ATOMIC CLOCKS: BASIC PRINCIPLES AND … tutorial on «Quartz crystal resonators and oscillators» 21.02.2014 7 Conférence Universitaire de Suisse Occidentale Programme doctoral en

21.02.2014

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Conférence Universitaire de Suisse OccidentaleProgramme doctoral en physique, Printemps 2014

1Atomic clocks: basic principles and applicationsLecture 1, Gaetano Mileti, 20.02.2014

ATOMIC CLOCKS: BASIC PRINCIPLES AND APPLICATIONS

Lecture 1 Introduction to the lecture and to atomic clocks – Cs thermal beam standards

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

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

20.02.2014



Introduction to the series of lecturesIntroduction to the topic and bibliography

Program of lectures

Organisation aspects

Lecture 1:

Introduction to atomic clocksBasic principles, categories and applications

Magnetic resonance and generalised Bloch equations

Tunable lasers and basics of atom-light interaction

Thermal Cs standards

PLAN OF LECTURE 1

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A) INTRODUCTION TO THE TOPIC AND BIBLIOGRAPHY

Picture:

View from ObservatoireCantonal de Neuchâtel, founded in 1858



HISTORICAL OUTLOOK

Tower clocks (1300)verge-and-foliot mechanism

Precision / Stabilityin seconds

per day

1 ns

1 s

100 ps

10 s

1000 s

Huygens Pendulum (1650)pendulum

Marine chronometers

(1750), Harrison

1 ms

Atomic clocks (1950)

Hydrogen Maser,

Caesium beam, Rubidium clock

Quartz oscillators

(1930)

1 s

Earth rotation

10 ns

10 ps

The metamorphosis oftime measurement

-3000 -1500 -170 800 1300 1600 19001700 2000

Marine chronometers Space atomic clocks

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OBSERVATOIRE CANTONAL DE NEUCHÂTEL (1858 – 2007)



• 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.

Time & Frequency conferences proceedings (including tutorials)

www.eftf.org (free) → EFTF-2014 in Neuchâtel (June 23-26 2014)www.pptimeeting.org (on subscription)www.ieee-uffc.org/main/publications/fcs/index.asp (on subscription)

European Time and Frequency Seminar (EFTS) – July 2014 in Besançon (F)NIST Time & Frequency Seminar – June 2014 in Boulder (CO, USA)

Previous editions of the CUSO lectures on atomic clocks (2010 & 2012)

ESSENTIAL BIBLIOGRAPHY FOR THESE LECTURES

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B) 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



C) REGISTRATION, REIMBURSEMENTS & EXAM

Please register if you have not done it yet: http://physique.cuso.ch/en/cours/3cycle/

Please fill the participation list (every Thursday)

You may ask for reimbursement of travel costs:

http://www.cuso.ch/programmes‐%C2%AD%E2%80%90doctoraux/administration/formulaires/

If you wish to take an exam and receive credits for your doctoral school:

- Please check with your PhD advisor and doctoral school responsible

- The exam is in the following form:

- You agree with me (and your PhD advisor) on a topic related to the lectures

- The topic may be also connected with your PhD thesis topic (if related to T&F)

- You give a seminar followed by Questions & Answers

Contacts:

[email protected], [email protected]

[email protected]; [email protected]

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1. Basic principles, categories and applications

2. Magnetic resonance and generalized Bloch equations

3. Tunable lasers and basics of atom-light interaction

4. Thermal Cs beam standards

CONTENTS OF LECTURE 1








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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

AtomsQuartz oscillator

Reference for the user (5 MHz)

Interrogation

Feed-back

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”

ATOMIC CLOCK: FREQUENCY-STABILIZED OSCILLATOR

This topic will be developedin lecture #2 & 6



WHY WE NEED TO STABILIZE THE QUARTZ?

Slide from: JohnVig, tutorial on «Quartz crystalresonators and oscillators»

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Magnetic resonance allows “spin flip”.

