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1

Atomic clocks and fundamental tests in Physics

Gaetano Mileti, Pierre Thomann, Sebastien Bize, Christophe Salomon, Claus Laemmerzahl

3ème cycle de la physique en Suisse Romande, Atomic clocks and fundamental tests in PhysicsG. Mileti, Introduction and vapour cell standards, 25.02.2010 - 1 -

Precision / Stabilityin seconds

per day

1 ns

1 s

100 psAtomic clocks

(1950)

Hydrogen

Maser,

Caesium beam,

Rubidium clock

Quartz oscillators

10 ns

10 ps

The metamorphosis oftime measurement

Marine chronometers Space atomic clocks


Tower clocks (1300)verge-and-foliot mechanism

10 s

1000 s

Huygens Pendulum (1650)pendulum

Marine chronometers

(1750), Harrison

1 ms

(1930)

1 s

Earth rotation

-3000 -1500 -170 800 1300 1600 19001700 2000

Program of lectures

February 25 Introduction and vapor-cell atomic clocks

G. Mileti, Université de Neuchâtel

March 4 H Masers and primary frequency standards

P. Thomann, Université de Neuchâtel


March 11 Optical frequency standards

S. Bize, SYRTE Paris

March 18 The ACES mission on the ISS

C. Salomon, ENS Paris

March 25 Atomic clocks in space for fundamental tests

C. Laemmerzahl, Universität Bremen

Essential specialized bibliography

• Jacques Vanier, Claude Audoin, “The Quantum Physics of

Atomic Frequency Standards”, Bristol: Adam Hilger, 1989.

• Claude Audoin, Bernard Guinot, Stephen Lyle, “The

Measurement of Time: Time, Frequency and the Atomic

Clock ”, Cambridge, (Original in french : Masson, 1998).


• Fritz Riehle, “Frequency standards – Basics and

applications”, Wiley-VCH, 2005.

• Special issue of Metrologia: “Special issue: fifty years of

atomic time-keeping: 1955 to 2005”, Volume 42,

Number 3, June 2005.

Introduction, vapour-cell atomic clocks and applications

Gaetano Mileti

([email protected])

Laboratoire Temps – Fréquence (LTF)


Laboratoire Temps – Fréquence (LTF)

(http://www2.unine.ch/ltf)

Institut de PhysiqueFaculté des Sciences

Université de Neuchâtel

Plan of the presentation

I. Introduction on the measurement of time

II. Stabilized oscillators and atomic clocks

III. Commercial Rubidium clocks and applications


III. Commercial Rubidium clocks and applications

IV. Current research on vapour-cell standards

2

Essential bibliography related to this lecture

Introduction on the measurement of time:

• Chapters 1-2-3 of book F. Riehle, Wiley-VCH, (2005)

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:

• PhD 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)

I. Introduction on measurement of time

1. Measurement of time, calendars, clocks and frequency standards

2. Time and frequency instability

3. Mechanical and piezoelectric oscillators

4. Accuracy and stability

5 First overview of applications and needs


5. First overview of applications and needs

What is a clock?


Picture:

View from

Observatoire

Cantonal de

Neuchâtel,

founded in

1858

“Clock = Oscillator + Counter”

~

“Oscillator”

Based on a periodical event,

supposedly “regular” and having a

period T (earth, pendulum, spring,

quartz, etc.)

Frequency f = 1 / T

14:32 26


9 192 631 770

“Counter”

Able to count the oscillations and

display the result in some manner

(escapement, gear, dial, hands, etc.)

“in” and/or “out” of the standard“Reference”:

Sometimes used to stabilize the oscillator and/or the clock

1. Measurement of time, calendars, clocks and

frequency standards

Examples of natural periodical events: earth rotation,

moon phases, seasons, etc. but also: heart beat,

“biological” time, etc.

Examples of needs and applications: agriculture, social

life (daily weekly annually etc ) sailing


life (daily, weekly, annually, etc.), sailing

(longitude), electronic equipment,

telecommunications, satellite navigation, etc.

Examples of developed tools: calendar (Julian,

Gregorian, …), sundial, clepsydra, tower clock,

pendulum, telescope, wrist watch, chronometer,

atomic clock…

Some concepts on measurement of time:

Julian date JD: used by astronomers. Day number

since 4713 BC (day starts at noon).

Modified Julian Date MJD: used in T&F metrology,

earth rotation studies, space research (MJD =

JD - 2400000.5).

Jan. 1st 2000 noon

= 2451545.0 JD

MJD = 0 on Nov. 17

1858 at 0 AM


Length Of the Day LOD and True solar time:

defined by earth rotation on its axis.

Universal Time (UT): agreed international time

scale referred to the first meridian.

The LOD varies by

30 minutes in 1 year

UT, UT1, UT2, UTC,

GMT

3

Definition in SI system

The second is the duration of 9 192 631 770periods of the radiation corresponding to the transition between the two hyperfine levels of

the ground state of cesium 133 (1967)

→ Atomic Time (TAI)

Definition of the second (see lecture 2 for details)


Hzh

EEFrequency 770631192912

0

F=4

F=3

6 S½

Atomic time (TAI) and astronomical time (UTC)


Leap second

Ideal and real oscillators

Ideal “oscillator” (or frequency standard)

Black box having an input (power supply) and an “ideal” output: for instance an absolutely

pure (accurate and stable) sinus with amplitude A and frequency 0

)2cos( 0tA

Spectral domain


Real “oscillator”

The amplitude and the frequency of the output fluctuate. These instabilities are observed and described by various techniques in the “time

domain” and in the “frequency domain”.

