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 uwe.sterr@ptb.de

Applying clocks means comparing them:

Loel Barr for NIST

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

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 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)

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

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

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

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

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

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

')'()'()(

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

Correlated interrogations

• Usefull for evaluation of systematic effects

• Comparison of nearby clocks • Frequency-ratio measurements

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

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

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”

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

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

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)

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

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)

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

Remote Clock Comparisons

N. Ashby, Relativity in the

Glopal positioning System,

Living Rev. Relativity 6, 1,

(2003)

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

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?

Fiber Link

G. Grosche et al., Opt. Lett. 34, 2270 (2009)

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

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

Clock comparisons

optical fiber based

Predehl et al., Science 336, 441 (2012)

Summer 2014

Green: existing White: to be connected Red: planned

Future: European fiber network

Applications

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.

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)

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

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

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.

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

Temporal variations of constants

C. M. Will, The Confrontation between General Relativity and Experiment, Living Rev. Relativity 9, 3 (2014)

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

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)

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

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

STE-QUEST Mission Overview

Local Lorentz invariance:

STE-QUEST Mission Overview

Gravitational Redshift:

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

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?

Levelling and Geoid

http://elte.prompt.hu/sites/default/files/tananyagok/gridsanddatums/ch07.html

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

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

Height inconsistencies

Gruber et al 2011

(GOCEplus study)

www.goceplushsu.eu

Differences European leveling network (EUVN-DA) vs. Heights from GPS + GOCE geoid

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