G. Mileti, Engelberg, 6.3.2007Laboratoire Temps - Fréquence - 1 -
Physics of atomic clocks
Gaetano Mileti
Laboratoire Temps – Fréquence (LTF)
(http://www2.unine.ch/ltf)
Institut de MicrotechniqueUniversité de Neuchâtel
G. Mileti, Engelberg, 6.3.2007Laboratoire Temps - Fréquence - 2 -
Laboratoire Temps – Fréquence (LTF)
newly created on February 1st 2007
(http://www2.unine.ch/ltf)
Rue A. L. Breguet 1(c/o Institut de Physique)Institut de MicrotechniqueUniversité de Neuchâtel
Prof. P. Thomann (Directeur du LTF)Dr. G. Mileti (Directeur adjoint du LTF)Dr. C. AffolderbachDr. C. SchoriDr. E. BreschiF. FüzesiP. Scherler
Open positions: 2 postdocs, 2 pHDs
Research activities
Primary Cs fountains (METAS)
Laser cooling
Rubidium clocks
Coherent Population Trapping
Chip scale atomic clocks
Stabilised laser diodes
Optical frequency standards
G. Mileti, Engelberg, 6.3.2007Laboratoire Temps - Fréquence - 3 -
Tower clocks (1300)verge-and-foliot mechanism
Precision / Stabilityin seconds
per day
1 ns
1 µs
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
G. Mileti, Engelberg, 6.3.2007Laboratoire Temps - Fréquence - 4 -
Overview
1. A few fundamentals on atomic clocks
2. Examples of atomic clock principles
3. Accuracy and stability of atomic clocks
4. New atomic clocks: exploiting laser pumping
and laser cooling
5. Trends for the (near) future
G. Mileti, Engelberg, 6.3.2007Laboratoire Temps - Fréquence - 5 -
Essential 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 version in
french : Masson, 1998).
• Special issue of Metrologia: “Special issue: fifty
years of atomic time-keeping: 1955 to 2005”,
Volume 42, Number 3, June 2005.
G. Mileti, Engelberg, 6.3.2007Laboratoire Temps - Fréquence - 6 -
1. Fundamentals on atomic clocks
1. Basic principle of an atomic clock
2. Nuclear magnetic resonance
3. The Bloch vector
4. Advantages of atomic clocks
5. Block diagram of an atomic clock
G. Mileti, Engelberg, 6.3.2007Laboratoire Temps - Fréquence - 7 -
1.1 Basic principle of an atomic clock
Interrogation
Reference for the user (5 MHz)
Feed-back
Quartz oscillator Atoms
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)
F=4
6 S½
F=3
Hzh
EEFrequency 7706311929120 =
−=ν
G. Mileti, Engelberg, 6.3.2007Laboratoire Temps - Fréquence - 8 -
1.2 Nuclear magnetic resonance (classical)
• Magnetic moment interacting with
a magnetic field
• Static :
⇒ Larmor precession
• +rotating magnetic field
⇒ magnetic resonance
)()()( tBtmtmdtd
rrr×⋅= γ
Br
mr
oBr
00 B⋅= γω
0ωω =
)(1 tBr
oBr
oBr
sr
)(1 tBr
π pulse
π/2 pulse
G. Mileti, Engelberg, 6.3.2007Laboratoire Temps - Fréquence - 9 -
1.3 The Bloch vector (Quantum)
Atom (or ensemble of atoms)
Interacting field (RF, microwave, optical)
Bloch vector (fictitious spin)
tie ω2E
1E
∝
spopulationofdifferencequadratureindipoleatomic
phaseindipoleatomic
wvu
h12 EE −
≈ω
• 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, π/2 pulses, etc.
sr
G. Mileti, Engelberg, 6.3.2007Laboratoire Temps - Fréquence - 10 -
Examples oBr
2E
1E
=
=
100
wvu
srAtoms in
fundamental state(no field) sr
oBr
2E
1E
=
=
−100
wvu
srAtoms after π
excitation(and field switched off) sr
oBr
2E
1E
Atoms after π / 2excitation
(and field switched off)⇒ quantum
superposition of states
=
=
0)sin()cos(
0
0
tt
wvu
s ωωr
sr
G. Mileti, Engelberg, 6.3.2007Laboratoire Temps - Fréquence - 11 -
Magnetic resonance allows spin flip.
