Atomic Clocks and Frequency StandardsThe Battel for Exactness
Matthias Reggentin
Humboldt-Universitat zu Berlin,Institut fur Physik
July 07, 2010
1 Time and Frequency Measurement through the years
2 Atomic Clock Concept
3 Microwave Frequency Standards
4 Outlook
M. Reggentin (HU-Berlin) Atomic Clocks and Frequency Standards July 07, 2010 2 / 39
Importance of (correct) Time Measurement
http://ageofsail.wordpress.com/
M. Reggentin (HU-Berlin) Atomic Clocks and Frequency Standards July 07, 2010 3 / 39
Importance of Time Measurement - Today
http://wikipedia.org/
M. Reggentin (HU-Berlin) Atomic Clocks and Frequency Standards July 07, 2010 4 / 39
Clocks & Frequency Standards
• fundamental importance time measurement• challenge - man made clocks
Rela
tive
unce
rtain
ty
10-1810-1610-1410-1210-1010-810-610-410-210-2
Year1.650 1.700 1.750 1.800 1.850 1.900 1.950 2.000 2.050
Cs beam
Cs fountain
state of the art opt. standards
Figure: development clocks, partially after [1]
[1] F. Riehle, Frequency Standards, Wiley, 1st ed. 2004M. Reggentin (HU-Berlin) Atomic Clocks and Frequency Standards July 07, 2010 5 / 39
Requirements Frequency Standard
• clock: basis frequency standard with frequency ν0 measure amount ofoscillation cycles, time T
T = n · 1
ν0
• precise/stable, accurate frequency(short-, longterm stability)
• reproducibility
• frequencies in absolute unit incomparison to other standards→ intrinsic - primary standards→ calibration - back tracking
M. Reggentin (HU-Berlin) Atomic Clocks and Frequency Standards July 07, 2010 6 / 39
Clocks & Frequency Standards
• atomic clocks transition inmicroscopic quantum systems
• new SI definition of time unit in1967: caesium primary standard
ω12
2>
1>
Definition
”The second is the duration of 9 192 631 770 periods of the radiationcorresponding to the transition between the two hyperfine levels of theground state of the caesium 133 atom.” [2]
[2] Comptes Rendus de la 13e CGPM (1967/68), 1969, 103
M. Reggentin (HU-Berlin) Atomic Clocks and Frequency Standards July 07, 2010 7 / 39
Atomic Clock Concept
• 2 separated oscillators
• one isolated reference, other read-out link
Reference osc.
Read-out osc.
Frequency synth
Clockwork
• reference oscillator quantum system
• read-out oscillator quartz crystal (piezoelectric)
M. Reggentin (HU-Berlin) Atomic Clocks and Frequency Standards July 07, 2010 8 / 39
Atomic Clock Concept
quantum system, two level system states |1〉, |2〉1 preparation one of the states
2 interaction with electromagnetic field
3 measure probability for transition
4 lock read-out oscillator on frequency of probability maximum
ω12
2>
1>
Prob
abilit
y
0
0,2
0,4
0,6
0,8
1
x·δω - ω12
M. Reggentin (HU-Berlin) Atomic Clocks and Frequency Standards July 07, 2010 9 / 39
133Cs Clocks - Beam clocks
http://www.nist.gov/M. Reggentin (HU-Berlin) Atomic Clocks and Frequency Standards July 07, 2010 10 / 39
133Cs Clocks - Beam clocks
• especial frequency standard• basic setup NIST (from [5] D. Sullivan, J. Res. Natl. Inst. Stand.
