PROGRAM OF CUSO LECTURES 2014 (3RD EDITION)

Thursday February 20, lecture # 1

G. Mileti, Laboratoire Temps-Fréquence (LTF), Université de Neuchâtel

Introduction to the lectures and to atomic clocks, Cs thermal beam standards

Thursday February 27, lecture # 2

L.-G. Bernier, Laboratoire de Photonique, Temps et Fréquence, Institut fédéral de métrologie (METAS)

Atomic time scale, Allan deviation, time transfer, Hydrogen Masers & its applications

Thursday March 6, lecture # 3

S. Schilt and R. Matthey, Laboratoire Temps-Fréquence (LTF), Université de Neuchâtel

Fundamentals in laser spectroscopy and laser frequency stabilisations. Examples of applications

Thursday March 13, lecture # 4

G. Mileti and C. Affolderbach, Laboratoire Temps-Fréquence (LTF), Université de Neuchâtel

Vapour cell standards, chip-scale atomic clocks, applications in telecommunications and navigation

Thursday March 20, lecture # 5

J. Guéna, LNE-SYRTE (Laboratoire National de Métrologie et d'Essais, SYRTE), Observatoire de Paris

Atomic fountains, primary frequency standards

Thursday March 27, lecture # 6

T. Südmeyer, LTF-UniNe and T. Kippenberg, Laboratoire de Photonique et Mesures Quantiques, EPFL

Introduction to optical combs and applications. Examples of recent developments.

Thursday April 3, lecture # 7

C. Salomon, Laboratoire Kastler Brossel, Département de Physique Ecole Normale Supérieure, Paris

Laser cooling and trapping of atoms. Bose-Einstein Condensation. The ACES experiment on the ISS

Thursday April 10, lecture # 8

S. Bize, LNE-SYRTE (Laboratoire National de Métrologie et d'Essais, SYRTE), Observatoire de Paris

Optical frequency standards and applications

2

Laser-cooled Microwave Frequency Standards

COSO-Conférence Universitaire de Suisse Occidentale Lecture 5, 20.03.2014Programme Doctoral de Physique – Printemps 2014

Jocelyne GUENA

3

Outline

� Introduction to atomic clocks� Principle of atomic clocks

� Definition of the SI second

� Accuracy of atomic time

� Introduction to atomic fountains� Principle of operation

� Moving molasses technique

� Experimental setups

� Ramsey fringes

� Noise sources and frequency instability� Frequency noise of the interrogation

oscillator

� Detection scheme

� Quantum projection noise

� Using a cryogenic sapphire oscillator

� Femtosecond-based microwave

� Systematic shifts and accuracy� Collisional frequency shift

� Black body radiation shift

� 2nd order Zeeman effect

� Microwave leaks

� Doppler Effect

� Other effects

� Accuracy budget

� Applications� Comparisons between Primary

Frequency Standards

� Absolute frequency measurements: 87Rb hfs, optical transitions

� Timescales (TAI, UTC, SI…)

� Remote comparison methods

� Towards a new definition of the SI second

� Tests of fundamental physical laws: Einstein’s Equivalence Principle (variation of the constants)

Note : Space clocks => Lecture # 7

4

INTRODUCTION TO ATOMIC CLOCKS

Principle of atomic clocks (1)

5

Goal: deliver a signal with stable and universal frequency

Bohr frequencies of unperturbed atoms are expected to be stable and universal

Building blocks of an atomic clock

Can be done with microwave or optical frequencies, with neutral atoms, ions or molecules

ε : fractional frequency offset

Accuracy: overall uncertainty on ε

y(t) : fractional frequency fluctuations

Stability: statistical properties of y(t), characterized by the Allan variance σy

2(τ)

macroscopic oscillator

atoms

interrogation

correction

output

Principle of atomic clocks (2)

6

How to probe the atomic transition:

The two main parameters:

the atomic quality factor

fluctuations of the measured transition probability for integration time Tc:

Scaling of the fractional frequency instability:

-20 -10 0 10 200.0

0.5

1.0

Tra

nsiti

on p

roba

bilit

y P

detuning

Example: optimized Ramsey interrogation

Ramsey fringesRamsey interrogation

2 Rabi interactions (π/2 pulses)

Energy levels of 133Cs and the definition of the SI second

7

133Cs

The second of the international system of units is defined by fixing the frequency of the hyperfine transition of 133Cs to a conventional value: 9 192 631 770 Hz

Direct link to the unit of length via the conventional value of the speed of light c : 299 792 458 m.s-1

« 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 »

Accuracy of atomic time (microwave clocks only)

8

1950 1960 1970 1980 1990 2000 201010-17

10-16

10-15

10-14

10-13

10-12

10-11

10-10

10-9

SI second basedon atomic time

SYRTE

PTB

NIST

Cold atoms

Microwave clocksSlope: gain of ~10 every 10 years

LPTF

PTBNIST

PTBNRCNBSVNIIFTRI

NPLNBSLSRH

FR

AC

TIO

NA

L A

CC

UR

AC

Y

YEAR

Best in 2014

2x10-16

9

INTRODUCTION TO ATOMIC FOUNTAINS

� Principle of operation� Moving molasses technique� Experimental setups� Ramsey fringes

Atomic fountains: Principle of operation

10

Detection

Nat ~2×109

σr ~1.5−3mm

T ~1µK

∆V ~2 cm.s-1

Vlaunch ~ 4m.s-1

H ~1m

T ~500ms

Tc ~0.8-2s

Selection

3

2

1F=3

F=4

F=4

F=3

F=3, mF=0

F=4, mF=0

Laser cooling:Lecture #7

A key technique to atomic fountains (and atom interferometers): the moving molasses

11

Example (133Cs):

Due to the first order Doppler effect, the frequency of the upper and lower laser beams is the same in the frame moving upwards at

δνl Frequency detuning

LNE-SYRTE FO2 fountain: vacuum chamber

12

Interrogation region with magnetic and thermal shields

Compensation coils

Optical molasses

Collimator for molasses beams

The 2 outermost shields are removed

SYRTE FOM : optical bench

13

Laser diode based system, can be made compact and reliable

Optical fibers

External cavity diode laser

Injection locked diode laser

Cs vapor cell

Acousto-optic modulator

Atomic fountains around the world

14

LNE-SYRTE (F) PTB (D) NIST (USA)

~ 10 fountains in operation (LNE-SYRTE, PTB, NIST, USNO, ON, INRIM, NPL,…) with an accuracy ~10-15 and in the low 10-16 for a few of them.

Several projects (NIM, KRIISS, VNIIFTRI, USP,...)

S. Bize et al., J. Phys. B: At. Mol. Opt. Phys. 38 (2005) S449, Wynands and Weyers, Metrologia 42 (2005) S64–S79, T P Heavner et al., Metrologia 42, 411 (2005), S. Weyers et al., Metrologia 38, 343 (2001),…

Ramsey fringes in an atomic fountain

15

-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

detuning (Hz)

0.94 Hz

Atomic quality factor:

Shot to shot fluctuations of the transition probability:

tran

sitio

n pr

obab

ility

P

NO AVERAGING

ONE POINT = ONE MEASUREMENT OF P

16

NOISE SOURCES AND FREQUENCY INSTABILITY

� Frequency noise of the interrogation oscillator

� Detection scheme� Quantum projection noise� Using a cryogenic sapphire oscillator� Femtosecond-based microwave

Example of a microwave synthesizer

17

Typical requirements:

- low phase noise, phase coherence with the reference signal

- fine PC-controlled frequency tuning, PC-controlled amplitude (P~ -60dBm)

- give access to « Zeeman » transitions

- reduced microwave leakage

The power spectral density of the fractional frequency fluctuations of the synthesized signal is written

Most critical part of the spectrum from a few times the Rabi frequency (few 100 Hz) to a fraction of the inverse cycle time (~ 0.1 Hz)

Effect of the frequency noise of synthesizers

18

How the frequency fluctuations of the microwave source are sampled:

Fractional frequency instability (for N>>1)

=>Limitation at the level of σy(τ)~10-13×τ -1/2 when microwave synthesis is based on a very good quartz oscillator

0 1 2 3 4

h(t)

time (s)