Magnetic resonance is a frequency selective phenomenon

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

Sig

nal

Probing frequency

Linewidth

0

0

Q

1

0

21

).(

2.0

NSQI

y

BASIC PHYSICA PRINCIPLE: MAGNETIC RESONANCE

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

: resonance «duration»



How to measure / evaluate the stability and accuracy?

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

• Statistical and non-statistical analysis

Inspired by: John Vig, tutorial on «Quartz crystalresonators and oscillators»

Systematic bias

Frequency :

Statistical fluctuations

STABILITY AND ACCURACY

Stable but not

accurate

Not stable and not

accurate

Not stable but

(relatively) accurate

Stable and

accurate

Stable but not

accurate

Not stable and not

accurate

Not stable but

(relatively) accurate

Stable and

accurate

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• Primary (Cs) – Secondary

• Passive – Active (H-Maser)

• Commercial (Rb, Cs, H)

• Ground or Space applications

• Laboratory – “In development”

• Microwave – Optical

• Neutral atoms – Ions – Molecules – Nuclear - …

CATEGORIES OF ATOMIC CLOCKS



Active Hydrogen maser (T4S)

Cs beam (Symmetricom)

Passive H‐maser (OSA)Rb cell clock (Spectratime)

Rb cell clock (Kernco)

Cs beam (OSA)

EXAMPLES OF COMMERCIAL ATOMIC CLOCKS

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Passive H‐maser (SpT)Rb cell clock (Spectratime) CSAC (NIST)

Miniature cell (LTF)

Rb cell laser pumped clock (LTF)

CSAC (Symmetricom)

EXAMPLES OF COMMERCIAL-SPACE-LAB ATOMIC CLOCKS



Cs1 & Cs2 beams and CSF1 & CSF2 fountains (PTB)

FOCS 1 fountain (METAS)F1 fountain (NIST) Ytterbium ion clock (NPL)

EXAMPLES OF PRIMARY AND OPTICAL CLOCKS

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Atomic referenceOscillator

Interrogation

Servo loop

GENERAL SCHEME OF ATOMIC CLOCKS



BLOC DIAGRAM OF AN ATOMIC CLOCK

Typically 5 or 10 MHz

9 192 631 770 Hz

Magnetic resonance

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Discriminatorslope D

Detection noise

Frequency noise

The most important parameters for the clock performances are: The resonance

quality factor Q The signal to

noise ratio S/N

IMPORTANT PARAMETERS



LIMITATIONS RELATED TO THE «LOCAL OSCILLATOR»

Tra

nsm

itted

ligh

t

Microwave frequencyLO (quartz)

- Direct AM noise and FM AM noise

- Aliasing effects (Phase noise)

“Dick effect”

2/1

1

22 2

nmnnoisePMy nfSC

2222)()()()( ls

ynoisePM

ynoiseI

ytotaly

Finally (in the case of cell standards):

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

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

This is a general limitation occurring in any type of atomic clock, including optical standards (see lecture “Optical Clocks”)

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EXAMPLE 1: RUBIDIUM VAPOUR CELL STANDARD

xmicrowaveresonator& source

vapourcell

Discharge lamp

QuartzLO

S

P

Double resonance

light

‐wave

Tra

nsm

itted

lig

ht

Microwave frequency

kHz

10-11 @ 1s10-13 @ 10’000s

This topic will bedeveloped in lecture #4



EXAMPLE 2: HYDROGEN MASER

100 kg

() 1/

10-13

@ 1s

10-15

@ 100s


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EXAMPLE 3: CS BEAM STANDARD

10-11 @ 1s but accurate and very stable in the long term



0

11Q

EXAMPLE 4: OPTICAL FREQUENCY STANDARDS

0:1010 →1015 Hz

This topic will be developedin lectures #3, 6 & 8

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MICROWAVE AND OPTICAL CLOCKS

This topic will be developedin lectures # 6 & 8



EXAMPLE OF RECENT ACHIEVEMENTS

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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

Future “smart” power grids ~ 0.000’000’1 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)

OVERVIEW OF APPLICATIONS AND NEEDS



Radioastronomy, Geodesy

(VLBI, Radioastron, etc.)