)( 02)()( ARe

tjettSignal

)( 02)()( ARe

tjettSignal

( ) ( ) ( ) ( ( ) )( )

t t j q t t ej tp 1

02

)()(:

ttxerrorTime

00 td

)(d

2td

)(d)(:

1

tttyerrorfrequencyNormalized

x

where

Oscillator model

Atomic clocks:

10-10 - 10-16


)()(: 0 ttfrequencyMeasured

nsfluctuatiorandomticdeterminist :)(

(t) is a random non stationary process

Tt

tTdtt

TLim )(

1 In general diverges

td

)(d

2)(

10

tty

Allan deviation)()(: 0 ttfrequencyMeasured

0

)(:

tyerrorfrequencyNormalized

1

)(1 K

K

t

tK dttyy

ld22


generalindivergesyvarianceTrue ky22:""

Two-samples variance (Allan variance):

212

12 )()( kky yy

deviationAllany :)(

How to measure the Allan deviation (normalized frequency fluctuations)

of a an oscillator? By comparing it to a better oscillator!


Source: John Vig, tutorial on «Quartz crystal resonators and oscillators»

4

Allan deviation () and noise processes (f)

y()tells us how our

oscillator

compares to an

ideal one over the


• Different types of noise processes affect differently the Allan deviation;

• Different applications require different (in)stabilities at given time scales

timescale



10-12

10-11

10-10Cs beam, magneticCs-beam, laser H-maser, activeH-maser, passiveRb cell, lampRb or Cs cell, laser CS cold

dev.

Example: frequency standards for satellite navigation


10-16

10-15

10-14

10-13

1 10 100 1000 104 105 106 107

Time interval (s)

Alla

n

For 30 cm accuracy

Maximal Time error:

1 nanosecond for

1s < t < 20’000 s

1410)000'20( sy

3. Mechanical and piezoelectric oscillators

Examples of oscillators that have been developed:

• The Foliot (~ 1300)

• The Pendulum (1657)

• The “Balancier spiral” (1673)


• … longitude on sea challenge (marine chronometers)

• 1950-1960: electromagnetic excitations of a tuning fork (diapason)

• 1960-1970: quartz oscillators

• More recently: MEMS-based oscillators

Simplified behavior of quartz oscillators



Oscillating frequencies

• The Pendulum 1 Hz

• The “Balancier spiral” 4 Hz

• Tuning fork (diapason) 300 Hz

• Watch quartz 32’768 Hz

• Microwave atomic transition 1-10’000’000’000 Hz

• Optical atomic transition 100-1000’000’000’000’000 Hz


p

In general: the higher the frequency, the better the time resolution

But:

• The resonance width and quality factor also matters

• The signal-to-noise ratio

• The problem of “counting”

5

4. Accuracy and stability


How to measure / evaluate the stability and accuracy?

• By comparing to a more stable and/or accurate oscillator

• Statistical and non-statistical analysis (see lecture # 2 on primary standards)

Source: John Vig, tutorial on «Quartz

crystal resonators and oscillators»

5. First overview of applications and needs

Agriculture (seasons) ~ 1’000’000 s

Calendar (solstices, equinoxes) ~ 100 ’000 s

Daily activities (professional, social, etc.) ~ 1’000 s

Determination of the longitude (sea navigation) ~ 1 s


Common electronic and telecommunication devices ~ 0.01 s

Advanced telecommunication devices ~ 0.000’001 s

Satellite navigation ~ 0.000’000’001 s

Scientific research and primary metrology < 0.000’000’000’1 s

Need of atomic clocks (in the device or to calibrate the device)

II. Stabilized oscillators and atomic clocks

1. Basic principle of a stabilized oscillator

2. Basic principle of an atomic clock

3. Fundamentals on magnetic resonance


4. Advantages and categories of atomic clocks

5. Applications of atomic clocks

1. Basic principles of a stabilized oscillator

Example 1 of a stabilized oscillator:

pendulum periodically stabilized

after earth rotation observation

Example 2 of a stabilized oscillator:

wrist-watch periodically stabilized


wrist watch periodically stabilized

after comparison to a more stable /

accurate clock (tower clock)

Examples 3 of a stabilized oscillator:

quartz oscillator locked to a GNSS

signal (GPS, GLONASS, GALILEO …)

2. Atomic clock (stabilized quartz)

AtomsQuartz oscillator

Reference for the user (5 MHz)

Interrogation

Feed-back


Definition in SI system

The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of

the ground state of cesium 133 (1967)

Hzh

EEFrequency 770631192912

0

F=4

F=3

6 S½

This would be the frequency of an atomic

clock in which the atomic transition is not

perturbed and the stabilisation “perfect”