Sensitivity function

Equation of the servo loop: correction at cycle k+1

G. Santarelli et al., IEEE Trans. Ultrason. Ferroelect. Freq. Contr. 45, 887 (1998)

G: Loop gain

Interrogation on the 2 sides of the fringe with frequency detuning alternatively +m, -mUse of the difference in transition probabilities to correct the oscillator frequency

involves the PSD at fourier components of the cycle frequency

Sensitivity function : definition and basic properties

Measurement of the transition probability

20

0 2 0 4 0 6 0 8 0 1 0 0

0

1 0 0

2 0 0

3 0 0

4 0 0

5 0 0

6 0 0

7 0 0

arbitrary units

t i m e ( m s )

e s t a t e

f s t a t e

t b / 2t st b / 2

The area Ae and Af of the time of flight signals is calculated. The transition probability is given by

� Insensitive to atom number fluctuations

� Insensitive to low frequency laser noise (FM, AM)

� Quantum efficiency ~100% (>100 detected photons/atom)

� Technical noise ~few 100 atoms

Quantum projection noise

21

For a single atom: - transition probability P:

- Variance of quantum fluctuations of P:

For an ensemble of Ndet uncorrelated atoms:

Contribution of the quantum projection noise to the frequency instability:

The fundamental limit to the measurement of the transition probability (for uncorrelated atoms)

Example: Ndet = 107, Qat = 1010, Tc = 1.5 s � σy ~ 1x10-14 @1s

Other detection noise sources (electronics, laser AM and FM,…) can be made negligible for Ndet ~106-107

Frequency instability: Fountain against H-maser

22

100 101 102 103 104

10-15

10-14

10-13

Typically, when using a very good quartz oscillator:

integration time τ(s)

frac

tiona

l fre

quen

cy in

stab

ility

Limiting term: phase noise of the quartz oscillator

Rb fountain vs. H-maser

Cryogenic sapphire oscillator (1)

23

Sapphire cryogenic oscillator from the University of Western AustraliaHigh quality factor sapphire resonator (Q ~ 4×109) at 12 GHz

Turning point of temperature sensibility: dν/dT = 0 near T=6K

SCO has extremely good short term stability (measured at UWA against a second SCO)

A. G. Mann et al., IEEE Trans. Instrum. Meas. 50, 519 (2001)

Cryogenic sapphire oscillator (2)

24

100 101 102 103 10410-19

10-18

10-17

10-16

10-15

Mod

ified

Alla

n D

evia

tion

Mod

σσ σσy(

ττ ττ)

Averaging time, ττττ, seconds

Hmaser

CSO

Reference

Ultra stable frequency reference based on the cryogenic oscillator

locked to a H-maser for long-term term stability

BVA quartz

D. Chambon et al. , Rev. Sci. Instrum. 76, 094704 (2005)

CSO

25

FO2 demonstrates short term instability of

close to the quantum limit, Ndet ~ 107

� Resolution of 10-16 in 7 hours

FO1 demonstrates quantum limited operation of a Cs fountain up to Ndet∼ 6x105

σy = 4x10-14 @1s

104 105 106

10-3

10-2

0.91 Nat

-1/2

σ y(τ)

Qatπ(

τ/T

c)1/

2

Nat

1 10 100 1000 1000010-15

10-14

10-13

Fountain vs. BVA Fountain vs. SCO (N

at/2)

Fountain vs. SCO (Nat~5 106)

fract

iona

l fre

quen

cy in

stab

ility

time (s)

G. Santarelli et al. PRL 82, 4619 (1999)

For purely quantum limited operation, we expect :

Quantum limited frequency stability

Optical frequency comb based ultra-low noise microwave

A new solution ?

Fs fiber comb driving FO2 fountain

100 101 102 10310-15

10-14

2.9x10-15 @ 1s

σ y(τ

)

τ (s)

3.5x10-14 τ-1/2

Atomic fountain

Fiber fsvsCSO

2.9x10-15 @ 1s

Fractional Frequency stability

J. Millo et al., Appl. Phys. Lett., 94, 141105 (2009)

Same result when CSO drive fountain

Quantum projection noise limited

106 atoms/shot

28

The continuous fountain approach

FOCS-2 at METAS in collab. with LTF Neuchatel

• Dick effect 500 times smaller.