Scientific Research, Instrumentation

(Microgravity, ACES, HYPER, etc.)

Navigation & Positioning

(Galileo, GPS, GLONASS, etc.)

Telecommunications

(Networks synchronisation, etc.)

Power distribution networks

(Smart power grids.)

Metrology, Time scales

(Primary and secondary standards, H-Masers)

OVERVIEW OF APPLICATIONS OF ATOMIC CLOCKS

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GNSS (GLOBAL NAVIGATION SATELLITE SYSTEM)

Example of European system GALILEO (GPS / GLONASS / COMPASS / Etc.)

In space: Rubidium, passive Hydrogen Maser (1° generation)

On earth: (quartz), Rubidium, Cesium beams, active H Masers (1° generation)

GIOVE-A (launched 28 Dec 2005) GIOVE-B (launched 26 April 08)

2011 and 2012: launch of first operational satellites (IOV – In Orbit Validation)



EUROPEAN SATELLITE NAVIGATION SYSTEM (GALILEO)

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WHY RB CLOCK AND PASSIVE H MASER ON GALILEO?

10-16

10-15

10-14

10-13

10-12

10-11

10-10

1 10 100 1000 104 105 106 107

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.

For 30 cm accuracy

Maximal Time error:

1 nanosecond for

1s < t < 20’000 s

1410)000'20( syAllan deviation will bedefined in lecture #2



VLBI (VERY LONG BASE INTERFEROMETRY)

H-Masers (10-15 @ ~1000-10’000 s) are used to increase the resolution

Angular resolution: ~ / Diameter

1 radio-telescope: ~ 1 mrad (10-3 rad)

2 radio-telescopes: ~ 1 nrad (10-9 rad)

Earth rotation: 1 mrad → 6 km → 14 s

c

B sin

B


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FUNDAMENTAL PHYSICS IN SPACE

Atomic Clock Ensemble in Space

Micro-gravity

Relativity

0

11Q This topic will be

developed in lecture #7








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CLASSICAL MAGNETIC RESONANCE (NMR)

Magnetic moment (or ensemble of magnetic moments) interacting with a magnetic field

Static magnetic field : Larmor precession

Static magnetic field and resonant rotating magnetic field : magnetic resonance

(frequency selective process)

)()()( tBtmtmdt

d

B

m

oB

00 B

0

)(1 tB

oB

oB

s

pulse

pulse)(1 tB

m

0B



LARMOR PRECESSION

Description of the system: Ensemble of paramagnetic particles exposed to a static magnetic field.

Magnetic moment:

Torque on :

Gyromagnetic ratio:

Evolution:

Result:The magnetic moment rotates around the magnetic field with the angular velocity

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MAGNETIC RESONANCE

What happens if we add a small rotating magnetic field ?

When the small perturbation produces a dramatic change of the magnetisation ⇒ resonance !

perturbation

Evolution of the total magnetisation:



MAGNETIC RESONANCE (IN ROTATING FRAME)

Evolution in the lab frame:

Evolution in the rotating frame:

fictitiousmagnetic field

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MAGNETIC RESONANCE: PULSE

Pi-pulse in the rotating frame Pi-pulse in the rotating frame Pi-pulse in the lab framePi-pulse in the lab frame



CLASSICAL BLOCH EQUATIONS (WITH RELAXATIONS)

2

)())()(()(

T

tmtBtmtm x

xxdt

d

2

)())()(()(

T

tmtBtmtm y

yydt

d

1

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

T

mtmtBtmtm z

zzdt

d

timerelaxationtransverseT

timerelaxationallongitudinT

:

:

2

1

Stationary solutions

22

121 /12 TTTFWHM (collisions and magnetic inhomogeneities)

0

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CLASSICAL BLOCH EQUATIONS (WITH RELAXATIONS)

Magnetic moments relax toward an equilibrium magnetisation due to collisions and B inhomogeneities.