Technol.106, 2001)
M. Reggentin (HU-Berlin) Atomic Clocks and Frequency Standards July 07, 2010 11 / 39
133Cs Clocks - Beam clocks
• 133Cs:
nuclear spin I = 7/2total spin J = 1/2⇒ hyperfine structure, states F = I ± J = 3, 4
• transition |F = 4,mF = 0〉 → |F = 3,mF = 0〉: ∆ν = 919263770 Hz(@ zero magnetic field)
• Zeeman split
F = 4
F = 3
mF = 0
mF = 0
mF = 4
mF = 3
M. Reggentin (HU-Berlin) Atomic Clocks and Frequency Standards July 07, 2010 12 / 39
133Cs Clocks - Beam clocks
Zeeman split in external magnetic field
inhomogeneous field:
~F = −µeff∇~B[6] Daniel A. Steck, ”Cesium D Line Data,” (revision 2.1.2, 12 August 2009)
M. Reggentin (HU-Berlin) Atomic Clocks and Frequency Standards July 07, 2010 13 / 39
133Cs Clocks - Beam clocks
M. Reggentin (HU-Berlin) Atomic Clocks and Frequency Standards July 07, 2010 14 / 39
Challenges - Broadening Processes
Aim
Interest in high Q =ω0
∆ω
Broadening processes:
• natural lifetime τl : ∆ωl ∝1
τl⇒ negligible i.e. 133Cs stable
• Doppler broadeningfrom energy, momentum conservation
+ absorption, − emission, relativistic calculation
⇒ ~ω = ~ω12 + ~~v1,2 · ~k ±(~ω)2
2m0c2− ~ω12
v21,2
2c2+ ...
M. Reggentin (HU-Berlin) Atomic Clocks and Frequency Standards July 07, 2010 15 / 39
Challenges - Broadening Processes
~ω = ~ω12 + ~~v1,2 · ~k ±(~ω)2
2m0c2− ~ω12
v21,2
2c2+ ...
2nd term first-order Doppler effect ⇒ Gaussian broadening
FWHM = ω12
√2ln2
kBT
mc2
3nd term recoil effect4nd term second-order Dopplereffect
Abso
rptio
n
0
0,5
1
ω - ω0
0
⇒ avoided by low temperature regime
M. Reggentin (HU-Berlin) Atomic Clocks and Frequency Standards July 07, 2010 16 / 39
Challenges - Broadening Processes
• Collision broadening: ∆ωcol ∝1
τcol∝ p ⇒ pressure reduction
• Intersection Time broadening
important contribution to the linewidth broadening
∆ωit ∝1
τit
solution enhancement τit
Electrical field
Atomic beam
v = s · τ
M. Reggentin (HU-Berlin) Atomic Clocks and Frequency Standards July 07, 2010 17 / 39
Challenges - Broadening Processes
• How slow an atomic beam can be made?
• Homogeneity of the electromagnetic field?
⇒ concept Ramsey spectroscopy (Nobel prize 1989)
M. Reggentin (HU-Berlin) Atomic Clocks and Frequency Standards July 07, 2010 18 / 39
Rabi Flopping
• atomic beam one interaction• two level system
⇒ solution: oscillating occupation probability
Figure: from [1] F. Riehle, FrequencyStandards
• excited state |2〉:
p2(t) =ΩR
Ω′Rsin2 Ω′Rt
2
Ω′2R = Ω2R + ∆ω2
ΩR : Rabi frequency
• amplitude decrease with∆ω
M. Reggentin (HU-Berlin) Atomic Clocks and Frequency Standards July 07, 2010 19 / 39
Ramsey Spectroscopy
• idea two separated interactions time τ and between no field inbetween for time T
⇒ probability for transition interference pattern
• near resonance |1〉 → |2〉
p(τ + T + τ) ' 1
2sin2 ΩRτ (1 + cos 2π(ν − ν12)T )
⇒ FWHM =1
2T
maximum for ΩRτ = π2 → π/2 pulses
[3] M. Ramsey, Phys. Rev. 78 (6), 1950[1] F. Riehle, Frequency Standards
Atomic beam
v = s · τ
Interaction
I II
M. Reggentin (HU-Berlin) Atomic Clocks and Frequency Standards July 07, 2010 20 / 39
Ramsey Spectroscopy
• enhancement signal linewidth
• amplitude, period nearly unaffected
[1] F. Riehle, Frequency Standards