• Less collisions.

• Different type of Cs fountain clock is an advantage for the atomic clock community (for comparison).

• Requires parabolic trajectory.

• Requires development of different kind of microwave cavity than the ones used in the pulsed fountain clocks.

• Continuous laser-cooling and preparation – continuous background light and magnetic fields.

• Laser-cooling and state preparation on a stream of atoms is less efficient than cooling on a trapped ball of atoms.

Laurent Devenoges, Evaluation métrologique de l'étalon primaire de fréquence à atomes froids de césium FOCS-2, Ph.D. thesis, Université de Neuchatel, 2012

J. Guéna, G. Dudle, & P. Thomann, EPJAP, 38, 183 (2007)

29

SYSTEMATIC FREQUENCY SHIFTS AND ACCURACY

� Collisional frequency shift� Black body radiation shift� 2nd order Zeeman effect� Microwave leaks� Doppler Effect� Other effects� Accuracy budget

Cold collision frequency shift

30

Typical inter-atomic distance:

Typical De Broglie wavelength:

In general, collisions tend to be dominated by s-waves:

� characterized by s-wave channel scattering length

Not true for 133Cs due to very low energy molecular resonances.

0.4 0.6 0.8 1.0 1.2-6000

-5000

-4000

-3000

-2000

-1000

0

1000

1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

pote

ntia

l ene

rgy

(K)

inter-nuclear distance (nm)

singlet state 1Σg

triplet state 3Σu

1+1

1+2

2+2

Inter-atomic potential curves

- long range: Van Der Waals interaction

- Size of the molecular region b ∼ 2 nm

Large collisional shift in Cs: can be ~10-13

Potentially limiting the accuracy to >10-15

P. Leo et al., PRL 86, 3743 (2001)

Clock shift for Cs (3,0)+(4,0)vs collision energy

3 methods to control the cold collision shift

- Change density precisely by 2 by interrupted adiabatic transfer during state selection

- Perform real-time measurement of the collision shift to cope with slow variations in cloud shape, atom number,…’’Differential measurement method’’

- Accurate extrapolation to zero density using the “adiabatic population transfer” method

- Operate with small atom number at the expense of a degraded frequency stability

- Tune the cold collision shift to zero

1

2

3

4

Selection sequence and evolution of the atomic state

100% 50%

Density and atom number ratio controlled to ~10-3

K. Szymaniec et al., PRL 98, 153002 (2006)

F. Pereira Dos Santos et al., PRL 89, 233004 (2002)

- Use a small source (MOT with moderate atom number) to reduce the effective temperature to ~100 nK

- Tune the population ratio between |g> and |e> during Ramsey interrogation to zero the collision shift

Note : collision shift with same atom number per second is smaller in FOCS2.

Transfer Full / Half

Cold collisions: 87Rb vs 133Cs

SYRTE

YALE

Theory

The shift in 87Rb is much (~50 to 100 times) smaller than in 133Cs

Atomic density changed by changing the MOT light intensity (40% uncertainty)

Differential measurements (interrogation oscillator H-maser)

In a MOT

Cavity pulling is taken into account and subtracted

0.0 0.5 1.0 1.5 2.0 2.5 3.0

-3

-2

-1

0

1

2

Csfract

iona

l fre

quen

cy s

hift

[10-1

5 ]

effective atomic density [107 cm-3]

SYRTE: Y. Sortais et al. , Phys. Rev. Lett. 85, 3117 (2000)YALE: C.Fertig and K.Gibble, Phys. Rev. Lett. 85, 1622 (2000)

33

SYSTEMATIC FREQUENCY SHIFTS AND ACCURACY

� Collisional frequency shift� Black body radiation shift� 2nd order Zeeman effect� Microwave leaks� Doppler Effect� Other effects� Accuracy budget

Blackbody radiation shift (1)

34

0 1x1014 2x1014 3x1014 4x10140

1

1

2

2

3

spec

tral d

ensi

ty (1

0-19 J

.m-3.H

z-1)

frequency (Hz)