Longitudinal and tranverse relaxation rates are different

The resulting equations are called Bloch equations:



STATIONARY (STEADY STATE) SOLUTIONS

Relaxation + Power broadening

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Available on the internet : Wolfram demonstrations projecthttp://demonstrations.wolfram.com/MagneticResonanceAndBlochEquations/

BLOCH EQUATIONS: INTERACTIVE DEMONSTRATION



GENERALISATION: THE BLOCH VECTOR (SEMI-CLASSIC)

2E

1E

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.

Atom (or ensemble of atoms)

Interacting field (RF, microwave, optical)

Bloch vector (fictitious spin)

tie

12 EE

spopulationofdifference

quadratureindipoleatomic

phaseindipoleatomic

w

v

u

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).

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EXAMPLES OF BLOCH VECTORS (AND ATOMIC STATES)

2E

1E

Atoms in fundamental state(no “resonance” field)

1

0

0

w

v

u

s

2E

1E

Atoms after excitation(and field switched off)

1

0

0

w

v

u

s

oB

s

oB

s

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



GENERALISATION: ATOM INTERACTING WITH EM FIELD

Spin 1/2+ magnetic field(classical or quantum)

Atom+ laser (dipolar approximation)

Atom+ microwave

852 nm(3.5 108 MHz) 9.2 GHz

.

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

B

S

momentelectricatomicd :̂

momentmagneticatomic:̂

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GENERALIZED BLOCH EQUATIONS

01

12

122

2

1

1

1

wwT

vw

wvT

uv

vuT

u

w

v

u

S

S

S

z

y

x

)(

)Im(

)Re(

1122

21

21

differencepopulation

momentdipoletheofcomponentquadraturein

momentdipoletheofcomponentphasein

222

1212

2

2

1212

0

222

1212

2

212

0

222

1212

2

120

11

1

1

1

TTTTT

ww

TTTT

wv

TTT

wu

st

st

st

0

Stationary solutions



THE BLOCH SPHERE

pi/2 pulse

pi/2 pulse

Coherent superpositionof states and

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WHAT HAPPENS IN AN ATOMIC CLOCK

Generalised magnetic resonance allows “spin flips”

It is a frequency selective phenomenon

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

Sig

nal

Probing frequency

Linewidth

Or series of pulses such asThe Ramsey scheme (/2)



ALKALI ATOMS IN A «MICROWAVE» CLOCK

Hydrogen-like atoms: 1 unpaired electron

Hyperfine structure: interaction of

Simplified structure:

Ground state:

(Thermal equilibrium)

nucleousewith

S1/2

P1/2

P3/2

lumière(1014 Hz)

micro-onde(109 -1010 Hz)

0

0

0

w

v

u

s

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THE CASE OF CESIUM AND RUBIDIUM

85Rb133Cs

5S1/2

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

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

87Rb

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

IJF



GENERAL SCHEME (OR SEQUENCE) IN ATOMIC CLOCKS

- Have the atoms available and as isolated as possible fromthe “outside” undesired interactions / perturbations;

- Put (or select) as many atoms as possible atoms in one(of the two) levels;

- Perform the “magnetic resonance” (in one or more steps);

- Detect the result of the “magnetic resonance” (leveltransition) ;

- Apply the necessary correction to the quartz oscillator

Open loop (synthesizer) or closed loop mode

0

0

0

s

1

0

0

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MOTIVATION

Some types of “traditional” atomic clocks exploit the atoms-light interaction(lamp-pumped Rubidium clocks)

Most of the new atomic clocks exploit stabilized lasers because they allow:

– A more efficient atomic state preparation / selection:

Examples: optical pumping in Rb, Cs, Maser

– An improved detection of atomic states (S/N):

Examples: optical pumping in Rb, Cs, Maser

– The possibility to slow (cool) or trap atoms

Examples: cold atoms frequency standards

– To explore new physical phenomena

Examples: Coherent Population Trapping

– The very existence of optical frequency standards

Note however that their use in some cases (commercial product, spaceapplications, etc.) require additional developments (reliability, cost, etc.)