9 192 631 770 Hz

Magnetic resonance


Typically 5 or 10 MHz

6

Lock-in detection


Resonance line-width, line Q, signal-to-noise ratio and frequency stability

0.08

0.10

0.12

0.14

ht [

V o

n 1

0k

]

1

0

: resonance «duration»


5.304x106

5.306x106

5.308x106

5.310x106

5.312x106

0.00

0.02

0.04

0.06

Tra

nsm

itte

d lig

h

6.84 GHz - Synthesiser frequency [Hz]

21

).(

2.0

NSQI

y

J. Vanier, L. Bernier, IEEE Trans. on Instr. and Meas., Vol. IM-30, No 4, Dec. 1981

0

0

Q

3. Fundamentals on magnetic resonance

• Magnetic moment interacting with

a magnetic field

• Static :

)()()( tBtmtmdt

d

B

m

oB


Larmor precession

• +rotating magnetic field

magnetic resonance

o

00 B

0

)(1 tB

oB

oB

s

pulse

pulse)(1 tB

The classical Bloch equations and NMR

2

)())()(()(

T

tmtBtmtm x

xxdt

d

2

)())()(()(

T

tmtBtmtm y

yydt

d

))(( mtmd

Stationary solutions


1

0 ))(())()(()(

T

mtmtBtmtm z

zzdt

d

timerelaxationtransverseT

timerelaxationallongitudinT

:

:

2

1

22121 /12 TTTFWHM

(collisions and magnetic inhomogeneities)

Spin 1/2+ magnetic field

(classical or quantum)

Atome+ laser

(dipolar approximation)

Atome+ champ RF

852 nm(3.5 108 MHz)

9.2 GHzB

S

Generalizing the Bloch equations

momentelectricatomicd :

momentmagneticatomic:


.

effBS

BSdt

Sd

BSH

fofofo Bb

dt

bd

EdH

ˆˆ

fmfmfm Bb

dt

bd

BH

ˆˆ

RFB

B

1

00

Laseropt

opt

Ed

11

120

RFRF

RF

B

1

1

120

momentelectricatomicd : momentmagneticatomic:

Generalized Bloch equations

1

w

v

u

S

S

S

z

y

x

)(

)Im(

)Re(

1122

21

21

différencepopulation

momentdipoletheofcomponentquadraturein

momentdipoletheofcomponentphasein

12

222

1212

2

120

1

1

TTT

wust

Stationary solutions


01

12

122

2

1

1

wwT

vw

wvT

uv

vuT

u

222

1212

2

2

1212

0

222

1212

2

212

0

11

1

TTTTT

ww

TTTT

wv

st

st

0

7

The Bloch vector (Semi-classic)

2E

1E

Atom (or ensemble of atoms)

Interacting field (RF, microwave, optical)

Bloch vector (fictitious spin)

tie

12 EE

spopulationofdifference

quadratureindipoleatomic

phaseindipoleatomic

w

v

u


• The state of an atom (2 levels) may be represented with

a vector (“Bloch vector”, or “Fictitious spin”) and its

behavior when interacting with a resonant field as a

magnetic moment in a magnetic field.

• Microwave transitions, optical transitions, /2 pulses, etc.

s

R. Feynman, F. Vernon, R. Hellwarth, “Geometrical representation of the Schrödinger equation for solving Maser problems”, J. App. Phys, Vol. 28, p. 49, (1957).

Examples of Bloch vectors

2E

1E

Atoms in fundamental state

(no field)

1

0

0

w

v

u

s

EAtoms after

it ti

0u

oB

s

oB


2E

1Eexcitation

(and field switched off)

1

0

w

vss

2E

1E

Atoms after excitation

(and field switched off) quantum

superposition of states

0

)sin(

)cos(

0

0

t

t

w

v

u

s

oB

s

General scheme (or sequence) in atomic clocks:

- Have the atoms available and as isolated as possible from

the “outside” undesired interactions / perturbations;

- Put (or select) as many atoms as possible atoms in one

(of the two) levels;

- Perform the “magnetic resonance”;

0

0

0

s

1

0

0


Perform the magnetic resonance ;

- Detect the result of the “magnetic resonance” (level

transition) ;

- Apply the necessary correction to the quartz oscillator

Open loop (synthesizer) or closed loop mode

Magnetic resonance allows spin flip.

It is a frequency selective phenomenonS

ign

al

Linewidth


In an atomic clock you exploit this phenomenon to frequency stabilise a quartz oscillator

In each type of clock it is realised on different species, in various configurations and with different detection techniques

Probing frequency

Alkali atoms in “microwave” clocks

• Hydrogen-like atoms: 1 unpaired electron

• Hyperfine structure: interaction of

• Simplified structure:

nucleousewith

P3/2


• Ground state:S1/2

P1/2

3/2

lumière(1014 Hz)

micro-onde(109 -1010 Hz)

0

0

0

w

v

u

s

87Rb133Cs


5S1/2

F=1

F=2mF = 0

mF = -1

mF= -2

mF = 1

mF = 2

mF = 0

mF = -1

mF = 1

6.8346 GHz5S1/2

F=2

F=3

3.0357 GHz

mF = 0

mF = -1

mF= -2

mF = 1

mF = 2mF = 3

mF = -3

mF = 0

mF = -1

mF= -2

mF = 1

mF = 2

87Rb

85Rb

6S1/2

F=3

F=4

mF = 0

mF = -1

mF= -2

mF = 1

mF = 2mF = 3

mF = -3

mF = 0

mF = -1

mF= -2

mF = 1

mF = 2mF = 3

mF = -3

9.1926 GHz

mF = 4

mF = -4

133Cs

8

4. Advantages of atomic clock (over quartz)

• All (isolated) atoms of the same element and isotope have an

identical structure (energy levels);

• These atoms provide a stable and accurate reference to frequency

stabilize an oscillator;

• It is a fundamental and intrinsic property;

• Less sensitive to environmental effects (temperature, vibrations, etc.)


