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Optical Clocks III
Applications
Dr. Uwe Sterr Physikalisch-Technische Bundesanstalt (PTB) AG 4.31: Unit of Length Bundesallee 100 38116 Braunschweig Paschenbau Room 118a Tel: 0531 592 4310 [email protected]
Applying clocks means comparing them:
Loel Barr for NIST
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Menue
Clock Comparisons – co-located clocks
• stability
• correlated interrrogations
Time and Frequency Transfer - remote clocks
• General Relativity
• Satellite
• Fibers
Applications
• fundamental tests of physics
• navigation
• geodesy
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John Harrison's H1, 1735 height 673 mm
(collections.rmg.co.uk)
Clocks & Definition of Time
Greenwich Mean Time (1884) Mechanical Clocks
fosc ≈ 1 Hz daily uncertainty ≈ 1 s/d
1 s = 1/86400 of the mean solar day
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John Harrison's H1, 1735 height 673 mm
(collections.rmg.co.uk)
Clocks & Definition of Time
Greenwich Mean Time (1884) Mechanical Clocks
fosc ≈ 1 Hz daily uncertainty ≈ 1 s/d
1 s = 1/86400 of the mean solar day
John Harrison's H4, 1759 diameter 132 mm
(collections.rmg.co.uk)
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Clocks & Definition of Time
Greenwich Mean Time (1884) Mechanical Clocks
fosc ≈ 1 Hz daily uncertainty ≈ 1 s/d
1 s = 1/86400 of the mean solar day
A. Scheibe and U. Adelsberger, Z. Phys. 127, 416 (1950)
Quartz Clocks (1930s)
fosc ≈ 60 kHz, daily uncertainty ≈ 1 ms/d
Atomic Cesium Clocks
fosc ≈ 9.2 GHz daily uncertainty ≈ 1 ns/d
earth rotation variations of ± 1.5 ms
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100
101
102
103
104
105
106
10-18
10-17
10-16
10-15
Sta
bil
ity
y(
)
Averaging time (s)
1 Hour 1 Day 1 Week
Local Comparisons: Stability
Strontium lattice clock stability
Estim
ate
d insta
bili
ty σ
y(τ)
Averaging time τ in s
Stability determines time
needed to get sufficiently
small statistical uncertainty.
Allan variance
21
2
2
1)( iiy yy
i
i
t
t
i dtt
y0
)(1
with average fractional
frequency
for uncorrelated yi:
222)( yiy y
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Noise and Instability
0
wp
S( )
S1/2
Smax
S)
) TC : cycle time
C
y
T
NSQK /
111)(
maxS
Kd
dS
valid for:
• detection noise,
• high frequency laser noise
but not for
• „true“ laser frequency noise that
is controlled
0Q
Stability for
uncorrelated, white
detection noise:
0
)()()(
SQ
Kd
dSN S
0
)(
QSK
N
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Quantum Projection Noise
after the interrogation the number
of independent excited atoms Ne is measured
i.e. the single particle quantum state
is projected to either the state |e> or |g>.
ee pNN 0
)1(0
2
eeN ppNe
Itano et al., PRA 47,3554 (1993)
00
)(N
TCy
TC : cycle time
105 Sr atoms, l = 698 nm, = 1 Hz: y ~ 1·10-17-1/2
|g>
|e>
single Yb ion, l= 436 nm, = 1 Hz: y() ~ 2·10-15 -1/2
pe
1
0.5
ecgc eg
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Sub-QPN Methods
C
y
T
N 00
)(
|↓>
|↑>
N0
∙∙∙ N
N 21
22
N0 independent particles
|↓, ↓ ... ↓>
|↑, ↑ ,... ↑>
212
maximally entangled particles (GHZ-state)
evolves like a single particle with E = N0∙E0
N0-particle state at end of spectroscopy:
00
)(N
TCy
Heisenberg limit
Quantum-projection noise limit
’ = /N0 , N0’ = 1:
J. J. Bollinger, W. M. Itano, D. J. Wineland and D. J. Heinzen,
Optimal frequency measurements with maximally correlated states, Phys. Rev. A 54, R4649 (1996)
∙∙∙
N
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Dick effect
Laser related instability:
Interrogation even with noise-free detection,
the atomic signal gives only frequency information on a
short time interval:
Frequency comparison usually uses all available time,
independent of spectroscopy.