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HYPERFINE OPTICAL PUMPING IN RUBIDIUM CLOCKS

S

P

Thermal equilibrium

S

P

Complete optical pumping

S

P

Partial optical pumping

Lamp Rb87 filter Rb85 cell Rb87

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




PLASMA DISCHARGE RUBIDIUM LAMP

excitation of a 87Rb lamp with an RF oscillator (~120 MHz)

Isotopic filtering with a 85Rb cell

+


Rb 85 - F= 2

Rb 87 - F= 2

Rb 85 - F= 3

Rb 87 - F= 1



Rb 85 - F= 2

Rb 87 - F= 2

Rb 85 - F= 3

Rb 87 - F= 1



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LASER-PUMPED RUBIDIUM (VAPOUR-CELL) CLOCKS

6.8 GHz

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

Laser (1 line, < 100 MHz wide)

3 GHz

Rb85 Optical filter

Lampe Rb87 filtre Rb85 Resonance cell

detector

Microwave cavity

Potential advantages of using a laser:

• Improve the stability

• Reduce the cost

• Reduce SWAP

• Possibility to introduce a redundancy

• Possibility to use other schemes

• Possibility to use of other atoms than

Rubidium (example: Cs)




LASER-PUMPED BEAM STANDARDS

Optical pumping

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Examples of employed 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 changed

Single mode, mode-hop free tuning

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

Low intensity and frequency noise

1.50um

ECDL

DFB

DBR

VCSEL

FP (RWL)

TUNABLE AND FREQUENCY-CONTROLLED LASER DIODES




S

P

-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]

Note:

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

LINEAR OPTICAL ABSORPTION (WITH A LASER)

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iRb

iRbI

hd

W cm

Jcm s ( )

( )[ / ]

[ ][ ] [ ]

22 1

][)(1069,2)(

)()( 22 cmg

g

g

o0

g o

o o

( )( ) ( )

2

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

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

ATOMS-LIGHT INTERACTION: LINE SHAPES



-2 .5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.50

2

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

Lines

hape

func

tion

g(

) [10

-10 .s

]

Optical frequency detuning [GHz]

g ei

erfc i( )

( )( )( )

( )

22 2

20

0ln2ln2 ln2

ln2 ln2

Re

Buffer gas(Lorentzian)

Homogeneousbroadening

Convolution of a gaussian with a Lorentzian

Voigt profile

BUFFER GAS BROADENING (OF ABSORPTION LINES)

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Ph

oto

curr

en

t

P iezo voltage

CO

21-

23

CO

22-

23

34

CO

32-

34

CO

33-

34

23Laser lockingrange for thepre l. exp. on

laser stabilisation

Laser lockingrange for the

clock

M ode hop

200 MHzResonance cell transmission(modified TNT RAFS)

Laser reference cell(natural Rb)

Rb 87 Rb 85

EXPERIMENTAL EXAMPLES (USING AN ECDL)



100

101

102

103

104

105

10-13

10-12

10-11

10-10

10-9

Spec Rb clock Doppler sub-Doppler

Sampling time (s)

Alla

n de

viat

ion

of th

e la

ser

freq

uenc

y y(

)

-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)

LASER FREQUENCY STABILIZATION

With a cm-scale cell

The laser stabilization method and the clock physical principle/parameters should be adapted in order

to match the desired clock performances. It is a key issue for the medium and long term stability.


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Diode &collimator

Tiltable support:grating & optical isolator

Piezo

Laser output

• beam collimation

• grating angle

sin2 a

• Cavity length

m

L

2

EXTENDED CAVITY LASERS



)](cos[),( 0 rtEêtrE L

forcepressureradiationoredissipativ

stab

forcedipolarorreactive

stab rrEvdêrEudêF )()()( 00

~ light-shift ~ absorption

Optical molassesOptical trapping (lattice, tweezers, etc.)