• Less aging, drift, warm-up time and retrace effect.

But:

• These atoms still interact with their environment (in and out of the

clock) which is responsible of the differences and drifts between the

standards;

• These atoms usually move: Doppler effect, collisions, etc.

• Primary (Cs) – Secondary → lecture 2 (P. Thomann)

Categories of atomic clocks (or frequency standards)


• Passive – Active (H-Maser) → lecture 2 (P. Thomann)

• Commercial (Rb, Cs, H) → lectures 1-2 (G. Mileti, P. Thomann)

• Laboratory – “In development” → all lectures

• Microwave – Optical → lecture 3 (S. Bize)

5. Applications of atomic clocks (general)

4 Radioastronomy, Geodesy

(VLBI, Radioastron, etc.)

4 Scientific Research, Instrumentation

(Microgravity, ACES, HYPER, etc.)

4 Navigation & Positioning


g g

(Galileo, GPS, GLONASS, etc.)

4 Telecommunications

(Networks synchronisation, etc.)

4 Metrology, Time scales

(Primary and secondary standards, H-Masers)

III. Principle of commercial Rubidium clocks and applications

1. The Rubidium frequency standards

• Principle of the clock

• Examples of realizations


a p es o ea at o s

2. Applications

• Navigation

• Telecommunications

1. The Rubidium frequency standard

Heart of the clock: a Rubidium buffer gas cell


5S1/2

F=1

F=2mF = 0

mF = -1

mF= -2

mF = 1

mF = 2

mF = 0

mF = -1

mF = 1

6.8346 GHz

87Rb

Rb partial pressure: 10-5 torr

(10-11-10-12 atoms)

Basic interactions (of the atoms in the cell)

Each atom in the vapor undergoes the following interactions:

• Collisions:

buffer gas, other atoms, walls

• Static magnetic field 5S1/2

F=2mF = 0

mF = -1

mF= -2

mF = 1

mF = 2

6 8346 GHz

87Rb


Static magnetic field

Collinear with laser propagation

• Resonant interaction with the optical beam

• Resonant interaction with a microwave fieldS

P

light

-wave

F=1mF = 0

mF = -1

mF = 1

6.8346 GHz

RFBH

ˆ

EdH

ˆˆ

9

Lampe Rb87 filtre Rb85 cellule Rb87

Optical pumping (hyperfine)


S

P

Thermal equilibrium

S

P

Complete optical pumping

S

P

Partial optical pumpingS

P

Hyperfine optical pumping

20

25

30

A]


-4 -2 0 2 4 6 80

5

10

15

20

D2 lines of Rb87

F = 1F = 2

Pho

tocu

rren

t [mA

Laser diode frequency [GHz]

Note:

With a slow frequency scan, this spectrum is visible only if there are collisions that “destroy” optical pumping.

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

S

P


Rb 87 - F=1

Optical frequency detuning [GHz]0 2 4 6 8

excitation d’une lampe 87Rb avec un oscillateur RF (~120 MHz)

filtrage isotopique par une cellule 85Rb


filtrage isotopique par une cellule 85Rb

+

Lampe Rb87

filtre Rb85

cellule de résonance Rb87

détecteur

cavité micro-onde

Double resonance


5.304x106

5.306x106

5.308x106

5.310x106

5.312x106

0.108

0.112

0.116

0.120

0.124

0.128

Tra

nsm

itte

d li

gh

t [V

on

10

k]


S

P

Double resonance

light

-wave

iRb

iRbI

hd

W cm

Jcm s ( )

( )[ / ]

[ ][ ] [ ]

22 1

][)(1069,2)(

)()( 22 cmg

g

g

o0

2natural width 5 9 MHz

Interaction with light: line shapesAbsorption rate:

number of photons absorbed per second by the atom (in level i)


g o

o o

( )( ) ( )

22 2

natural width 0 5.9 MHz(Lorentzian)

For an atom at rest

22ln24ln22

ln2)(

)(20

20

cM

Tkg Be

Doppler (inhomogeneous)

broadening: (Gaussian) 527 MHz, for Rb @ 60°C

10

4

6

8

10

12

14

16

18

20

= 200 MHz

= 400 MHz

= 600 MHz

= 1 GHz

Rubidium 87 - D2T = 60°C = 527 MHz

= 100 MHz

No broadening

nesh

ape

func

tion

g(

) [10

-10 .s

]

Buffer gas(Lorentzian)