Spectral density of blackbody radiation

Cs D1 and D2 lines

894 and 852 nm

Peak:1.7×1013 Hz (λ~17µm)

Resulting frequency shift: most of the effect is the differential DC Stark shift

Sensitivity to temperature fluctuations (Cs): -2.3×10-16 K-1

clocktransition

clocktransitionperturbed

W. Itano et al., Phys. Rev. A 25, 35 (1982)E. Simon, P. Laurent, and A. Clairon, Phys. Rev. A 57, 436 (1998)V. G. Pal'chikov, Y. S. Domnin and A. V. Novoselov , J. Opt. B 5, S131 (2003)K. Beloy, U. I. Safronova, A. Derevianko, Phys. Rev. Lett. 97, 040801 (2006)E. J. Angstmann, V. A. Dzuba, V. V. Flambaum, Phys. Rev. Lett. 97, 040802 (2006)

Blackbody radiation shift (2)

35

Sensitivity to temperature fluctuations (Cs): -2.3×10-16 K-1

� Reducing temperature fluctuations with operation at room temperature

innermost layer with high thermal conductivity, well isolatedfrom environment

⇒⇒⇒⇒ good temperature uniformity < 0.1 K & no large gradients between inner region and environment

Control of temperature and thermal gradients in the interrogation region with 3 sensors along the innermost layer & measurements every hour during fountain operation

� Operating at cryogenic temperature:2 Nitrogen-cooled Cs fountains under development (NIST and INRIM)

Al

Second order Zeeman effect

36

580 600 620 640 660 680 700 720 740 760 7800.84

0.86

0.88

0.90

0.92

0.94

0.96

0.98

1.00

prob

abilit

é de

tran

sitio

n

désaccord micro-onde (Hz)

A static B field is applied on purpose to spectrally resolve the mF=0 to mF=0 transition:

The B field is measured and made homogeneous using the mF=+1 to mF=+1 transition

(Earth field ~300mG)

sensitivity to field fluctuations: 9.3 10-16.nT-1

Homogeneity ~10-3 or 100 pT (1 µG)

Stability ~10-5 or 1 pT (10 nG) from 1s to several days

Switchable microwave synthesizers designed to control microwave leaks

� Optimized and tested with heterodyne phase transient analyzer

� Powerful test and suppression of microwave leaks

37

Interaction of atoms with uncontrolled leakage field outside the Ramsey cavity can cause large frequency shifts

D. Chambon et al., IEEE Trans. Ultrason. Ferroelect. Freq. Contr. 54, 729 (2006)

Mach-Zehnder interferometric switch

Doppler effect: Distributed Cavity Phase shift (1)

Our approachCollab. with K. Gibble, Pennstate Univ.

� Finite element model of the phase gradients + Monte-Carlo computation of the atomic response in degraded situations

� Validation against experiments � Computation of the shift under optimized clock operation

The microwave resonator: TE011 cylindrical copper cavity with 2 feedthroughs at cavity midsection

+ Non perfect reversal of atomic trajectories

� residual Doppler shift

Finite conductivity of copper ⇒ residualtravelling wave + large standing wave ⇔ wavewith spatially varying phase shift

� A very hard 3D problem : Several parameters involved: cavity geometry, atomic cloud position and velocity distributions, microwave power, detection geometry

DCP (2): Computation of the perturbed field

� Perturbation of boundary conditions

H0 defines Boundary Conditions (BC) on walls for f, g based on:

� Use an azimuthal decomposition of the perturbed field:

� For each m, a 2D numerical problem (r,z) instead of a single very hard 3D problemAtoms travel near centre, are mostly sensitive to lowest order terms. Practically: m= 0,1,(2)

δ: skin depth(finite conductivity)

( )0H H i gα= + +r r r

( )0 1E iE i fα= − −rr r

0

Lossy wallsAnd feeds

g: perturbed fieldH0 for perfectly conducting walls

DCP model: R. Li & K. Gibble, Metrologia 41, 376 (2004) id. 47, 534 (2010)

DCP (3): Validation against experimentJ. Guéna et al., PRL. 106, 130801 (2011)