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
Sign
al
Probing frequency
Linewidth
G. Mileti, Engelberg, 6.3.2007Laboratoire Temps - Fréquence - 12 -
1.4 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.
G. Mileti, Engelberg, 6.3.2007Laboratoire Temps - Fréquence - 13 -
Simplified behavior of quartz oscillators
G. Mileti, Engelberg, 6.3.2007Laboratoire Temps - Fréquence - 14 -
1.5 Block diagram of an atomic clock
G. Mileti, Engelberg, 6.3.2007Laboratoire Temps - Fréquence - 15 -
2. Examples of atomic clock principles
1. Categories and applications of atomic clocks
2. Alkali atoms in “microwave” clocks
3. Principle of thermal Cesium beams
4. Principle of Rubidium vapor cell standard
5. Other principles of atomic clocks
G. Mileti, Engelberg, 6.3.2007Laboratoire Temps - Fréquence - 16 -
2.1 Categories and applications of atomic clocks (or frequency standards)
• Primary (Cs) - Secondary
• Passive – Active (H-Maser)
• Commercial (Rb, Cs, H) – Laboratory – “In development”
• Microwave - Optical
G. Mileti, Engelberg, 6.3.2007Laboratoire Temps - Fréquence - 17 -
Applications of atomic clocks
4 Radioastronomy, Geodesy
(VLBI, Radioastron, etc.)
4 Scientific Research, Instrumentation
(Microgravity, ACES, HYPER, etc.)
4 Navigation & Positioning
(Galileo, GPS, GLONASS, etc.)
4 Telecommunications
(Networks synchronisation, etc.)
4 Metrology, Time scales
(Primary and secondary standards, H-Masers)
G. Mileti, Engelberg, 6.3.2007Laboratoire Temps - Fréquence - 18 -
2.2 Alkali atoms in “microwave” clocks
• Hydrogen-like atoms: 1 unpaired electron
• Hyperfine structure: interaction of
• Simplified structure:
• Ground state:
nucleousewith µµ rr
S1/2
P1/2
P3/2
lumière(1014 Hz)
micro-onde(109 -1010 Hz)
=
=
000
wvu
sr
G. Mileti, Engelberg, 6.3.2007Laboratoire Temps - Fréquence - 19 -
133Cs87Rb
5S1/2
F=1
F=2mF = 0mF = -1mF= -2
mF = 1mF = 2
mF = 0mF = -1
mF = 1
6.8346 GHz5S1/2
F=2
F=3
3.0357 GHz
mF = 0mF = -1mF= -2
mF = 1mF = 2mF = 3
mF = -3
mF = 0mF = -1mF= -2
mF = 1mF = 2
6S1/2
F=3
F=4
mF = 0mF = -1mF= -2
mF = 1mF = 2mF = 3
mF = -3
mF = 0mF = -1mF= -2
mF = 1mF = 2mF = 3
mF = -3
9.1926 GHz
mF = 4
mF = -4
87Rb
85Rb
133Cs
G. Mileti, Engelberg, 6.3.2007Laboratoire Temps - Fréquence - 20 -
2.3 Principle of thermal Cs beams Stern-Gerlach (State selection) and Ramsey interrogation
0)cos()sin(
0
0
tt
ωω
=
000
sr
−100
010
−100
G. Mileti, Engelberg, 6.3.2007Laboratoire Temps - Fréquence - 21 -
Destruction of fringes contrast due to atomic velocity
distribution
G. Mileti, Engelberg, 6.3.2007Laboratoire Temps - Fréquence - 22 -
2.4 Principle of Rb cell standards
Optical pumping, Double resonance , Collisions, Light-shift
Lampe Rb87 filtre Rb85 cellule Rb87
S
P
Thermal equilibrium
S
P
Complete optical pumping
S
P
Partial optical pumping
G. Mileti, Engelberg, 6.3.2007Laboratoire Temps - Fréquence - 23 -
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
G. Mileti, Engelberg, 6.3.2007Laboratoire Temps - Fréquence - 24 -
excitation d’une lampe 87Rb avec un oscillateur RF (~120 MHz)
filtrage isotopique par une cellule 85Rb
+
G. Mileti, Engelberg, 6.3.2007Laboratoire Temps - Fréquence - 25 -
Optical pumping, Double resonance, Light-shift, Collisions
cavité micro-onde
détecteur
Lampe Rb87
filtre Rb85
