REMINDER FROM LECTURE 1)



Each atom in the vapor undergoes the following interactions:

• Collisions: buffer gas, other atoms, walls

• Static magnetic fieldUsually collinear with laser propagation

• Resonant interaction with the optical beam

• Resonant interaction with a microwave field

In lecture # 1, we have shown how these interactions may be described

S

P

light

‐wave

5S1/2

F=1

F=2mF = 0mF = -1mF= -2

mF = 1mF = 2

mF = 0mF = -1

mF = 1

6.8346 GHz

87Rb

RFBH

ˆ

EdH

ˆˆ

BASIC INTERACTIONS OF THE ATOMS IN THE CELL



S

P

Thermal equilibrium

S

P

Complete optical pumping

S

P

Partial optical pumping

Lamp Rb87 filter Rb85 cell Rb87

HYPERFINE OPTICAL PUMPING (WITH LAMP AND FILTER)

Absorption spectrum of natural rubidiumD2 line (780 nm)with 30 mb of nitrogen

Rb 85 - F= 2

Rb 87 - F= 2

Rb 85 - F= 3

Rb 87 - F= 1

Optical frequency detuning [GHz]0 2 4 6 8



Rb87 LampRb85 filtre

Rb87 resonance cell

détector

Microwave cavity

5.304x106 5.306x106 5.308x106 5.310x106 5.312x1060.108

0.112

0.116

0.120

0.124

0.128

Tra

nsm

itted

ligh

t [V

on

10k

]

6.84 GHz - Synthesiser frequency [Hz]

S

P

Double resonance

light

‐wave

DOUBLE RESONANCE (WITH A DISCHARGE LAMP)



I

III

1II

III

tiIIIIIIRb

IIIIII

tiIIII

III

IIIIII

tiIIII

III

IIII

eii

e

e

)()(

)(Im)(

)(Im)(

12

121

121

2

22

22

2

2

1

1

Bloch equations approach

« Fictitious » spinU: dipole component in phaseV: dipole component out of phaseV: difference of population

)-(

0//1

1

vwwvuv

vuu

RATE EQUATIONS WITH A 3-LEVELS MODEL



I II

tiIII e

0 2 ( )I II ll

( ) ( )

( )

Im

ll 0 1

1

4 I IIi t

I II Rb I IIi t

e

i i e

2

2

0 22)(1

Rb2

124 / ll

i i Spin Exchange i Wall Collisions i Buffer GasCollisions / / / i 1,2

)(22 21// III

Broadening (relaxations):

Rate equations (equivalent to Bloch equations):

Stationary solution:

Note: here the interaction with light is described as a relaxation process

RELAXATION PROCESSES AND STATIONARY SOLUTIONS



variation du flux d'énergie

lumineuse

=

nombre d'atomes rencontrés par

les photons

x

nombre de photons absorbés par atome

et par seconde

x énergie

d'un photon

[W / cm2] [1 / cm2] [1 / s] [J]

I n l hn l h

I I Rb

II II Rb

222

222

)(442

)()(

Rb

IIIIIIIIIRbhlnI

llll

Linearabsorption

Opticalpumping

Micro-wave

Clock signal

THEORETICAL “CLOCK” DOUBLE RESONANCE SIGNAL



5.304x106 5.306x106 5.308x106 5.310x106 5.312x1060.108

0.112

0.116

0.120

0.124

0.128

Tra

nsm

itted

ligh

t [V

on

10k

]

6.84 GHz - Synthesiser frequency [Hz]

Resonant photons (typical values):

– 2·1012 / (s ·mm2) incident

– 6·1011 / (s ·mm2) transmitted

– 1.5·1011 / (s ·mm2) Double Resonance

MEASURED “CLOCK” DOUBLE RESONANCE SIGNAL



0 20 40 60 80 1000

100

200

300

400

500

600

1° h

arm

onic

sig

nal w

idth

[Hz]

Nitrogen pressure [mbar]

Exemple expérimentalAvec une celluleCylindrique de 1-2 cm3

Parois

Gaz + Spin-Exchange

EFFECT OF COLLISIONS

Experimental example with a 1 x 2 cm cylindrical cell

Alternative: use of inner wall coating (like in H Masers)



EXAMPLES OF RB CLOCKS (OBSERVATOIRE NE 1985-1995)



EXAMPLE OF COMMERCIAL PRODUCTION (SPECTRATIME NE)



GPS (USA) GLONASS (RU) GALILEO (EU)

Other similar developments:Rb clock for Cassini-Huygens mission, China (Wuhan, etc.) and Japan (Anritsu, etc.)

EXAMPLES OF SPACE RB CLOCKS



Communications:

SDH (Synchronous Digital Hierarchy) CCITT G811,G812 Mobile communications base stations reference clock Spread Spectrum secure radio communication systems Digital Radio&Video Broadcast systems (DRB , DVB)

Instrumentation:

Telecom SDH synch. Test sets , Cellular base stations test sets … Synthesizers, Counters , Laboratory , Metrology GPS time receivers.