� Current limitation due to fluctuations of atomic trajectories � better cavities would be desirable

� m=0 shifts vs µwave amplitude� Rabi oscillations as a stringenttest of atomic distributions

� Measurements of m=1 shifts (phase gradients)

vs fountain tilt angle

Differential frequency shift between Right/Left feeding of cavity

vs µwave power

� Uncertainty on the DCP shift reduced by ~3

No free parameters

Predicted m=0 shift at optimal amplitude dν/ν= 4×10-18

Other systematic shifts

41

Cold collisions + cavity pulling-real-time measurement and extrapolation with adiabatic passage method

Black body radiation-static polarizability, calculations, stabilization and measurement of T

Second order Zeeman effect-proper shielding and homogeneity, spectroscopy of the “Zeeman” transitions

Residual first Doppler effect (due to phase gradients in the Ramsey cavity)-careful design of the cavity, sym.-asym., π/2-3π/2-…, change clock tilt angle

Microwave lensing: Effect of microwave interactions on atom motion(“microwave recoil”, “lensing due to magnetic dipole interaction”)

-calculations Microwave leaks

-careful design, control using a microwave switch, …Microwave spectrum (spurious side bands, synchronous phase modulation,…)

-careful design and characterization of synthesizers, π/2-3π/2… measurements, change timing and synchronization

Ramsey pulling, Rabi pulling, Majorana transitions-careful design and characterization of the B field, calculations

Background gas collisions-earlier measurements, recent calculations for atomic fountains

Second order Doppler effect-order of magnitude => negligible

Currently achieved accuracy: 2-3x10-16

K. Gibble, PRL 97, 073002 (2006), R. Li et al., Metrologia 48, 283 (2011)

Accuracy budget of LNE-SYRTE fountains

Other most accurate fountain’s : Total Type B uncertainties- NPL-CsF2 2.1x10-16

- PTB-CsF2 3.1x10-16

- NIST-F1 3.1x10-16

J. Guéna et al., IEEE Trans. Ultrason. Ferroelect. Freq. Contr. 59, 391 (2012)

Fractional frequency corrections & uncertainties in units of 10-16

43

APPLICATIONS

� Comparisons between Primary Frequency Standards

� Absolute frequency measurements� Timescales� Remote comparison methods� Towards a new definition of the SI

second

� Tests of fundamental physical laws

44

Fountain comparisons

45

LNE-SYRTE ATOMIC CLOCK ENSEMBLE

Hg, opt

Sr, opt

Cs, µW

Cs, µW

Rb, Cs, µW

H, µW

Phaselock loop

τ~1000 s

FO1 fountain

FO2 fountain

FOM transportable fountainOptical lattice clock

Optical lattice clock

Macroscopic oscillator

Cryogenic sapphire Osc.

H-maser

Comparison between two atomic fountain clocks at the 10-16 level

46

( ) 16102.2s00050 −×==τσ y

Mean fractional frequency difference = 4 x 10-16

fully compatible with the accuracy of each of the two clocks.

C. Vian et al., IEEE Trans. Instrum. Meas. 54, 833 (2005)

The 2 fountains FO1, FO2 measure the H-maser frequencyFor the comparison data are averaged over synchronous time intervals

47

Key features of FO2 Rb/Cs dual fountain

� Dichroic collimators �co-located optical molasses

� 780nm light: home made interference filter based ECDL

� Rb, Cs clouds launched simultaneously at slightly different heights: 0.881m, 0960m

J. Guéna et al., IEEE Trans. on UFFC 57, 647 (2010)

Balistic flight Detected Rb/Cs TOF

87Rb

Since 2009, 2 clocks in 1

48

Rb/Cs frequency comparisons to 10-16 stat. unc.

