Atomic Clocks and Frequency Standards

Transcription

The Battel for Exactness
Matthias Reggentin
Humboldt-Universität zu Berlin,
Institut für 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)
July 07, 2010
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Importance of (correct) Time Measurement
http://ageofsail.wordpress.com/
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Importance of Time Measurement - Today
http://wikipedia.org/
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Clocks & Frequency Standards
• fundamental importance time measurement
• challenge - man made clocks
Relative uncertainty
10-2
10-4
10-6
10-8
10-10
Cs beam
10-12
10-14
10-16
10-18
1.650
Cs fountain
state of the art opt. standards
1.700
1.750
1.800
1.850
Year
1.900
1.950
2.000
2.050
Figure: development clocks, partially after [1]
[1] F. Riehle, Frequency Standards, Wiley, 1st ed. 2004
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Requirements Frequency Standard
• clock: basis frequency standard with frequency ν0 measure amount of
oscillation cycles, time T
T =n·
1
ν0
• precise/stable, accurate frequency
(short-, longterm stability)
• reproducibility
• frequencies in absolute unit in
comparison to other standards
→ intrinsic - primary standards
→ calibration - back tracking
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Clocks & Frequency Standards
2>
• atomic clocks transition in
microscopic quantum systems
• new SI definition of time unit in
ω12
1967: caesium primary standard
1>
Definition
”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 the caesium 133 atom.” [2]
[2] Comptes Rendus de la 13e CGPM (1967/68), 1969, 103
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• 2 separated oscillators
• one isolated reference, other read-out link
Reference osc.
Frequency
synth
Clockwork
Read-out osc.
• reference oscillator quantum system
• read-out oscillator quartz crystal (piezoelectric)
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quantum system, two level system states |1i, |2i
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
2>
Probability
1
ω12
0,8
0,6
0,4
0,2
1>
0
x·δω - ω12
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133
Cs Clocks - Beam clocks
http://www.nist.gov/
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133
• especial frequency standard
• basic setup NIST (from [5] D. Sullivan, J. Res. Natl. Inst. Stand.
Technol.106, 2001)
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133
• 133 Cs:
nuclear spin I = 7/2
total spin J = 1/2
⇒ hyperfine structure, states F = I ± J = 3, 4
• transition |F = 4, mF = 0i → |F = 3, mF = 0i: ∆ν = 919263770 Hz
(@ zero magnetic field)
• Zeeman split
mF = 4
F=4
mF = 0
mF = 3
F=3
mF = 0
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133
Zeeman split in external magnetic field
inhomogeneous field:
~ = −µeff ∇B
~
F
[6] Daniel A. Steck, ”Cesium D Line Data,” (revision 2.1.2, 12 August 2009)
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133
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Challenges - Broadening Processes
Aim
Interest in high Q =
ω0
∆ω
Broadening processes:
1
τl
⇒ negligible i.e. 133 Cs stable
• natural lifetime τl : ∆ωl ∝
• Doppler broadening
from energy, momentum conservation
+ absorption, − emission, relativistic calculation
⇒ ~ω = ~ω12 + ~~v1,2 · ~k ±
2
v1,2
(~ω)2
−
~ω
+ ...
12
2m0 c 2
2c 2
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2
v1,2
(~ω)2
~ω = ~ω12 + ~~v1,2 · ~k ±
−
~ω
+ ...
12
2m0 c 2
2c 2
2nd term first-order Doppler effect ⇒ Gaussian broadening
1
FWHM = ω12
kB T
2ln2
mc 2
3nd term recoil effect
4nd term second-order Doppler
effect
Absorption
r
0,5
0
0
ω - ω0
⇒ avoided by low temperature regime
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• Collision broadening: ∆ωcol ∝
1
τcol
∝ p ⇒ pressure reduction
• Intersection Time broadening
important contribution to the linewidth broadening
∆ωit ∝
Atomic beam
1
τit
solution enhancement τit
v=s·τ
Electrical field
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• How slow an atomic beam can be made?
• Homogeneity of the electromagnetic field?
⇒ concept Ramsey spectroscopy (Nobel prize 1989)
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Rabi Flopping
• atomic beam one interaction
• two level system
⇒ solution: oscillating occupation probability
• excited state |2i:
p2 (t) =
0
ΩR
2 ΩR t
sin
Ω0R
2
2
2
Ω02
R = ΩR + ∆ω
ΩR : Rabi frequency
• amplitude decrease with
Figure: from [1] F. Riehle, Frequency
∆ω
Standards
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Ramsey Spectroscopy
• idea two separated interactions time τ and between no field in
between for time T
⇒ probability for transition interference pattern
• near resonance |1i → |2i
p(τ + T + τ ) '
⇒ FWHM =
1 2
sin ΩR τ (1 + cos 2π(ν − ν12 )T )
2
1
2T
Interaction
I
maximum for ΩR τ =
π
2
Atomic beam
→ π/2 pulses
II
v=s·τ
[3] M. Ramsey, Phys. Rev. 78 (6), 1950
[1] F. Riehle, Frequency Standards
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Ramsey Spectroscopy
• enhancement signal linewidth
• amplitude, period nearly unaffected
[1] F. Riehle, Frequency Standards
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Ramsey Spectroscopy - pseudo spin picture
density matrix ρ11 ρ22 probability state |1i |2i:
ρ11 ρ12
ρ=
ρ21 ρ22
Optical Bloch equations (with ρ̃12 ≡ e −iδt ρ12 ,ρ̃21 ≡ e +iδt ρ21 ):