Motivations: reduce the Doppler effect, increase interaction time, etc. 1

0

LASER RADIATIVE FORCES


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35










133CS CLOCK TRANSITION

Clock transition

Hydrogen‐like atom

Fine structure: LS coupling

Hyperfine structure: IS coupling

The fundamental term 6 2S1/2splits in two hyperfine levels(total ang. momentum F= I J = 7/2 1/2 = 3 or 4), separated by E1 = h 9.2 GHz and with a 2F+1‐fold degeneratacy

F’=5F’=4F’=3F’=2

F’=4

F’=3

251 MHz201 MHz

1168 MHz

151 MHz

9192 MHz

6 2P3/2

6 2P1/2

6 2S1/2F = 4

F = 3

D

1

= 895 nm

D2

= 852 nm

= 3.5 1014Hz

6 2P

Structure fine Structure hyperfineCoulomb

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36



133CS CLOCK (MAGNETIC DIPOLE) TRANSITION

Clock transition

Two-level atom :

Magnetic dipole interaction: Cesium ground state :

We lift the degeneracy with a magnetic field.

Evolution of the system:

Resonant behavior:



ATOMIC BEAM FREQUENCY STANDARDS

1

0 Linewidth

Rabi pedestal

Ramsey fringe

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37



MAGNETIC SELECTION



ATOMIC BEAM FREQUENCY STANDARDS

Stern-Gerlach (State selection) and Ramsey interrogation

0

0

0

s

0

)cos(

)sin(

0

0

t

t

1

0

0

0

1

0

1

0

0

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38



RAMSEY SCHEME

For a monokinetic beam



ONE RF INTERACTION: RABI RESONANCE

One interaction between RF field and atoms, of duration

Atoms starting in the ground state

The resulting state is given by solving Bloch equations.It depends on the RF field frequency detuning :

RF ?

t=0 t=0 t=0

t=t=

t=

with

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39



ONE RF INTERACTION: RABI RESONANCE

Wings, valid for >> 1 :

Rabi resonance :

RF

with



TWO RF INTERACTIONS: RAMSEY INTERROGATION

Generation of Ramsey fringes : two Rabi interactions with separated by a free evolution time T

RF ?

RF

T

T=‐

T=

=0

Evolution of the Bolch vector :

1st Rabi” pulse 2nd Rabi” pulseFree precession

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41



RAMSEY SCHEME WITH MONOKINETIC CS BEAM



RAMSEY SCHEME: NON-MONOKINETIC CS BEAM

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42



COLD ATOMIC BEAM CLOCKS (FOUNTAINS)

-100 -50 0 50 1000.0

0.1

0.2

0.3

0.4

01.01.01 14:25:06

Lock

-in s

igna

l

M icrowave frequency detuning

Thermal beam: v = 100 m/s, = 5 ms = 100 Hz

Cold fountain: v = 4 m/s, = 0.5 s = 1 Hz

Next step: microgravity

1

0 Linewidth




PRIMARY FREQUENCY STANDARDS

Systematic bias

Frequency :

Statistical fluctuations

See lecture of J. Guénat for an updated version of the accuracy

budget of fountains


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43



ATOMIC TIME (TAI) AND ASTRONOMICAL TIME (UTC)

Leap second




• Compact high performance and miniature atomic clocks findmany applications in every day life (positioning, telecoms, etc.)

• Atomic clocks (and stabilized lasers) are key instruments forfundamental physics experiments on ground and in space

• Thanks to the latest discoveries in atomic physics and photonics(or photon engineering) the precision of atomic clocks is beingimproved down to 10-17 and beyond

• More precisely, it is the manipulation of atoms photons andthe availability of tunable laser sources and optical combswhich is allowing such dramatic improvements

00

0 1)( stabilityIn

: cooling0: going optical

SUMMARY

21.02.2014

44



Prof. Gaetano MiletiLaboratoire Temps – Fréquence (LTF)

Faculté des Sciences, Université de NeuchâtelAvenue de Bellevaux 51

CH-2000 Neuchâtel, Switzerland

www.unine.ch/ltf

THANK YOU FOR YOUR ATTENTION !

Documents

ATOMIC CLOCKS: BASIC PRINCIPLES AND … tutorial on «Quartz crystal resonators and oscillators» 21.02.2014 7 Conférence Universitaire de Suisse Occidentale Programme doctoral en