cellule de résonance Rb87
S
P
Double resonance
light
µ-wave5.304x106 5.306x106 5.308x106 5.310x106 5.312x106
0.108
0.112
0.116
0.120
0.124
0.128
Tra
nsm
itted
ligh
t [V
on
10kΩ
]
6.84 GHz - Synthesiser frequency [Hz]
G. Mileti, Engelberg, 6.3.2007Laboratoire Temps - Fréquence - 26 -
G. Mileti, Engelberg, 6.3.2007Laboratoire Temps - Fréquence - 27 -
2.5 Other principles of atomic clocks (or frequency standards)
• Hydrogen Masers
• Ion traps
• Optical standards
(molecules, etc.)
see talk of R. Holzwarth
G. Mileti, Engelberg, 6.3.2007Laboratoire Temps - Fréquence - 28 -
3. Accuracy and stability of atomic clocks
1. Accuracy and stability
2. Primary frequency standards
3. Short-term frequency stability
4. Drift, aging and environmental effects
5. The role of the quartz oscillator and the LO
G. Mileti, Engelberg, 6.3.2007Laboratoire Temps - Fréquence - 29 -
3.1 Accuracy and stability
G. Mileti, Engelberg, 6.3.2007Laboratoire Temps - Fréquence - 30 -
3.2 Primary frequency standards
G. Mileti, Engelberg, 6.3.2007Laboratoire Temps - Fréquence - 31 -
Figure: de P. Gill, «ESA Harmonisation mapping meeting», October 6 2005
G. Mileti, Engelberg, 6.3.2007Laboratoire Temps - Fréquence - 32 -
3.3 Short-term frequency stability
5.304x106 5.306x106 5.308x106 5.310x106 5.312x1060.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Tran
smitt
ed li
ght [
V on
10k
Ω]
6.84 GHz - Synthesiser frequency [Hz]
0
0
ωω
∆=Q
21
).(2.0 −
= τσNSQ
Iy
J.Vanier, L.Bernier, IEEE Trans. on Instr. and Meas., Vol. IM-30, No 4, Dec. 1981
Note: linewidth is not everything
G. Mileti, Engelberg, 6.3.2007Laboratoire Temps - Fréquence - 33 -
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.
G. Mileti, Engelberg, 6.3.2007Laboratoire Temps - Fréquence - 34 -
3.4 Drift, aging and environmental effects
buffer-gas mixture:
40 45 50 55 60 65
-1100
-1080
-1060
-1040
-1020
-1000
39 µW 11 µW "no" light
reso
nanc
e sh
ift (H
z)
Cell temperature (°C)
7400
7450
7500
7550
7600
30 µW 11 µW "no" light
reso
nanc
e sh
ift (H
z)
pure N2
pure Ar
45 50 55 60 653252
3253
3254
3255
3256
3257
3258
reso
nanc
e sh
ift (H
z)
Cell temperature (°C)
pure N2: 1.6·10-9 /K
gas mix: < 6·10-11 /K
long-term stability:temperature within few mK
clock stability around 10-14
G. Mileti, Engelberg, 6.3.2007Laboratoire Temps - Fréquence - 35 -
3.5 The role of the quartz oscillator and LO
Microwave frequency
LO (quartz)
- Direct AM noise and FM → AM noise
- Aliasing effects (Phase noise)
“Dick effect”
Tran
smitt
ed li
ght
See Deng et al., PRA 59 (1) 773 (1999)
( ) ( ) 2/1
1
22 2 −
∞
=− ⋅= ∑ ττσ φ
nmnnoisePMy nfSC See Mileti et al.,
IEEE J. of Q. Electr. 34 (2) 233 (1998)
Finally:
( ) ( ) ( ) ( )2222 )()()()( τστστστσ lsy
noisePMy
noiseIy
totaly ++≈
G. Mileti, Engelberg, 6.3.2007Laboratoire Temps - Fréquence - 36 -
4. New atomic clocks: exploiting laser pumping and laser cooling
1. Tunable diode lasers
2. Optically-pumped thermal Cesium beam
3. Laser-pumped vapour cell standard
4. Coherent Population Trapping (CPT)
5. Cold atoms clocks
6. Other standards using diode lasers
G. Mileti, Engelberg, 6.3.2007Laboratoire Temps - Fréquence - 37 -
4.1 Tuneable diode lasers
Potential advantages of using diode lasers:
• 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.