Missing atomic information during dark time leads to
additional fluctuation:
2
01
2 )(2
)(g
gkfS k
c
k
yy
Dick effect:
t
co
olin
g &
lo
ad
ing
coo
ling
& loa
din
g
de
tection
de
tection
inte
roog
atio
n
inte
roog
atio
n
......
t
t
g(t)
(t)
X X0
cT
dttgtttS0
')'()'()(
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Correlated interrogations
M. Takamoto, T. Takano, H. Katori, Frequency comparison of optical lattice clocks beyond the Dick limit, Nat. Phot. 5, 288 (2011)
• Interrogate two clocks at the same time, only compare during that time: • Laser noise cancels – works for different clocks • Laser coherence time still limits maximum Interrogation time
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Correlated interrogations
• Usefull for evaluation of systematic effects
• Comparison of nearby clocks • Frequency-ratio measurements
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Correlated interrogations
C.W. Chou, D. B. Hume, M. J. Thorpe, D. J. Wineland, T. Rosenband, Quantum Coherence between Two Atoms beyond Q = 1015. Phys. Rev. Lett. 106, 160801 (2011)
With Ramsey method, interrogation time > laser coherence time fi >> p, f is resolved
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Optical Frequency Comb
(m) = ceo + m frep
(m)
ceo frep
Time domain:
fs-laser with repetition-
frequency frep
Frequency domain:
equidistant comb
of narrow lines
t
1/frep
T.
Hänsch
J. Hall
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ceo frep optical frequency
a a
Clock Laser
BP
microwave
m·frep
femtosecond laser spectrum
n = ceo + n·frep
x2 x ceo
Optical Frequency Comb
• tight lock of comb and use beats directly
• do math in real time and cancel comb fluctuations –
“transfer oscillator method”
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100
101
102
103
104
105
106
10-17
10-16
10-15
10-14
10-13
Cs fountain clock
Yb single ion clock
estimate Sr lattice clock
fra
ctio
na
l in
sta
bili
ty
y(
)
averaging time (s)
1 hour 1 day 1 weekPreliminary
300 m • Very high stability • uB(Sr) = 2.9 × 10-17
Optical frequency comparison Yb+/ Sr
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Frequencies of Sr lattice clocks
Baillard et al., Eur. Phys. J. D 48, 11 (2008) Falke et al., Metrologia 48, 399 (2011) D. Akamatsu at al., Appl. Phys. Exp. 7, 012401 (2014) Campbell et al., Metrologia 45, 539 (2008) Yamaguchi et al., Appl. Phys. Exp. 5, 022701 (2012) Hong et al., Opt. Lett. 34, 692 (2009) Le Targat et al., Nature Com. 4, 2109 (2013) , Falke et al. arXiv:1312.3419 (2014)
USA
France
USA
Japan
Germany
Japan
Japan
France
Germany
Japan
Sr clocks under development: Italy, GB, China
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Remote Clock Comparisons
http://tf.nist.gov/time/twoway.htm
TIC(A) = A - B + dTB + dBS + dSBA + dSA + dRA + SB (1)
TIC(B) = B - A + dTA + dAS + dSAB + dSB + dRB + SA (2)
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Long-Distance Clock comparisons
satellite based
two-way satellite time and frequency transfer TWSTFT
D. Piester, et al., IEEE UFFC 55, 1906 (2008)
1 d
ay
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Remote Clock Comparisons General Relativity: coordinates: • Position r, q, f • Time t
Time t is different from proper time .
Metric near rotating Earth in Geopotential U:
• Gravitational redshift U/c2
• Second order Doppler shift v2/2c2
• Sagnac effect
Comparison by transportable clock:
F. Riehle, Frequency Standards, Wiley 2004
Lg = 6.969291∙10-10 : gravitational potential on geoid
G. Petit and P. Wolf, Astron. Astrophys. 286, 971-977 (1994)
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Time Transfer by EM-Signals
Metric near rotating Earth in Geopotential U:
• Gravitational redshift U/c2
• Sagnac effect
Electromagnetic signals: ds2 = 0
F. Riehle, Frequency Standards, Wiley 2004
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Remote Clock Comparisons
N. Ashby, Relativity in the
Glopal positioning System,
Living Rev. Relativity 6, 1,
(2003)
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fiber based clock comparisons
frequency
standard 1
frequency
standard 2
opt. fiber
transfer laser
1.5 µm
transfer laser
1.5 µm
frequency comb frequency comb
l1 l2
> 100 km
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Clock comparisons SMF 28 standard Telecom Fiber
Specifications
How many photons arrive after 900 km from 10 mW input at 1540 nm?