461 days of Rb/Cs comparisons over 2010-2013

Resolution of 10-16 @ 40 days

Href / FO2-RbHref / FO2-Cs ⇒ FO2-Rb / FO2-Cs on synchronous intervals

FO2-Rb / FO2-Cs frequency instability

100 days

Instability is well understood

49

Absolute frequencymeasurements

87Rb hyperfine frequency measurements

J. Guéna et al., IEEE Trans. UFFC 57, 647 (2010)S. Bize et al., J. Phys. B: At. Mol. Opt. Phys. 38, S44 (2005)H. Marion et al., Phys. Rev. Lett. 90, 150801 (2003)Y. Sortais et al., Phys. Scripta T95, 50 (2001)S. Bize et al., Europhys. Lett. 45, 558 (1999)

� Our best determination: February 2012 to August 20126 834 682 610.904 312(3) Hz (4.4x10-16)

⇒ New definition of 87Rb secondary representation (CCTF-2012)

J. Guéna et al., Metrologia 51, 108 (2014)

νRb / νCs measurements : FO2-Rb vs FO2-Cs or FO1, or FOM since 1998

νRb 2004recommended value

FO2 dual

14 years

2004 recommended uncertainty

Least square fit to a constant:Fit std. error 1.7x10-16

Consistency of data: χ2=0.41, Q=0.96 goodness-of-fit

Error bars: Systematic unncertainties

ν(87Rb): First atomic transition to be recognized by BIPM as a secondary representation of the SI second (2004)

� Last campaign Sr against the 3 Cs fountains

Limitations: fountains stability and accuracy, short meas. time (TiSa comb), short meas. time + collisions

Overall unc. 3.0x10-16

stat. unc. only 1.2x10-16

Le Targat R et al. Nature Commun. 4, 2109 (2013), ArXiv:1301.6046

⇒ Recommended value for the Sr optical clock (CCTF 2012)

Sr1 vs FO2-Cs ~4x10-14 @1s

Short term instability

Absolute frequency measurements: Sr vs Cs at SYRTEMore in Lecture #8, S. Bize

Other absolute frequency measurements using FOM

� H(1S-2S) at MPQ, Garching

�40Ca+ in Innsbruck

PRL 92, 230802 (2004)PRL 84, 5496 (2000)PRL 102, 023002 (2009)PRL 107, 203001 (2011)

J. Phys. B 38, S44 (2005)C.R. Physique 5, 829 (2004)PRL 90, 150801 (2003)

These measurements + QED ⇒ a determination of the charge radius of the proton at 5 sigma from result of spectroscopy with Hµ: “the µ PUZZLE”

Note: other use of FOM : testing the engineering & flight models

of PHARAO/ACES space clock at CNES, Toulouse

More in lecture # 7, Ch. Salomon

53

Application in timescales

54

International Atomic Time (TAI)

� Several PFS reports/month. Accuracy of TAI-SI: ~3x10-16

timescale elaborated at BIPMSee “Circular” T at www.bipm.org

Algorithms optimize stability & reliability

Steering

G. Petit, Metrologia 40, S252-S256 (2003)A. Bauch et al., Metrologia 43, 109 (2006)

� TAI calibration by Cs fountainsMeasurement, over 30 days, of the average frequency of the H-maser connected to EAL

LNE-SYRTE: 40% of all calibrations since 1999

SI second: average over the PFS’s

55

Example of fountain measurement of H-maser frequency

from October 2008 to June 2013More than 1000 days of cumulated data

H-maser- Fountainfrequency

H889, H890: KvarzH816: Symmetricom

H889 long term behaviour of well fitted by a lineardrift ∼ -1.1x10-16 /day + an exponentional relax. τ = 96 days

Allan deviation of residuals

Jan 2012-June 2013

Interruptions:- refill of cryo and brief reoptimizations;- Measurements of systematics

Data used to provide monthly calibrations of the H-maser with typical uncertainties

uB ~ 4.5 x 10-16

uA ~ 1 x 10-16

ulink/maser ~ 1.5 x 10-16

56

� Local timescales UTCk (based on local commercial clocks) are now steered to atomic fountains in several NMIs� ~H-maser(s) calibrated with fountain(s) almost continuously� 1 ns stability over 2 months� 10-16 metrology “in the field”

� UTC(OP) ~ timescale for ACES at SYRTE

Local timescales

UTC(OP)Note improvement in stability since steering is applied

Differences between UTC and UTCk

steering

Remote comparisons: tests of satellite T&F transfer links

� With FOM abroad, test of frequency transfer link using GPS PPP technique

Frequency of FOM - TAI from BIPM Circular T

Also test of the gravitational redshift correction

� Comparison of FO2-Rb with Rb fountainsat USNO (Washington DC), through GPSPPP technique