G. Mileti, Engelberg, 6.3.2007Laboratoire Temps - Fréquence - 38 -
1.50um
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 VCSEL
Etc.
FP (RWL)
ECDL
DFB
DBR
5 cm
VCSEL
G. Mileti, Engelberg, 6.3.2007Laboratoire Temps - Fréquence - 39 -
Laser spectral cacterisationExam
ple
1:
het
erodyn
e fr
equen
cy s
pec
trum
Exam
ple
2:
mode-
hope
free
tunin
g r
ange
Laboratory ECDL vsLaboratory ECDL
ESA-ECDL vs DBR ESA-ECDL vs DFB
Laboratory ECDL DBR DFB
133.2 133.6 134.0 134.4-39
-38
-37
-36
-35
-34
-33
550 kHz
dBm
Fourrier frequency [MHz]
129 130 131 132 133 134 135 136 137 138 139-66
-65
-64
-63
-62
5 MHz
dBm
Fourrier frequency [MHz]132 133 134 135 136 137 138
-38
-36
-34
-32
-30
-28
2 MHz
29.05.2003 15:27:57
Am
plitu
de [d
Bm
]
Fourrier frequency [MHz]
>> 15 GHz
Abs
orpt
ion
Wavelength
8 GHz
wavelength
Mode hop
Rb 87 Rb 85
4 GHz
Phot
ocur
rent
Wavelength
G. Mileti, Engelberg, 6.3.2007Laboratoire Temps - Fréquence - 40 -
100 101 102 103 104 105
10-13
10-12
10-11
10-10
10-9
Spec Rb clock Doppler sub-Doppler
Sampling time τ (s)
Alla
n de
viat
ion
of th
e la
ser f
requ
ency
σy(τ
)
-50 0 50 100 150 200 250
-0.1
0.0
0.1
0.2
sign
al d
'erre
ur U
err (
V)
fréquence laser (MHz)
Laser frequency stabilisation
G. Mileti, Engelberg, 6.3.2007Laboratoire Temps - Fréquence - 41 -
4.2 Optically-pumped thermal Cs beam
G. Mileti, Engelberg, 6.3.2007Laboratoire Temps - Fréquence - 42 -
4.3 Laser-pumped vapour cell standardcavité micro-onde
Lampe Rb87 filtre Rb85
6.8 GHz
Rb87 Discharge lamp(several lines, > 1 GHz wide)
Laser (1 line, < 100 MHz wide)
3 GHz
Rb85 Optical filter
détecteur
cellule de résonance Rb87
Potential advantages:
• More efficient pumping
• Improved S/N
• Long term stability
• Power / Weight / Volume
• Redundancy
G. Mileti, Engelberg, 6.3.2007Laboratoire Temps - Fréquence - 43 -
Laser-pumped Rb prototypeESA-funded project
Volume for control electronics(300cm3,currently empty)
• adapted resonance cell,
• lamp removed,
(empty volume!)