OTHER APPLICATIONS OF RB CLOCKS



+ price !



Examples of Laser diodes

Solitary Fabry-Perot (FP) Extended cavity lasers (ECDL) Distributed Bragg Reflectors (DBR) Distributed Feedback (DFB) FP with DBR optical fiber Vertical Cavity Surface Emitting (VCSEL) MEMS based ECDL and VCSELs Discrete mode lasers Etc.

780, 795, 852, 894nm the atom may be changedSingle mode, mode-hop free tuningTypical specs: 5-10 mW, LW < 5 MHzLow intensity and frequency noise

1.50um

ECDL

DFB

DBR

VCSEL

FP (RWL)

TUNABLE AND FREQUENCY-CONTROLLED LASER DIODES



-4 -2 0 2 4 6 80

5

10

15

20

25

30

D2 lines of Rb87

F = 1F = 2

Phot

ocur

rent

[ mA]

Laser diode frequency [GHz]

-4 -2 0 2 4 6 80

50

100

150

200

250

300

350

400

450

Maximal slope : 600 Hz / GHz


Rubi

dium

clo

ck fr

eque

ncy

[Hz]

Laser diode frequency [GHz]-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

F=2

Total(F=1)+(F=2)

F=1

Ligh

t shi

ft (1

0 -7

)

Laser wave length

0 2 4 6 8 103500

3505

3510

3515

3520

3525

(0,1 mW/ mm2)

(S = 90 mm2)

Fit : 3500,4 + 2,31 x I

Fit : 3500,3 + 2,45 x I

Laser tuned to F=1

Laser tuned to F=2

"Clo

ck" F

requ

ency

[Hz]

Photocurrent [m A]

dfclock/dIlaser

dfclock/dflaser

LIGHT-SHIFT EFFECT (AC STARK SHIFT)



-4 -2 0 2 4 6 80

5

10

15

20

25

30

D2 lines of Rb87

F = 1F = 2

Phot

ocur

rent

[ mA]


-4 -2 0 2 4 6 80

50

100

150

200

250

300

350

400

450



Rubi

dium

clo

ck fr

eque

ncy

[Hz]


-1000 -800 -600 -400 -200 0 200 400 600 8000.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

10-8

Refere

nce a

bsor

ption

line

"10

MH

z" C

lock

freq

uenc

y (-

9'99

9'99

6) [H

z]

Laser frequency detuning [MHz]

-200 -180 -160 -140 -120 -100 -80 -60 -40 -20 0 200.64

0.68

0.72

0.76

0.80

0.84

0.88

"zer

o lig

ht-s

hift"

lase

r fre

quen

cy

Rb8

7 C

O 2

1-23

Rb8

7 C

O 2

2-23

2·10-9

Reference saturated absorption"1

0 M

Hz"

clo

ck fr

eque

ncy

(-9'

999'

996)

[Hz]

Laser frequency detuning [MHz]

LIGHT-SHIFT EFFECT (AC STARK SHIFT)

This effect exists also with lamps but its control is different when using a laser source.



1 2 3 4 5 6 7 8 9 10

10-13

10-12

4.10-14

9.10-14

2,5.10-13

RIN = 1.10-12

4.10-12

9.10-12

5 KHz/Hz0,5

10 KHz/Hz0,5

20 KHz/Hz0,5

50 KHz/Hz0,5Slaser = 100 KHz/Hz0,5

Pred

icte

d A

llan

devi

atio

n y

-

1/2

DC Photocurrent [A]

21

).(2.0

NSQ

Iy

EFFECT OF THE LASER AM AND FM NOISE (SHORT-TERM)

Noise subtraction is possible!

Fundamental limit: shot noise.



RUBIDIUM VAPOR CELL – CELL FILLING SYSTEM

LTF cell filling facility Cell temperature coefficient

• Typical TC ≈ 1x10-11/K2

• Clock instability ≤ 1x10-15

132

130

128

126

124

122

120

118

116

114

reso

nanc

e fre

quen

cy s

hift

[Hz]

656055504540

Cell temperature [°C]

data quadratic fit

TINV

Light-shift

x109

300

290

280

270

260

250

240

706050403020100-10Laser Power (uW)

Fe3 Fe23 Fe13

Sig

nal

Laser frequency

Fe3Fe23

Fe13

Freq

uenc

y sh

ift a

t 6.8

GH

z (H

z)

Laser power (uW)

Cellno.

Batch no.