Homogeneousbroadening

Convolution of a

Optical absorption line in a buffer gas cell


-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.50

2

4Li

Optical frequency detuning [GHz]

g ei

erfc i( )

( )( )( )

( )

22 2

20

0ln2ln2 ln2

ln2 ln2

Re

Convolution of a gaussian with a

Lorentzian

Voigt profile

curr

en

t

CO

21-

23C

O 2

2-2

3

CO

32

-34

CO

33-

34

23 Mode hop

Laser reference cell

Rb 87 Rb 85

Experimental example


Pho

to

Piezo voltage

34

Laser lockingrange for theprel. exp. on

laser stabilisation

Laser lockingrange for the

clock

200 MHzResonance cell transmission(modified TNT RAFS)

Laser reference cell(natural Rb)

Rate equations with a 3-levels model

I

III

1

II

III Bloch equations approach

« Fictitious » spin

U: dipole component in phaseV: dipole component out of phase

)-(

0//1

1

vw

wvuv

vuu


II

tiIIIIIIRb

IIIIII

tiIIII

III

IIIIII

tiIIII

III

IIII

eii

e

e

)()(

)(Im)(

)(Im)(

12

12

1

12

1

2

22

22

2

2

1

1

V: dipole component out of phaseV: difference of population

I II ( ) ( )

Im

ll 0 14 I IIi te

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

)(22 21// III

Broadening (relaxations):

Rate equations (equivalent to Bloch equations):

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


tiIII e

0 2 ( )I II ll

( )

1I II Rb I II

i ti i e

2

2

0 22)(1

Rb

2124 / ll

Stationary solution:

300

400

500

600

c si

gnal

wid

th [

Hz]

Exemple expérimentalAvec une celluleCylindrique de 1-2 cm3

Parois

Gaz + Spin-Exchange

Collisions (relaxations)


0 20 40 60 80 1000

100

200

1° h

arm

onic

Nitrogen pressure [mbar]

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 hI I Rb

Measured signal (locally)


n l hII II Rb

222

222

)(442

)()(

Rb

IIIIIIIIIRbhlnI

llll

Linearabsorption

Opticalpumping

Micro-wave

Clock signal

11

0.124

0.128

on

10

k]

The double resonance (DR) signal


5.304x106

5.306x106

5.308x106

5.310x106

5.312x106

0.108

0.112

0.116

0.120

Tra

nsm

itte

d li

gh

t [V

o


Photons:

– 2·1012 / (s ·mm2)

incident

– 6·1011 / (s ·mm2)

transmitted

– 1.5·1011 / (s ·mm2)

Double Resonance

Rubidium clocks developed in Neuchâtel (~ 1985 to ~ 1996)


Commercial production for ground and space (Temex, now Spectratime)


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

Space Rubidium clocks


Other similar developments:

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

4. Rubidium clocks applications

• Satellite navigation

In space: Rubidium, passive Hydrogen Maser, thermal Cesium

On earth: (quartz), Rubidium, thermal Cesium, active / passive H Masers

GIOVE-A (DEC 05) GIOVE-B (2007)


Rubidium clocks for Galileo


Source: Pascal Rochat et al., SSOM meeting in Engelberg, 2007

12

Galileo system


Source: Pascal Rochat et al., SSOM meeting in Engelberg, 2007

Other applications of Rubidium clocks

4 Communications:

4 SDH (Synchronous Digital Hierarchy) CCITT G811,G812


4Mobile communications base stations reference clock 4 Spread Spectrum secure radio communication systems4 Digital Radio&Video Broadcast systems (DRB , DVB)

4 Instrumentation:

4 Telecom SDH synch. Test sets , Cellular base stations test sets …4 Synthesizers, Counters , Laboratory , Metrology4 GPS time receivers.

3ème cycle de la physique en Suisse Romande, Atomic clocks and fundamental tests in PhysicsG. Mileti, Introduction and vapour cell standards, 25.02.2010 - 69 - 3ème cycle de la physique en Suisse Romande, Atomic clocks and fundamental tests in Physics

G. Mileti, Introduction and vapour cell standards, 25.02.2010 - 70 -


+ price !

IV. Current research on cell standards

1. Use of tunable and frequency-controlled laser diodes

• Tunable and frequency-stabilized laser diodes

• The laser-pumped Rb clock

• Use of wall-coated cells


2. CPT cell standards and chip-scale atomic clocks

• Coherent Population Trapping

• Chip-scale atomic clocks

3. Summary and conclusions

13

Prof. P. Thomann (directeur) Dr. G. Mileti (DR, dir.- adjoint)

Dr. C. AffolderbachDr. E. Breschi

Dr. G. Di Domenico Dr. D. Hoffstetter

Dr. A. Joyet Dr. R. Matthey

Dr. S. SchiltDr. C. Schori

T. Bandi (doctorant)

Laboratoire Temps-Fréquence

Université de Neuchâtel


T. Bandi (doctorant)V. Dolgovskiy (doctorant)

D. Miletic (doctorante)L. Devenoges (doctorant)

M. Pellaton (doctorant)N. Bulatovic (doctorant)

F. GruetJ. Di FrancescoM. Durrenberger

P. Scherler M. Vallery-Muegeli

(http://www2.unine.ch/ltf)