Physics package(200cm3)
RAFS resonator module:
Stabilised laser head:
G. Mileti, Engelberg, 6.3.2007Laboratoire Temps - Fréquence - 44 -
-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
Maximal slope : 420 Hz / GHz
Rubi
dium
clo
ck fr
eque
ncy
[Hz]
Laser diode frequency [GHz]-1000 -800 -600 -400 -200 0 200 400 600 800
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
10-8
Referen
ce ab
sorpt
ion lin
e
"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
"10
MH
z" c
lock
freq
uenc
y (-
9'99
9'99
6) [H
z]
Laser frequency detuning [MHz]
Light-shiftShift of the resonance frequency induced by the optical radiation (I, ν)
G. Mileti, Engelberg, 6.3.2007Laboratoire Temps - Fréquence - 45 -
4.4 Coherent Population Trapping (CPT)
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
G. Mileti, Engelberg, 6.3.2007Laboratoire Temps - Fréquence - 46 -
4.5 Cold atoms clocks
)](cos[),( 0 rtEêtrE L φω +⋅⋅=Radiative forces:
4444 34444 21444 3444 21
forcepressureradiationoredissipativ
stab
forcedipolarorreactive
stab rrEvdêrEudêF )()()( 00 φ∇⋅⋅⋅⋅+∇⋅⋅⋅=
~ light-shift ~ absorption
Optical trapping (lattice, tweezers, etc.) Optical molasses
Motivations: reduce the Doppler effect, increase interaction time, etc.
G. Mileti, Engelberg, 6.3.2007Laboratoire Temps - Fréquence - 47 -
Sisyphus cooling: a combination of effects
G. Mileti, Engelberg, 6.3.2007Laboratoire Temps - Fréquence - 48 -
Application to cold atoms clocks:
Thermal beam: v = 100 m/s, T = 5 ms∆ν = 100 Hz
Fountain: v = 4 m/s, T = 0.5 s∆ν = 1 Hz
Cold beam in micro-gravity: v = 0.05 m/s, T = 5 s∆ν = 0.1 Hz
G. Mileti, Engelberg, 6.3.2007Laboratoire Temps - Fréquence - 49 -
Pulsed fountain
-100 -50 0 50 1000.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.5 0.0 0.5 1.00.0
0.2
0.4
0.6
0.8
1.0
Frequency(Hz)
0.94 Hz
G. Mileti, Engelberg, 6.3.2007Laboratoire Temps - Fréquence - 50 -
G. Mileti, Engelberg, 6.3.2007Laboratoire Temps - Fréquence - 51 -
Continuous fountain
0.3
0.2
0.1
0.0
Tran
sitio
n pr
obab
ility
/ a. u
.
-1000 0 1000fRF - fCs / Hz
0.3
0.2
0.1
-15 -10 -5 0 5 10 15
mF = 0
Main motivations:
reduce the effects of LO phase noise (stability) and
collisions (accuracy)
G. Mileti, Engelberg, 6.3.2007Laboratoire Temps - Fréquence - 52 -
5. Trends for the (near) future
(Optical frequency standards: see next talk)
• Chip-scale atomic clocks
Stable reference
See Knappe et al., Appl. Phys. Lett., 85, (9), 2004
G. Mileti, Engelberg, 6.3.2007Laboratoire Temps - Fréquence - 53 -
RbRb
alignment and bonding
-0.03 -0.02 -0.01 0.00 0.01 0.02 0.03
-1.1
-1.0
-0.9
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
Abs
orpt
ion
[arb
.]
Frequency [arb.]
87Rb
85Rb
G. Mileti, Engelberg, 6.3.2007Laboratoire Temps - Fréquence - 54 -
Physics & micro-technology in chip scale atomic clocks:
• Micro-fabrication of the atomic resonator
• Behavior of the confined atoms: collisions, wall-coating, etc.
• Ideal clock scheme: double resonance, Coherent Population Trapping, etc.
• Miniature optical source: control of the optical spectrum and its effects
• Miniature microwave sources: PM noise
• Overall clock electronics: consumption, etc.
• Assembly and packaging, reliability, wafer-scale production, etc.