M. Reggentin (HU-Berlin) Atomic Clocks and Frequency Standards July 07, 2010 21 / 39
Ramsey Spectroscopy - pseudo spin picture
density matrix ρ11 ρ22 probability state |1〉 |2〉:
ρ =
(ρ11 ρ12
ρ21 ρ22
)Optical Bloch equations (with ρ12 ≡ e−iδtρ12,ρ21 ≡ e+iδtρ21):
uvw
=
ρ21 + ρ12
i(ρ21 − ρ12)ρ22 − ρ11
d
dt
uvw
=
ΩR
0δ
×u
vw
*) i.e. P. Meystre and M. Sargent, Elementsof Quantum Optics
u
w
v
M. Reggentin (HU-Berlin) Atomic Clocks and Frequency Standards July 07, 2010 22 / 39
Ramsey Spectroscopy - pseudo spin picture
density matrix ρ11 ρ22 probability state |1〉 |2〉:
ρ =
(ρ11 ρ12
ρ21 ρ22
)Optical Bloch equations (with ρ12 ≡ e−iδtρ12,ρ21 ≡ e+iδtρ21):
uvw
=
ρ21 + ρ12
i(ρ21 − ρ12)ρ22 − ρ11
d
dt
uvw
=
ΩR
0δ
×u
vw
*) i.e. P. Meystre and M. Sargent, Elementsof Quantum Optics
u
w
v
M. Reggentin (HU-Berlin) Atomic Clocks and Frequency Standards July 07, 2010 23 / 39
Ramsey Spectroscopy - pseudo spin picture
density matrix ρ11 ρ22 probability state |1〉 |2〉:
ρ =
(ρ11 ρ12
ρ21 ρ22
)Optical Bloch equations (with ρ12 ≡ e−iδtρ12,ρ21 ≡ e+iδtρ21):
uvw
=
ρ21 + ρ12
i(ρ21 − ρ12)ρ22 − ρ11
d
dt
uvw
=
ΩR
0δ
×u
vw
*) i.e. P. Meystre and M. Sargent, Elementsof Quantum Optics
u
w
v
M. Reggentin (HU-Berlin) Atomic Clocks and Frequency Standards July 07, 2010 24 / 39
Ramsey Spectroscopy - pseudo spin picture
density matrix ρ11 ρ22 probability state |1〉 |2〉:
ρ =
(ρ11 ρ12
ρ21 ρ22
)Optical Bloch equations (with ρ12 ≡ e−iδtρ12,ρ21 ≡ e+iδtρ21):
uvw
=
ρ21 + ρ12
i(ρ21 − ρ12)ρ22 − ρ11
d
dt
uvw
=
ΩR
0δ
×u
vw
*) i.e. P. Meystre and M. Sargent, Elementsof Quantum Optics
u
w
v
δ·T
M. Reggentin (HU-Berlin) Atomic Clocks and Frequency Standards July 07, 2010 25 / 39
Ramsey Spectroscopy - pseudo spin picture
from [1] F. Riehle, Frequency Standards
M. Reggentin (HU-Berlin) Atomic Clocks and Frequency Standards July 07, 2010 26 / 39
Ramsey Spectroscopy - pseudo spin picture
interference pattern
Prob
abili
ty f
or |2
>
0
0,2
0,4
0,6
0,8
1
δ = (ν - ν0) [2πT]-15 -10 -5 0 5 10 15
Figure: from [5] D. Sullivan, J. Res. Natl.Inst. Stand. Technol.106, 2001
M. Reggentin (HU-Berlin) Atomic Clocks and Frequency Standards July 07, 2010 27 / 39
133Cs Clocks - Beam clocks
http://www.ptb.de/
M. Reggentin (HU-Berlin) Atomic Clocks and Frequency Standards July 07, 2010 28 / 39
133Cs Clocks - Beam clocks, optical pumping
• enhance signal to noise ratio
• optical pumping for state selection
• detection optical transition
• a) pumping, b) detection flourescence photons
from [1] F. Riehle, Frequency Standards
M. Reggentin (HU-Berlin) Atomic Clocks and Frequency Standards July 07, 2010 29 / 39
133Cs Clocks - Beam clocks, optical pumping
• basic layout
from [1] F. Riehle, Frequency Standards
M. Reggentin (HU-Berlin) Atomic Clocks and Frequency Standards July 07, 2010 30 / 39
133Cs Clocks - Beam clocks, performance
• challenge cavity:
length (∆ν = 1/2T )
versus
additional phase shift due to manufacturing limitsrelative uncertainty:
• NIST: NIST-7: 4.4× 10−15
• PTB: CS1: 8× 10−15
[5] D. Sullivan, et al, J. Res. Natl. Inst. Stand. Technol.106, 2001
[7] A. Bauch, 42 (2005),Metrologia 42, 2001
M. Reggentin (HU-Berlin) Atomic Clocks and Frequency Standards July 07, 2010 31 / 39
133Cs Clocks - fountain clocks
One step further!