Quadratic behaviour

inversion point TINV (± 2°C)

3120 1 Yes 56°C

3125 2 Yes 58°C

3131 3 Yes 56°C

3134 4 Yes 53°C

Goodreproducibility

C. Affolderbach, F. Droz, G. Mileti, IEEETrans. on Instrumentation & Measur., Vol.55, No. 2, pp. 429-435, (2006).



STATE-OF-THE-ART LASER-PUMPED RB CLOCK

Laserhead

PhysicsPackage

Clock assembly

25 c

m

23 cm 25 mm glass cell Volume (LH+PP) < 1.7 liters Mass (LH+PP) < 2 kg

T. Bandi, C. Affolderbach, C. E. Calosso, and G. Mileti, High-Performance Laser-Pumped Rubidium Frequency Standard for Satellite Navigation, Electronics Letters, Vol. 47, No. 12, p. 698–699, (2011) + talk and poster at this conference.



EXAMPLE OF PROJECT: MCLOCKS (EMRP JRP-IND55)

Compact and high-performing microwave clocks for industrial applications

Objective:

Realization of clocks joining features of commercial Rb clocks with performances of Hmaser: frequency stability 10-13 at 1 s and in the 10-15 range for day.

Tasks:

1) Pulsed optical pumping (POP) clock implementation of a Rb cell clock optimizing thesize, the reliability and suitability to operate in industry-like environment.

2) Isotropic cooling use of Rb atoms to overcome the limits of the previousimplementation made with Cs. It is a clock based on cold atom and can provide anaccuracy specification.

3) CPT technique implementation of a particularly compact clock.

Slide courtesy of Salvatore Micalizio, INRIM



MCLOCKS (EMRP JRP-IND55)

The consortium

INRIM (Coordinator) Pulsed Rb clock

OBSPARIS (SYRTE) Rubiclock

UFC (Femto-St) CPT clock

Tubitak CPT clock and industrial tests

Muquans Rubiclock

LTF-UniNe Support on cells, lasers, wave, cavity and physics




POP RB CLOCK: OBJECTIVES IN THE JRP


AOMLaser

zLMicrowaveSynthesizer

RF Oscillator

Optical Signal

= Switch

OCXO

Servotp

t1 T

td

Magnetic ShieldsW Cavity

C-field coil

Cell

• Lab prototype compact prototype• New Physics Package (INRIM+UniNe);• Transportable device: clock in a “box”

Improved performances:

• Reducing laser noise transfer(INRIM-OBSPARIS);

• Reducing Dick effect (low-noise electronicsINRIM-UFC);

• Increasing S/N ratio (multi-pumping technique,INRIM);

• Improved thermal design;• Test in an industry-like environment (UME)



RUBICLOCK: A COMPACT CLOCK BASED ON COLD ATOMS

Slide courtesy of Luigi De Sarlo, SYRTE

T = 35 K, Nat ~ 106

- Simple laser cooling

- Ramsey interrogation

Based on more than 10 years of R&D at LNE-SYRTE

Operation on Cs demonstrated,

Short-term relative stability ~ 2.3 x 10-13

Long-term relative stability ~ 3 x 10-15

Accuracy (estimated) ~ 10-15

Rb clock under development :

- bring cold-atoms tech to the industry

- provide a replacement to GPS+Cs Clockensemble



10‐9

10‐10

10‐11

10‐12

10‐13

10‐141 s 10 s 100 s 1000 s 104 s 105 s

Compact atomic clocks

Telecoms(s)

Navigation(ns)

2‐5 L

0.05‐0.5 L

< 0.02 L

STABILITY OF RB CLOCKS

Power grids



10 -16

10 -15

10 -14

10 -13

10 -12

10 -11

10 -10

1 10 100 1000 10 4 10 5 10 6 10 7

Cs beam, magneticCs-beam, laser H-maser, activeH-maser, passiveRb cell, lampRb or Cs cell, laser CS cold

Time interval (s)

Alla

n de

v.COMPARISON OF RB, CS & H FREQUENCY STANDARDS



GENERAL PROPERTIES OF RUBIDIUM CLOCKS

• Passive, microwave, secondary frequency standard

Main frequency shift due to collisions (several kHz, 10-6)

Stability @ 1s: 10-12-10-10, @10’000 s: 10-14-10-11

• Produced commercially

Probably several 10’000s per year, price: 1k – 5k $

• They have ground and space applications

Instrumentation, telecommunication, power grids, navigation, etc.

• Current R&D includes

Miniaturization, cost reduction, stability improvement



Prof. Gaetano MiletiLaboratoire Temps – Fréquence (LTF)Faculté des Sciences, Université de NeuchâtelAvenue de Bellevaux 51CH-2000 Neuchâtel, Switzerland

www.unine.ch/ltf

THANK YOU FOR YOUR ATTENTION !