1. Use of tunable laser diodes

Lampe Rb87 filtre Rb85 cellule de résonance Rb87

détecteur

cavité micro-onde


6.8 GHz

Rb87 Discharge lamp(several lines, > 1 GHz wide)

Laser (1 line, < 100 MHz wide)

3 GHz

Rb85 Optical filter

Potential advantages:

• More efficient pumping

• Improved S/N

• Long term stability

• Power / Weight / Volume

• Redundancy

Examples of Laser diodes

Solitary Fabry-Perot (FP)

Extended cavity lasers (ECDL)

Distributed Bragg Reflectors (DBR)

Distributed Feedback (DFB)

FP with DBR optical fiber

V ti l C it S f E itti (VCSEL)

1.50um

ECDL

FP (RWL)

Tuneable and frequency-controlled diode lasers


Vertical Cavity Surface Emitting (VCSEL)

MEMS based ECDL and VCSELs

Discrete mode lasers

Etc.

780, 795, 852, 894nm

Single, mode, mode-hop free tuning

Typical specs: 5-10 mW, LW < 5 MHz

Low intensity and frequency noise

DFB

DBR

VCSEL

Potential advantages of stabilized lasers in

atomic clocks

• More efficient atomic state preparation / selection:

Examples: optical pumping in Rb, Cs, Maser

• Improved detection of atomic states (S/N):

Examples: optical pumping in Rb, Cs, Maser

• Possibility to slow (cool) or trap atoms


Examples: cold atoms frequency standards

• Explore new physical phenomena

Examples: Coherent Population Trapping

• Miniaturization, etc.

Open issues: availability, reliability, cost, etc.

Diode &collimator

Tiltable support:grating & optical isolator

• beam collimation

• grating angle

sin2 a

• Cavity length

m

L

2

Extended-cavity diode lasers


Piezo

Laser output

Exam

ple

1:

het

erodyn

e fr

equen

cy s

pec

trum

Laboratory ECDL vsLaboratory ECDL ESA-ECDL vs DBR ESA-ECDL vs DFB

133.2 133.6 134.0 134.4-39

-38

-37

-36

-35

-34

-33

550 kHz

dB

m

F i f [MH ]

129 130 131 132 133 134 135 136 137 138 139-66

-65

-64

-63

-62

5 MHz

dB

m

132 133 134 135 136 137 138-38

-36

-34

-32

-30

-28

2 MHz

Am

plitu

de [d

Bm

]

Fourrier frequency [MHz]

Laser spectral cacterisation


Exam

ple

2:

mode-

hop

e fr

ee t

unin

g r

ange

Laboratory ECDL DBR DFB

Fourrier frequency [MHz] Fourrier frequency [MHz]29.05.2003 15:27:57Fourrier frequency [MHz]

>> 15 GHz

Ab

sorp

tion

Wavelength

8 GHz

wavelength

Mode hop

Rb 87 Rb 85

4 GHz

Ph

oto

curr

ent

Wavelength

14

10-10

10-9

Spec Rb clock Doppler sub-Doppler

freq

uenc

y y

()

Laser frequency stabilisation

-50 0 50 100 150 200 250

-0.1

0.0

0.1

0.2

sig

nal d

'err

eur

Uer

r (V

)

fréquence laser (MHz)


100 101 102 103 104 105

10-13

10-12

10-11

Sampling time (s)

Alla

n d

evi

atio

n of

the

lase

r

Compact and frequency-stabilized laser head


C. Affolderbach, G. Mileti, A compact laser head with high-frequency stability for Rb atomicclocks and optical instrumentation, Review of Scientific Instruments, Volume 76,073108, (2005)

Physics package(200cm3)

Volume for control electronics(300cm3,

• adapted resonance cell,

• lamp removed,

(empty volume!)

Laser-pumped Rb prototype (Neuchâtel)ESA-funded project


Stabilised laser head:

(300cm ,currently empty)

RAFS resonator module:

(empty volume!)

C. Affolderbach, F. Droz, G. Mileti, Experimental demonstration of a compact and high-performancelaser-pumped Rubidium gas-cell atomic frequency standard, IEEE Transactions onInstrumentation and Measurements, Vol. 55, No. 2, pp. 429-435, April (2006)

Laser-pumped Rb demonstrator (Neuchâtel)ESA-funded project


PP volume: 1.1 L

Overall volume: 2.4 L

Performance goal:

Stability of a Passive H Maser

(9·10-13·-1/2 demonstrated)

C. Affolderbach, R. Matthey, F. Gruet, G. Mileti, Realisation of a compact laser-pumped Rubidium frequencystandard with < 1x10-12 stability at 1 second, EFTF-2010

Stability results with LP-Rb clock

9x10-13 -1/2


-4 -2 0 2 4 6 80

50

100

150

200

250

300

350

400

450

Maximal slope : 600 Hz / GHz


Rub

idiu

m c

lock

fre

quen

cy [

Hz]

-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 (

10 -7

)

Laser wave length

(dfclock/dIlaser and dfclock/dflaser)