• laser cooled atomic clocks
• two approaches:
→ enhance T→ reduce phase shiftfrom cavity
• fountain design
http://www.nist.gov/M. Reggentin (HU-Berlin) Atomic Clocks and Frequency Standards July 07, 2010 32 / 39
133Cs Clocks - fountain clocks
• two interactions π/2-pulses(Ramsey)
• one cavity
⇒ reduced phase shift
• laser cooled atoms 2 µK ,enhanced T
[8] R. Wynands et al, Metrologia 42, 2005
M. Reggentin (HU-Berlin) Atomic Clocks and Frequency Standards July 07, 2010 33 / 39
133Cs Clocks - fountain clocks
process
[8] R. Wynands et al, Metrologia 42, 2005
M. Reggentin (HU-Berlin) Atomic Clocks and Frequency Standards July 07, 2010 34 / 39
133Cs Clocks - fountain clocks
• cold atoms - Magneto Optical Trapor Optical Molasse
• lifting atoms with cδν/ν12 for
laser upwards: ν = ν12 + δν
laser downwards: ν = ν12 − δν• state selection:
from cooling in |F = 4,mF 〉
π-pulse |F = 4,mF = 0〉 →|F = 3,mF = 0〉
”laser-pushing” other states|F = 4,mF 〉 → |F ′ = 5,mF 〉
[8] R. Wynands et al, Metrologia 42, 2005
M. Reggentin (HU-Berlin) Atomic Clocks and Frequency Standards July 07, 2010 35 / 39
133Cs Clocks - fountain clocks, performance
• today’s measurement standardPTB: CSF2 2009
• relative uncertainties:
PTB CSF2: 0.8× 10−15
NIST NIST-F1: 1× 10−15
(0.5× 10−15)
http://www.nist.gov/
M. Reggentin (HU-Berlin) Atomic Clocks and Frequency Standards July 07, 2010 36 / 39
133Cs Clocks - fountain clocks, performance
remaining problems:
• cold collision shift⇒ density reduction→ increased statistical noise⇒ other atomic species 87Rb
• increasing flight time→ not possible on earth⇒ experiments in micro
gravity
http://www.esa.int/
M. Reggentin (HU-Berlin) Atomic Clocks and Frequency Standards July 07, 2010 37 / 39
Outlook
http://www.dlr.de/
• 2001 PHARO project
• 2010 ISS module ACESuncertainty ∼ 10−16 regime
• next generation on earth optical frequency standards for atomic clocks
• uncertainty < 10−17 regime
M. Reggentin (HU-Berlin) Atomic Clocks and Frequency Standards July 07, 2010 38 / 39
Bibliography
[1] F. Riehle, Frequency Standards, Wiley, 1st ed. 2004
[2] Comptes Rendus de la 13e CGPM (1967/68), 1969, 103
[3] M. Ramsey, A Molecular Beam Method with Separated OscillatingFields, Phys. Rev. 78 (6), 1950
[4] P. Meystre and M. Sargent, Elements of Quantum Optics,Springer, 4th ed. 2007
[5] D. Sullivan, et al, Primary Atomic Frequency Standards at NIST,J. Res. Natl. Inst. Stand. Technol.106, 2001
[6] Daniel A. Steck, ”Cesium D Line Data,” available online athttp://steck.us/alkalidata (revision 2.1.2, 12 August 2009)
[7] A. Bauch, The PTB primary clocks CS1 and CS2 Metrologia 42,2005, J. Res. Natl. Inst. Stand. Technol.106, 2001
[8] R. Wynands et al, Atomic fountain clocks ,Metrologia 42, 2005
M. Reggentin (HU-Berlin) Atomic Clocks and Frequency Standards July 07, 2010 39 / 39