38Conférence Universitaire de Suisse OccidentaleProgramme doctoral en physique, Printemps 2014

Lecture 4 : Vapour cell atomic frequency standardsCPT and miniature atomic clocks, C. Affolderbach, 13.03.2014

ATOMIC CLOCKS: BASIC PRINCIPLES AND APPLICATIONSLECTURE 4: VAPOUR CELL ATOMIC FREQUENCY STANDARDSPART 2: COHERENT POPULATION TRAPPING (CPT) AND MINIATURE ATOMIC CLOCKS

13.03.2014

Christoph Affolderbach and Gaetano Mileti

([email protected], [email protected], )

CUSO – Conférence Universitaire de Suisse OccidentaleProgramme doctoral de Physique – Printemps 2014



Motivation

3. Coherent Population Trapping (CPT)A. Basic CPT phenomenonB. CPT-based atomic clocks

4. Miniature & chip-scale atomic clocksA. Motivation and applicationsB. Generic technologiesC. Examples of realizationD. Recent trends

OUTLINE



BASIC CELL CLOCK SCHEMES

Double-resonance

1 light field (optical pumping), and 1 microwave field (interrogation)

2cm

Coherent Population Trapping (CPT)

2 light fields, Simultaneous preparation and interrogation

Laser source

Rbcell

• Employs coherent laser effects potential for new & improved clocks

(first proposal: Cyr et al., IEEE TIM, 1993)

• No microwave cavity needed more radical clock miniaturization

Cavity size scales with the clock transition wavelength.e.g. 87Rb: 6.8GHz = 4.4 cm

(one can go slightly smaller: dielectric loading, special structures)

Laser source

Rbcell

Det.

fMicrowave = fHFS = fclock

Light 2 light fields:f1 – f2 = fHFS = fclock

u-wavesource

cavity

Servoloop

u-wavesource

Servoloop

Det.

P

S

P

S

fuwave

trans

mis

sion few %

fuwave

trans

mis

sion ≤ 1 %



PART 1

COHERENT POPULATION TRAPPING



First observation:

Dark lines in Na fluorescence excited by a pulsed laser

G. Alzetta et al., Il Nuovo Cimento 1976 & 1979

COHERENT POPULATION TRAPPING

“The resonant character of these lines is pointed out by the change of their position when thelaser mode spacing is varied. In fact, they occur where the magnetic‐field value matches [i.e.tunes into resonance] a ground‐state hyperfine transition with a frequency difference betweentwo laser modes.”

• multi‐optical‐frequency resonance

• very narrow lines (á optical linewidth)

• absence of fluorescence (i.e. absorption) on resonance

H

Laser beam



Simple 3-level systeme.g. 87Rb

BASIC CPT EFFECT

|3

|2

|1

12

L

R

HFS

Apply & scan only 1:

1(E3- E1) / h(L =0)

trans

mis

sion

5S1/2, F=1, mF=0

5S1/2, F=2, mF=0

5P1/2, or 5P3/2(unresolved)

Keep 1 fixed, scan only 2:

2R =0tra

nsm

issi

on

R = 1 – 2 – hfs =0CPT resonance condition:

“dark line”

Laser source

Rbcell

Det. Abs

orpt

ion,

flu

ores

cenc

e

Fluorescence:~ absorption,anisotropic



3-level “-system”

CPT: 3-LEVEL SCHEME

2 1~C 21 ie

2 1~NC 12 ie

0 ~C3 222

21int iti ReH

01~NC3 2int iti ReH for R=0

|3 |3

|2|NC

|1|C

12

L

R

1, 2

HFS

New basis

R = 1 – 2 – hfs

Properties of |NC- no excitation by the 2 light fields- Eigenstate of Hint: stationary- depends on relative phase of laser fields- requires phase-stable fields !

Coupling to |3 with fields 1 & 2

Destructive interference of excitation amplitudes



-system with relaxations:

DENSITY MATRIX DESCRIPTION

|3

|2

|1

12

L

R

HFS

R = 1 – 2 – hfs

• symmetric system:Relaxation opt = 32 = 31

Rabi frequency g = g1 = g2

• neglected one-photon background• Lorentzian lineshape with:

32

31

12

Solution of density-matrix

Absorption

Dispersion



Kramers-Kronig relation:Absorption resonance is always accompanied by dispersion in the refractive index

NUMERICAL RESULTSab

sorp

tion

abso

rptio

n

Ref

ract

ive

inde

x (

rel.

units

)

Light absorption for 3-level system

• vanishing absorption at R = 0• narrow linewidth, determined by 12

• steep dispersion at R = 0,combined with vanishing absorption ! “slow-light”, optically controlled all-optical light switching



3‐level system solution :CPT LINESHAPES: LASER INTENSITY

SII2 FWHM 12

IIIA

SCPT

2

~

FWHM slope CPTA

~ I1

~ I1

~ const.

~ I2

~ const.

~ I2

212 W/cm1 GI optS

CPT saturation intensity:IS

CPT on Cs D2 line, buffer‐gas cell:

1000‐times lower than optical saturation intensity: slow ground‐state relaxation !

very low light intensities are sufficient



Typical situation:(buffer-gas cell)

CPT SIGNAL DETECTION

For improved signal-to-noise (S/N) ratio in the detection: Use FM modulation of one of the laser fields (1) and lock-in detection.