 

u
ρ̃21 + ρ̃12
 v  = i(ρ̃21 − ρ̃12 )
ρ22 − ρ11
w
 
   
u
ΩR
u
d  
v
=  0  × v 
dt
w
w
δ
w
v
u
*) i.e. P. Meystre and M. Sargent, Elements
of Quantum Optics
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ρ11 ρ12
ρ=
ρ21 ρ22

 

u
ρ̃21 + ρ̃12
 v  = i(ρ̃21 − ρ̃12 )
ρ22 − ρ11
w
 
   
u
ΩR
u
d  
v
=  0  × v 
dt
w
w
δ
w
v
u
of Quantum Optics
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ρ11 ρ12
ρ=
ρ21 ρ22

 

u
ρ̃21 + ρ̃12
 v  = i(ρ̃21 − ρ̃12 )
ρ22 − ρ11
w
 
   
u
ΩR
u
d  
v
=  0  × v 
dt
w
w
δ
w
v
u
of Quantum Optics
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ρ11 ρ12
ρ=
ρ21 ρ22

 

u
ρ̃21 + ρ̃12
 v  = i(ρ̃21 − ρ̃12 )
ρ22 − ρ11
w
 
   
u
ΩR
u
d  
v
=  0  × v 
dt
w
w
δ
w
δ·T
v
u
of Quantum Optics
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from [1] F. Riehle, Frequency Standards
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interference pattern
Probability for |2>
1
0,8
0,6
0,4
0,2
0
-15
-10
-5
0
5
δ = (ν - ν0) [2πT]
10
15
Figure: from [5] D. Sullivan, J. Res. Natl.
Inst. Stand. Technol.106, 2001
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133
http://www.ptb.de/
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133
Cs Clocks - Beam clocks, optical pumping
• enhance signal to noise ratio
• optical pumping for state selection
• detection optical transition
• a) pumping, b) detection flourescence photons
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133
Cs Clocks - Beam clocks, optical pumping
• basic layout
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133
Cs Clocks - Beam clocks, performance
• challenge cavity:
length (∆ν = 1/2T )
versus
additional phase shift due to manufacturing limits
relative 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
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133
Cs Clocks - fountain clocks
One step further!
• laser cooled atomic clocks
• two approaches:
→ enhance T
→ reduce phase shift
from cavity
• fountain design
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133
• 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
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133
process
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133
• cold atoms - Magneto Optical Trap
or 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 i
π-pulse |F = 4, mF = 0i →
|F = 3, mF = 0i
”laser-pushing” other states
|F = 4, mF i → |F 0 = 5, mF i
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133
Cs Clocks - fountain clocks, performance
• today’s measurement standard
PTB: CSF2 2009
• relative uncertainties:
PTB CSF2: 0.8 × 10−15
NIST NIST-F1: 1 × 10−15
(0.5 × 10−15 )
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133
Cs Clocks - fountain clocks, performance
remaining problems:
• cold collision shift
⇒ density reduction
→ increased statistical noise
⇒ other atomic species 87 Rb
• increasing flight time
→ not possible on earth
⇒ experiments in micro
gravity
http://www.esa.int/
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Outlook
• 2001 PHARO project
• 2010 ISS module ACES
uncertainty ∼ 10−16 regime
http://www.dlr.de/
• next generation on earth optical frequency standards for atomic clocks
• uncertainty < 10−17 regime
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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 Oscillating
Fields, 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 at
http://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
July 07, 2010
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Atomic Clocks and Frequency Standards

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