Can amplification help? What about no-cloning theorem?
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Fiber Link
G. Grosche et al., Opt. Lett. 34, 2270 (2009)
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Limitations
P. A. Williams, W. C. Swann, and N. R. Newbury, J. Opt. Soc. Am. B, 25, 1284-1293 (2008), C. E. Calosso, al., arXiv:1405.5895v2 (2014)
single trip should be compensated
estimated from measured round trip phase:
remaining uncompensated fiber noise:
t
0
0 L0
t
z
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Amplifiers
Erbium-doped Amplifier:
gain: 30 dB - bidirectional
Bandwidth: 20 THz
Noise figure: low ~ 5 dB
Raman Amplifier:
gain: 30 dB
Bandwidth: ~ THz
Noise figure: low, ~ 5 dB
Brillouin Amplifier:
Bandwidth: ~20 MHz
Noise figure: large ~ 18 dB
M.N. Islam, IEEE J. Sel. Topics Quant. Electron. 8, 548 (2002)
O. Terra and G. Grosche and H. Schnatz, Opt. Express 18, 16102 (2010)
O. Terra, PhD Thesis, Hannover 2010
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Clock comparisons
optical fiber based
Predehl et al., Science 336, 441 (2012)
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Summer 2014
Green: existing White: to be connected Red: planned
Future: European fiber network
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Applications
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Tests of Fundamental Physics Einstein Equivalence Principle (EEP): (1) LLI
(2) LPI
(3) UFF
Local Lorentz Invariance
Local Position Invariance
Universality of Free Fall
(aka: weak equivalence principle)
Violation of Local Position Invariance → a = f(Ugrav) or a = f(t)
J.-P. Uzan, Varying constants, Gravitation and Cosmology, Living Reviews in Relativity 14, (2011)
General Relativity is incompatible with Quantum Physics: Unified Theory must show deviations.
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Variation of Constants
• Are the fundamental constants constant in time and in space?
• first asked by Paul Dirac 1937.
• „Big number hypothesis“: Big Numbers H0/h just accidential or deeper physics – depend on age on universe?
• Fundamental constants?
• Need to be pure numbers, as units are arbitrary.
J.-P. Uzan, Varying Constants, Gravitation and Cosmology, Living Rev. Relativity 14, 2 (2011)
P. A. M. Dirac, The Cosmological Constants, Nature 139, 323 (1937)
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Fine-Structure Constant
http://de.wikipedia.org/wiki/Feinstruktur_%28Physik%29#mediaviewer/Datei:Hydrogen-Fine-Hyperfine-Levels.svg
Hydrogen Spectrum:
G. Drake (Ed.) Springer Handbook of Atomic, Molecular, and Optical Physics, Springer 2006
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Fine-Structure Constant
Hydrogen Spectrum:
G. Drake (Ed.) Springer Handbook of Atomic, Molecular, and Optical Physics, Springer 2006
Finestructure is relativistic effect Strongly dependent on Z and on electron configuration
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Variation of Constants
Quasar absorption spectra:
J.-P. Uzan, Varying Constants, Gravitation and Cosmology, Living Rev. Relativity 14, 2 (2011)
Indications of a Spatial Variation of the Fine Structure Constant, Phys. Rev. Lett. 107, 191101 (2011)
Latest Theory:
a depends on direction in space.
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Variation of fundamental constants
Indications from astronomical observations that fundamental constants in the early universe were different from present values.