( see course of 06.03.2014, by S. Schilt & R. Matthey)

• linewidth: 100Hz – 10 kHz range• contrast: ≤ 1 % (max. few %)

Laser source

Rbcell

Det.

tMtiEE m101 sin exp t

Lock-in amplifier

mon 1 ...2 M M 01110 JJS

... M M 11-10 JJC

direct access to absorption & dispersion can exploit the steep dispersion at low light absorption dispersive line-shapes for locking in atomic clocks

Lowest-order signals• in-phase: phase-shift (dispersion) information

• quadrature: absorption information

jj iT j-exp transmission:



A REAL MULTI-LEVEL SYSTEM

87Rb D1-lineZeeman sub-structure (in magnetic field):

“trap” state

• + light polarization (circular)• optical transitions selection rule m = +1

Laser source

Dc magnetic field

cell4-plate

• pumping of atoms to the F=2, mF=2 state

• reduced atomic population in mF=0 states

not all -systems are simultaneously “dark”

reduced useful clock signal

Standard scheme & setup:



Example: 87RbExcited-state hyperfine-structure:

A REAL MULTI-LEVEL SYSTEM (2)

D1 line 795nm

D2 line 780nm

Optical selection rules: F= 0, ±1

D1-line:

• stronger signal(less atoms lost)

• narrower linewidth(less coherence lost)

D2

D2

D1

D1

D1

D2

M. Stähler et al., Opt. Lett. 2002

one-photon transitions to F’= 1 or 4 loss channels on the D2-line



PHASE-STABLE LIGHT-FIELD GENERATION

Laser diode 2

Phase-lockedloop

Laser diode 1

2 Phase-locked lasers

fmod

fopt

External modulator(Electro-optical modulator)

Laser diode EOM

fmod

foptfopt

Direct modulation(laser current)

Laser diode

fmod

fmod = fhfs

+ ideal 2-color light field+ full freedom of parameters– needs 2 lasers– fast PLL electronics

+ only one laser + easy implementation– bulky modulator– multi-frequency light field

+ only one laser + easy & direct– limited modulation bandwidth– strong amplitude modulation– multi-frequency light field

fmod = fhfs or fmod = fhfs /2,typ. 1.5 to 9 GHz



OPTICAL EXCITATION SCHEMES

fopt

2 phase-locked lasers:+ all light power contributes to CPT

resonances

fopt

fopt

fmod = fhfs

fhfs

fmod = fhfs /2

carrier

(carrier)

-1

-1 +1

Laserspectrum

Atomic absorption

Modulation at fmod = fhfs:– off-resonant sidebands only add

background and noise to the signal, not CPT signal

– P(nth SB) ~ Jn (M)

Modulation at fmod = fhfs/2 :– off-resonant sidebands add background

and noise– residual carrier can deteriorate CPT– Pcarrier = 0 for M ≈ 2.4

+12



CPT ATOMIC CLOCKS

A SELECTION



FIRST CPT ATOMIC CLOCK PROPOSAL

1993 !

87Rb

Edge-emitting diode laser at 780nm

fm = 6.83 GHz / 6 = 1.14GHz

Clock transition linewidth = 6 kHz

(at 6.8GHz, with buffer-gas)



CPT ATOMIC CLOCK: HELSINKI UNIVERSITY OF TECHNOLOGY

M. Merimaa et al., JOSAB 2003.

Clock loop

Laser loop Laser spectrum

3.0 GHz



CPT clock using the Cs D2 line.

One of the first studies on VCSEL-based CPT atomic clocks.

Optical and microwave loops use the same signal, at different modulation frequencies.

CPT ATOMIC CLOCKS AT NIST

S. Knappe et al., JOSAB 2001.J. Kitching et al., El. Lett. 2001.

Pure-gas cell

Temperature-compensated cell

Compact physics package

Optical laser lock loop

CPT clock loop



Light shift:Variation of the “clock” transition frequency due to variations in light frequency or intensity.

Increasing modulation index M (mod. power) Favours more negative intensity light shift

Also affects frequency light shift “quadratic” only

Control button for light shifts

LIGHT SHIFT IN CPT CLOCKS

M. Zhu et al., Proc. PTTI 2000.

F. Levi et al., Trans. UFFC 2000.

fopt

Laserspectrum

Atomic absorption

carrier

Ligh

t shi

ft



• optical CPT excitation

• detect the microwave field emitted by the ground-state coherence

• maser approach: high-Q cavity (Q=8000)

THE CPT MASER

EOM drive ~ 3.4 GHzM ≈ 2.4

F. Levi et al., Proc. EFTF 2004.



Main limitations:

• low microwave power levels

• detection noise

THE CPT MASER

good clock stability

optical detection still preferable

F. Levi et al., Proc. EFTF 2004.



• goal: increased signal contrast• one frequency-modulated laser to excite CPT (beam-1, fmod=3.4 GHz)• one additional, single-frequency laser• generates an optical frequency to satisfy the 4-beam Raman condition

4-WAVE MIXING WITH CPT

V. Shah et al., Opt. Lett. 2007.

demonstrates the possibilities with non-linear techniques

somewhat complicated setup…

100 nW



• 87Rb CPT scheme using a VCSEL

• conventional cell and physics package

• smaller than most OCXO, < 50 cm3

• applications: UMTS, holdover, etc.