Light-shift


-4 -2 0 2 4 6 80

5

10

15

20

25

30

D2 lines of Rb87

F = 1F = 2

Pho

tocu

rren

t [mA

]


Laser diode frequency [GHz]g

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"

Freq

uenc

y [H

z]

Photocurrent [m A]

15

-4 -2 0 2 4 6 80

50

100

150

200

250

300

350

400

450



Rub

idiu

m c

lock

fre

quen

cy [

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

Refer

ence

abs

orpt

ion

line

"10

MH

z" C

lock

freq

uen

cy (

-9'9

99'

996

) [H

z]

Light-shift (AC Stark effect)Shift of the resonance frequency induced by the optical radiation (I, )


-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]1000 800 600 400 200 0 200 400 600 800"

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 li

gh

t-sh

ift"

lase

r fr

equ

en

cy

Rb

87 C

O 2

1-23

Rb

87

CO

22-

23

2·10-9

Reference saturated absorption

"10

MH

z" c

lock

freq

uen

cy (

-9'9

99'

996

) [H

z]

Laser frequency detuning [MHz]

Light-shift: some strategies to reduce it

2-zones 2-lasers with LIF

double-bulb Maser


S

P

example of pulse sequence (adapted from [10])

light

-wave

0.5 ms

0.2 ms

2.6 ms

pulseddouble-bulb Maser

See Godone et al., PRA 70 023409 (2004)

Pulsed Rb clock (INRIM-Torino)

AOMLaser

zL

HeterodyneDetector

Optical Signal

Microwave Cavity Cell

z


L

MicrowaveSynthesizer

RF Oscillator

= SwitchOCXO

Servo

A. Godone, S. Micalizio, C. E. Calosso, F. Levi, The pulsed Rb clock, IEEE Transactions on UFFC, Volume: 53 Issue:3 p. 525-529, (2006)

Light-shift suppression

(reducing dfclock/dIlaser and dfclock/dflaser)

by adding sidebands on the laser

shift unmodulated

Calculated light shift on F=1no mod.

laser frequencylight

shi

ft

M=2 4M=2 4

experimental result:


-2000 -1000 0 1000 2000

Clo

ck f

requ

en

cy

Laser carrier frequency detuning [MHz]

3·10-8

0modulated,

different intensities1 2-1 0 1 2-1 0

fmod = 400 MHz

Carrier detuning (GHz)

Ligh

t shi

ft

M=2.4M=2.45·10-85·10-8

C. Affolderbach, C. Andreeva, S. Cartaleva, T. Karaulanov, G. Mileti, D. Slavov, Light shift suppression in laseroptically-pumped vapour-cell atomic frequency standards, Applied Physics B, Volume 80, N. 7, (2005)

Drift, aging and environmental effects

7450

7500

7550

7600

30 W 11 W "no" light

reso

nanc

e sh

ift (

Hz)

3255

3256

3257

3258

ce s

hift

(Hz)

pure N2: 1.6·10-9 /K

buffer-gas mixture:

pure N

Example of the Rb standards


40 45 50 55 60 65

-1100

-1080

-1060

-1040

-1020

-1000

39 W 11 W "no" light

reso

nanc

e sh

ift (

Hz)

Cell temperature (°C)

7400

45 50 55 60 653252

3253

3254

reso

nan

c

Cell temperature (°C)

gas mix: < 6·10-11 /K

pure N2

pure Ar

long-term stability:

temperature within few mK

clock stability around 10-14

The role of the quartz oscillator and LO

Tra

nsm

itted

ligh

t

Microwave frequency

LO (quartz)

- Direct AM noise and FM AM noise

- Aliasing effects (Phase noise)

“Dick effect”

Example of the laser-pumped Rb clock


Dick effect

2/1

1

22 2

nmnnoisePMy nfSC

2222)()()()( ls

ynoisePM

ynoiseI

ytotaly

Finally:

See Deng et al., PRA 59 (1) 773 (1999)

See Mileti et al., IEEE J. of Q. Electr. 34 (2) 233 (1998)

16

10-12

RIN = 1 10-12

4.10-12

9.10-12

0 5

20 KHz/Hz0,5

50 KHz/Hz0,5

Slaser

= 100 KHz/Hz0,5

devi

atio

n y

-

1/2

Effect of laser AM and FM noise


1 2 3 4 5 6 7 8 9 10

10-13

4.10-14

9.10-14

2,5.10-13

RIN 1.10

5 KHz/Hz0,5

10 KHz/Hz0,5

Pred

icte

d A

llan

d

DC Photocurrent [A]

2. CPT cell and chip-scale standards

S

P

Coherent Population Trapping“dark” state


Potential advantages of using CPT:

• No microwave cavity

• Reduced light-shift

Open issues: 2-colours coherent laser source, signal contrast

Examples of past or on-going developments

• Rubidium CPT Maser (INRIM)

F. Levi et al., Realization of a CPT Rb maser prototype for Galileo, FCS-EFTF 2003

• Pulsed Cs CPT standard (SYRTE)

N. Castagna et al., Investigations on continuous and pulsed interrogation for a CPT atomic

clock, IEEE Trans UFFC, 2009 Feb;56(2):246-53.