Al+/Hg+
Yb+ Hg+
d ln α / dt (10-15/year)
d ln
Ry
/ d
t (1
0-1
5/y
ear)
E. Peik Nuclear Physics B (Proc. Suppl.) 203 – 204, 18 (2010)
Comparisons of different types of clocks can provide comparable resolution: (dα/dt)/α ≈ 10-16/year
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Temporal variations of constants
C. M. Will, The Confrontation between General Relativity and Experiment, Living Rev. Relativity 9, 3 (2014)
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Tests of gravitational red shift
Levine und Vessot
Columbus module
with ACES
Time dilation measurement Hafele, Keating (1972): 10% test Alley et al. (1976): 1% test
Frequency shift measurement Pound and Rebka (1960): 10% test Pound and Snider (1965): 1% test
Solar spectral lines Effect observed (Rowland und Jewell ~ 1890)
6
„Gravity Probe A“ (1976): Hydrogen maser as atomic clock
- Rocket flight to 10 000 km altitude - verified gravitational time dilation with 7 x 10-5 uncertainty (Vessot et al. 1980)
„ACES“ (ca. 2016): Cold Cs microwave clock
- ISS at 400 km altitude - goal: 2 x 10-6 uncertainty
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Tests of Local Position Invariance
Coupling of constants
to Sun‘s gravitational
field?
S. Blatt et al., Phys. Rev. Lett. 100, 140801 (2008)
annual orbit of Earth through solar gravity potential: U/c² ~ 10-10
Sr optical clocks versus Cs clocks
V. V. Flambaum and A. F. Tedesco, Phys. Rev. C 73 (2006)
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STE-QUEST Mission Overview
On board instruments:
• 85Rb/87Rb atom interferometer – test universality of free fall
• atomic clock / < 10-16 – gravitational red shift in field of
Earth
• microwave time- and frequency link – gravitational red shift in
t ~ 100 fs/day, / ≈10-18 in a few days field of Sun and Moon
• optical link based on
laser communication terminal: / ≈10-18 in 1 h
Ground segment:
• worldwide ensemble of optical clocks / ≈10-18
Space-Time Explorer - QUantum Equivalence principle Space Test
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STE-QUEST Mission Overview
On board instruments:
• 85Rb/87Rb atom interferometer – test universality of free fall
• atomic clock / < 10-16 – gravitational red shift in field of
Earth
• microwave time- and frequency link – gravitational red shift in
t ~ 100 fs/day, / ≈10-18 in a few days field of Sun and Moon
• optical link based on
laser communication terminal: / ≈10-18 in 1 h
Ground segment:
• worldwide ensemble of optical clocks / ≈10-18
STE-QUEST investigated as one of 4
ESA M3 candidate missions
In January 2014 finally not selected due
to financial and technological issues.
Space-Time Explorer - QUantum Equivalence principle Space Test
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STE-QUEST Mission Overview
Local Lorentz invariance:
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STE-QUEST Mission Overview
Gravitational Redshift:
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Relativistic Geodesy
• Gravitational Redshift
– Clocks at higher altitude tick faster
– Geoid as reference for UTC
– 1 meter: 10-16 relative frequency shift
fhigh
fref
h hc
g
f
ff
2
ref
refhigh
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Relativistic Geodesy
• Gravitational Redshift
– Clocks at higher altitude tick faster
– Geoid as reference for UTC
– 1 meter: 10-16 relative frequency shift
fhigh
fref
h hc
g
f
ff
2
ref
refhigh
At your age: What is older? Your head or your feet? And by what? Really?
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Levelling and Geoid
http://elte.prompt.hu/sites/default/files/tananyagok/gridsanddatums/ch07.html
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The Earth‘s geoid
• equipotential surface, shape water would take at rest under Earth‘s gravity and rotation
Sea floor
Sea surface
• only in past decades – GOCE, GRACE satellite missions: uncertainty of geoid reduced to 30 – 50 cm
• deduced from extensive gravitational force measurements and calculations
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Relativistic Geodesy with Clocks
ocean
surface
geoid U0
surface clock@geoid U0
UP= U0 + U
Vermeer, Reports of the Finnish Geodetic Institute 83(2),1 (1983); Bjerhammar, Bull. Geodesique 59, 207 (1985)
• relativistic frequency change:
• gravity potential U : Newtonian + centrifugal terms
• height:
2
0
c
UUZ P
g
c
g
UUH OP
P
2
Chronometric Levelling
U
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Height inconsistencies
Gruber et al 2011
(GOCEplus study)
www.goceplushsu.eu
Differences European leveling network (EUVN-DA) vs. Heights from GPS + GOCE geoid
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Differential tides Paris – Braunschweig
10−¹⁷
Detection of tide effect within reach of optical clocks!
Day of the year 2012
expected signal:
private comm. Ludger Timmen IFE Hannover