• power consumption: 5W at 25°C

COMMERCIAL PRODUCT

J. Deng et al., Proc. EFTF&IFCS 2008.



PART 2

MINIATURE ATOMIC CLOCKS



Bring atomic timing precision to the size and power range previously covered by quartz oscillators

MINIATURE ATOMIC CLOCKS: MOTIVATION

PrimaryStandard

CommercialBeam Clock

CompactAtomic Clock

WristwatchQuartz

Accuracy: 10‐15 10‐13 10‐11 10‐7 10‐5Timing error: 10ns/yr 1s/yr 0.1s/day 100s/day 1s/daySize: 107 cm3 104 cm3 100 cm3 1‐10 cm3 10 mm3

Power: kW 100’s W 1 W 100 mW 10 WCost: >$1 M $50 k $2,000 $100 $1

PrecisionQuartz

Decreasing performance and size/power/cost

MiniatureAtomic Clock

New clocks !

10‐101s/day 10 cm3

120mW$300



Main goals

• small size portable & mobile instrumentation• low power cons. battery-powered devices• 10-11 stability improvement compared to quartz (1s timing)• low unit price parallel micro-fabrication techniques• improved aging & shock behavior, compared to quartz


Applications

• network synchronization• improved hold-over capabilities • secure communication• improved GNSS / positioning receivers• mobile end-user equipment • …

Ultimate development goals (e.g. US DARPA CSAC project)

Stability: ≤ 6x10‐10 ‐1/210‐11 at > 3’600s

Size: 1 cm3

Power: 30 mWTiming error: 1 s/day

runs ≈ 7 days from a smartphone battery

Power: 30 mW



subtitle

text

MINIATURE ATOMIC CLOCK APPLICATIONS



J. Kitching et al., Appl. Phys. Lett 2002.

TOWARDS CHIP-SCALE ATOMIC CLOCKS

Proposal for a chip-scale atomic clock:

Use of micro‐fabrication technology & CPT Wafer-level assembly of all components:

dicing

Miniature clock physics package

Compo

nents wafers



COMPONENTS:

MICRO-FABRICATED ALKALI CELLS

VCSEL DIODE LASERS



Buffer-gas: avoids ground-state relaxation by collisions with the cell walls.

Diffusion:

Collisions:

Total:(Cs in Ne)

LIMITATIONS IN BUFFER-GAS CELLS

gas

Rb

S. Brandt, Phys. Rev. A 1997.

CPT line,Cs + Ne

1/ p

p

CPT linewidth depends on cell size and gas pressure

to be optimized for a miniature cell



CPT-line Q-factor (f0/), 1mm cell size

SHORT-TERM STABILITY AND BUFFER-GAS CELL SIZE

Coated cell

Buffer-gas cell

≈ 5x10-11

J. Kitching et al., Appl. Phys. Lett 2002.

Predicted short‐term stability:(at optimized temperature, etc.)

2/1

0 //2.0

fNSy

nalkali (T),Ilaser

Ilaser Pgas

Optical absorption: 20 kPa - cell

≈ 500 Hz



Main requirements and challenges

• Reactive alkalis

Hermetic cell sealing, under vacuum compatible cell materials

(Si + glass ok, metals? )

• sealing at elevated temperatures

control of alkali quantity control of buffer-gas pressure incompatible with anti-relaxation wall coatings

(known paraffines have low melting points)

• reliability of cells !

MICRO-FABRICATED VAPOR CELLS

Technologies overview

• cell sealing

anodic bonding low-temperature sealing

• different cell geometries one or 2 chambers spherical

• alkali filling

metallic: beam dispensing, pipetting post-activation: chemical, electrolytic



MICRO-FABRIATED CELLS WITH ANODIC BONDING

J. Kitching et al., Metrologia 2005, S. Knappe et al., Opt. Lett. 2005.

Glass‐Si‐glass anodic bonding (NIST process): Refined alkali filling:



Dia=5 mm

L =10x10 mm 200 - 500 um

500-2000 um

Silicon wafer

Photolithography and cavity etching by DRIE

Wafer-level anodic bonding of Si with glass

Dicing

Cell closing / Anodic bonding of glass lid

200 - 500 um

Rb deposition

Dia=5 mm

L =10x10 mm 200 - 500 um

500-2000 um

Silicon wafer

Photolithography and cavity etching by DRIE

Wafer-level anodic bonding of Si with glass

Dicing

Cell closing / Anodic bonding of glass lid

200 - 500 um

Rb deposition

Y. Pétremand, et al., Proc. EFTF 2010

SWISS ANODIC BONDING TECHNOLOGY

IMT‐SAMLAB



POST-ACTIVATED VAPOUR CELLS

L. Nieradko et al., FEMTO-ST (Besançon) & Wroclaw UT



POST-ACTIVATED VAPOUR CELLS (C’TD)

A-L. Liew et al., Appl. Phys. Lett. 2007 F. Gong et al., Rev. Sci. Instrum. 2006

700 V540 °C

Cs-enriched glass

Cs liberation from CsN3

• liberates Cs and N2 buffer-gas in sealed cells• activation by UV light• explosive !

Electrolytic release of Cs in sealed cellsLiberate Cs from glass by electrolytic exchange with Na+ ions



MICRO-FABRICATED VAPOUR CELLS

J. Eklund et al., MEMS 2007.K. Tsujimoto et al., MEMS 2011.

Sacrificial glass-frit channel sealingAt 470°C, 250 kPa

Micro glass-blown cells



SWISS SPECIAL MINIATURE CELLS

R. Straessle et al., MEMS 2012.Y. Pétremand et al., JMM 2012.

IMT‐SAMLAB

4-mm size Rb cellsMicro-fabrication technology for precise control of cell geometryMulti-stack anodic bonding: Thick glass core wafer 2 Si layers + 2 glass windows 4 steps of anodic bonding

Indium cell sealingLow-temperature sealing (≤ 140°C) alkali control & wall coatings

Working alkali cells

5mm



High modulation bandwidth CPT !

LIGHT SOURCES: VCSEL

www.ulm-photonics.de www.oclaro.com

Low‐power light sources

Higher relaxation frequency R for a VCSEL: mainly due to the higher photon density p0 in the resonator

pR

pA 0

A: laser gainp: photon lifetime in resonator

0.45 mW@ 2mA≈ 12%

Typical linewidths≈ 20 – 100 MHz



Fabrication process:Chip size:Phase noise: Power consumption:Frequency tuning step: Output RF power:

Phase noise @ 4.6 GHzCircuit architecture

CMOS 130 nm1.7 x 1.2 mm = 2 mm2

-86 dBc/Hz @ 5 kHz15 mW (vdd = 1.2 V)0.5 mHz (10-13)0 dBm

Chip photography

Obtained results

Y. Zhao, S. Tanner, P-A. Farine, ESPLAB-EPFL

This low power, highly integrated and high performance frequency synthesizer is suited for realizing chip-scale atomic clocks.

Stability with Cs micro-cell and ASIC

Exp. Evaluation by LTF-UniNe: L. Schneller, F. Gruet, C. Affolderbach

SINGLE-CHIP 4.6 GHZ SYNTHESIZER FOR CS CPT CSAC

Y. Zhao et al., IFCS-EFTF 2013



MINIATURE ATOMIC CLOCK REALIZATIONS

AN OVERVIEW




• Fully micro-fabricated physics package

• 75mW power dissipation

FIRST PIONEERING PROTOTYPES AT NIST

S. Knappe et al., Appl. Phys. Lett. 2004

1mm

with drift

drift removed



SYMMETRICOM CSAC PROTOTYPE

R. Lutwak et al., Proc. PTTI 2007.

• CPT on Cs D1-line (894nm)• VCSEL operating at 85°C• Temperature-compensated cell• 1cm3 PP



SYMMETRICOM CSAC PROTOTYPE

R. Lutwak et al., Proc. PTTI 2007.

Pcb with PP

Power budget

• 1 cm3 PP volume • 15 cm3 total volume• 125 mW consumption• 10 MHz output

• 0.35 cm3 PP volume • ≈1 cm3 total volume• 30 mW consumption• 4.6 GHz output (uncal.)• No shields, etc.

Limit from the 1cm3 PP:Impact of electronics !

0.35 cm3 PP clock



SYMMETRICOM CSAC PRODUCT

www.symmetricom.com



SOME OTHER DARPA-CSAC PROTOTYPES

J. F. DeNatale et al., Proc. IEEE 2008.

Teledyne scientific Corp.87Rb CPT on D1-line, folded beam geometry 1 cm3 volume 30 mW power consumption (with electron.)

Honeywell Aerospace Research87Rb CPT on D1-line, 1.7 cm3 volume 57 mW power consumption (with electron.)

Yougner et al., Proc. Transducers 2007.

5¢



ESA-PROJECT: MUSO

Miniature Ultra-Stable Oscillator

For secure satellite communication

• low-power VCSEL laser (795nm)

• miniature Rb cells

100% Swiss-Made !