• CW Rubidium CPT standard with


• CW Rubidium CPT standard with

buffer-gas or wall-coating (LTF-UniNe)

E. Breschi, G. Kazakov, R. Lammegger, B. Matisov,L. Windholz, and G. Mileti, Influence of LaserSources with Different Spectral Properties on theperformance of Vapor Cell Atomic Clocks Basedon lin lin CPT, IEEE Transactions on UFFC,V. 56, N. 5, p. 926, May (2009)

LTF CPT standard using a Rb wall-coated cell (ASRH-FNS)

Example of research on CPT


Example of recent research on CPT


Towards chip-scale atomic clocks


Stable referenceSee Knappe et al., Appl. Phys. Lett., 85, (9), 2004

17

MEMS technology in 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

Physical principle and processes

o Magnetic resonance scheme, large number of collisions, etc.

Laser source (photons)

o Stable wavelength, narrow spectrum, ~ 100 W, low noise, etc.

Atomic vapour cell (atoms)

o Sealed, stable and reliable “container” of alkali atoms (~ 10 mm3)

Main building blocks for a chip-scale atomic clock:


Control electronics

o Low consumption thermostat, locking, etc. (~ 10 mW)

Local oscillator

o Low consumption and low phase noise microwave source

Example of clock specifications: 30 mW, 10-11 @ 1000s, 1 cm3

Examples of application: replace quartz oscillators

Examples of US prototypes


mUSO projectESA-funded project, collaboration between Spectratime SA, LTF-UNINE and EPFL (ESPLAB, SAMLAB)


C. Schori, G. Mileti, B. Leuenberger, P. Rochat, CPT Atomic Clock based on Rubidium 85, EFTF-2010.

Other Swiss and European on-going research:

• Cs CPT chip-scale atomic clock

D. Miletic, C. Affolderbach, E. Breschi, C. Schori, Christian, G. Mileti, M.

Hasegawa, Madoka, R. Chutani, Ravinder, P. Dziuban, R. Boudot,

Rodolphe, V. Giordano, C. Gorecki, Fabrication and spectroscopy of Cs

vapour cells with buffer gas for miniature atomic clock, EFTF-2010

• Wall-coating and CPT and double-resonance

E. Breschi, G. Mileti, Dark resonance in wall-coated cell for Rb-clocks, EFTF-2010


E. Breschi, G. Mileti, Relaxation of HF-ground state coherence of Rb atoms contained

in wall-coated cell, The 19th International Conference on Laser Spectroscopy (ICOLS

2009), Hokkaido (Japan), 7-13 June (2009)

T. Bandi, C. Affolderbach, G. Mileti, Study of Rb00 hyperfine double resonance

transition in a wall coated cell, EFTF-2010

• Chip-scale double-resonance

Miniature atomic clock and quantum sensors, SNF-Sinergia project, LTF-EPFL (SAMLAB,

LMTS, LEMA, LPM) collaboration

REFERENCE CELL

ATOMIC RESONATOREOM

BEAM SPLITTER

www.mac-tfc.eu


FIBER COUPLER

DFB

18

Miniature atomic vapor cells and applications


Neuchâtel miniature atomic vapor cells (LTF-SAMLAB)

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

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

200 - 500 um

Rb deposition


Cell closing / Anodic bonding of glass lidCell closing / Anodic bonding of glass lid

Y. Pétremand, R. Strässle, D. Briand, C.Schori, G. Mileti, P.Thomann and N. de Rooij, Low Temperature Indium-based Sealing of Microfabricated Alkali Cells for ChipScale Atomic Clocks, EFTF-2010

Besançon miniature atomic vapor cells (UFC-FEMTO)


Potential applications:

• Chip-scale frequency references

• Chip-scale atomic clocks (microwave

and optical)

• Chip-scale atomic magnetometers

Miniature alkali vapour cells


University of

Neuchâtel (LTF)

and EPFL (IMT-

SAMLAB)

• Chip-scale gyroscopes

In the future:

• Atom chips

• Quantum computing

• Quantum communication

Miniature wavelength reference

Demonstrated


J. Di Francesco, F. Gruet, C. Schori, C. Affolderbach, R. Matthey, G. Mileti, Y. Salvadé, Y.Petremand, N. de Rooij, Evaluation of the stability of a VCSEL stabilised to a micro-fabricated Rubidium vapour cell, Photonics Europe 2010

0.0

0.2

0.4

0.6

0.8

1.0

85Rb, F=3

tcell

=60°C

tcell

=82°C

tcell

=110°C

No

rmal

ized

Tra

nsm

issi

on

Laser Frequency

85Rb, F=2

)000'1001(

910

ss

y

stability:

Summary and conclusions (cell standards)

• Rb/Cs vapor frequency standards constitute a well

established technology which used in every day life

applications (telecoms, GNSS, instrumentation, etc.)

• They also a very active field of scientific research, along

three main directions:


Studying the atoms-photons resonant interaction;

Developing improved atomic clocks;

Miniaturization (reduction of power and prize)

• Key basic technologies:

Laser sources, vapor-cells, microwave source and cavity

precision / atomic clocks and fundamental tests in … clocks and fundamental tests in physics ......

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