C. Schori et al., Proc. EFTF 2010.



EU-FP7: MAC-TFC

Miniature Atomic Clock for Timing, Frequency Control and Communication

For ground‐based applications

• Low‐power VCSEL on Cs D1‐line (Ulm)

• Miniature Cs cells (Besançon, Neuchâtel, Wroclaw)

• Full miniature electronics (Neuchâtel)

Cs-Cells VCSEL-Laser

ASIC microwave electronics

All key components are developed within the project consortium !

Test setup

www.mac‐tfc.eu

Packaging

Clockdemonstrator



SWISS MINIATURE ATOMIC CLOCK (SWISS–MAC )

Swiss–MAC

Slide courtesy of Jacques Haesler and Steve Lecomte, CSEM

Assembled prototype



DOUBLE-RESONANCE MINIATURE ATOMIC CLOCKS

A. Braun et al., Proc. PTTI 2007

“End-state clock” (W. Happer, 2003)

• Strong end-state double-resonance• Requires magnetic field lock• microwave coupling loops



RECENT TRENDS IN





new components for a miniature double-resonance clock

demonstrate clock operation

SINERGIA PROJECT: MINIATURE ATOMIC CLOCKS AND SENSORS

UniNe: LTF

EPFL:SAMLAB, LEMA,LMTS, LPM2

5mm

Microfabricated Rb-cells: new geometries and low-temperature bonding

Miniature Rb lamp

LTCC packaging

Miniature micro-wave resonator

Miniature DR clock demonstrator & stability:5.5x10-12 -1/2 and < 10-12 at > 100 s

http://macqs.epfl.ch/

10-13

2

4

68

10-12

2

4

68

10-11

Ove

rlapp

ing

Alla

n D

evia

tion

y(

)

1 10 100 1000Integration Time, , [s]

S/N limit: 5.5 x 10-12 -1/2

Shot Noise Limit: 2.5 x 10-12 -1/2



MINIATURE MICROWAVE CAVITY

Volume: < 0.9 cm3

Loaded Q = 26 Injected power a few W Power loss 50 nW Fine tuning range > 100 MHz Patent submitted

M. Violetti et al., European Microwave Week 2012

6 mm



MINIATURE DISCHARGE LAMPS FOR MINIATURE DR CLOCK

1 cm

V. Venkatraman et al., Trans. UFFC 2012 & Appl. Phys. Lett. 2014

Dielectric Barrier Discharge (DBD)• Micro-fabricated cell with Al-electrodes

500 µm Pyrex

500 µm Pyrex2 mm Si

Al Electrodes

Cavity filled with few µl of Rb + 70 mbar of Argon

5 mm

• 2 to 500 MHz RF drive• ≈10 mW RF power coupled to the cell 100W light output

LMTS+SAMLAB

Optical pumping and Zeeman DR in a micro-cell



MEMS TECHNOLOGY FOR TIME & FREQUENCY

• Need of low-consumption, low-weight and low-cost T&F devices

Example: GNSS receivers able to lock on PRN signals

• Key MEMS-based building blocks:

– Resonators

– Filters

– Oscillators

– (Chip-scale atomic clocks)

e.g. Q = 15’248at f = 1.46 GHz( = 95 kHz)



SUMMARY

• CPT-based clocks exploit coherence effects from 2-colour laser systems:purely optical interrogation, but stringent laser requirements

• Miniature atomic clocks bring atomic timing precision from a quartz outlinedevice:

o Typically s timing stabiltiy at 1 day: holdover capabilities,for communication networks and smart grid

o Low power consumption: mobile applications or remote networks

• Miniature atomic clocks based on alkali-cells are well-established, a product is available in the USA

• Interesting research on alternative approaches is ongoing :

• Miniature cell clocks using DR scheme

• Non-cell miniature clock schemes for improved long-term stability(cold atoms, ions, …)



CPT

G. Alzetta et al., Il Nuovo Cimento B 36, 5 (1976) & Il Nuovo Cimento B 52, 204 (1979)E. Arimondo, Progress in Optics vol. 35, 257 (1996)C. Affolderbach, PhD Thesis, Bonn 2002.M. Stähler et al., Opt. Lett. 27, 1472 (2002)Related reading: S. E. Harris, Physics Today 50, 36 (1997), L. V. Hau et al., Nature 397, 594 (1999)

CPT clocks

S. Knappe et al., JOSAB 18, 1545 (2001)J. Vanier, Appl. Phys. B 81, 421 (2005)

Miniature atomic clocks

S. Knappe, Comprehensive Microsystems vol.3, 571 (2007)

Time&Frequency conference proceedingswww.eftf.org (free)www.pptimeeting.org (free)www.ieee-uffc.org/main/publications/fcs/index.asp (on subscription)

REFERENCE LITERATURE

ATOMIC CLOCKS: BASIC PRINCIPLES AND · PDF fileIntroduction to the lectures and to atomic...

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