Connectedto EAL

Frequency stability: FO2Rb – Rb(USNO)

Not connectedto EAL

58

� Challenges for the use of optical clocks � Need for better remote comparisons� Need for better flywheel oscillators� Need to reach an international consensus

� High accuracy absolute frequency measurements � � best possible link to the current definition� CIPM establishes a List of Recommended Transitions, some of which are

recognized as Secondary Representation of the SI Second. For these, a recommended value and uncertainty is established

� First SRS recognized in 2004: Rb-hfs� At the 19th CCTF (2012): 8 SRS+3 Recommended Transitions� LNE-SYRTE contributed to: Rb-hfs, Sr, Hg, Ca+, H(1S-2S)

Towards a new definition of the SI second

Optical clocks under development (Lecture #7) : much better performances than best atomic fountain clocks : ‘’Should we change the definition of the SI second ?’’

� Submission to the CCTF WG PFS, similarly to PFS� � Calibration reports included in Circular T� Revised recommended value for 87Rb at the 2012 CCTF

� SYRTE measurements (uncertainty 4.4x10-16)� BIPM determination against the TAI ensemble� � 6 834 682 610.904 312 Hz, rec. unc. : 1.3x10-15

� Link to the TAI ensemble with a statistical uncertainty of ~1.1x10-16

� Since June 2013, FO2-Rb calibrations contribute to steering TAI � An experimentation of what could be done with optical frequency standards

59

First contribution to TAI with a SRS : 87Rb

Using FO2-Rb measurements of a H-maser over 2009-2013

2012 reference value of 87Rb for all points

J. Guéna et al., Metrologia 51, 108 (2014)

TAI frequency - FO2-Rb

Average: -0.1 x10-16 ± 1.1x10-16

(Q=0.999, RB=0.606)

Analysis of TAI data in Petit & Panfilo, IEEE TIM 60, 6,1550 (2013)

60

Testing Fundamental Physical Laws with Clocks

� The unification of gravity with the electroweak and strong interactions in a consistent theory

Unify General Relativity and Quantum Mechanics

� Most unification theories (e.g. string theories) allow or even predict violation of Einstein’s Equivalence Principle on which General Relativity is based

� Clocks are tools of choice to probe the structure of the curved space-time in relation with gravity:

As an example, Local Position Invariance: variation of natural constants with time and gravitational potential

61

Motivations

Atomic Transitions and Fundamental Constants

� Atomic transitions and fundamental constants

� Electronic transition: νopt ∝ R∞c. Frel(α) α: fine structure constant

� Hyperfine transition: νhfs ∝ R∞c.[α² Frel(Zα)]. g.(me/mp)

� molecular vibration and rotation => √(me/mp), me/mp

Electronic transitions test α alone (electroweak interaction)

Hyperfine (and molecular) transitions bring sensitivity to the strong

interaction via g-factor and µ=me/mp

g is not a fundamental constant of the Standard Model can be related to the light quark mass mq/ΛQCD

Relativistic effects

� Any atomic transition has a sensitivity to one particular combination

involving only 3 dimensionless constants: α, µ=me/mp, mq/ΛQCD

δ ln(ν/R∞c) ≈ kα δ ln(α)+ kµ δ ln(µ)+ kq δ ln (mq/ΛQCD)

3 sensitivity coefficients

� With QED+QCD: sensitivity of a transition to the 3 parameters

α, µ=me/mp, mq/ΛQCD

Atomic Transitions and Fundamental Constants

V.A. Dzuba and V.V. Flambaum, PR A77, 012515 (2008); T.H. Dinh et al, PR A79, 054102 (2009)

• kα accuracy: < 1 to 10%

• kµ accuracy: << 1%• kq accuracy ?

Diverse clock comparisons: frequency ratios� separate electroweak and strong interaction

� provide redundancy and signatures

� What to expect?� 0 with increasing precision � constraints to unification theories

� ≠0 � reveal physics beyond GR and the Standard Model?

� Complementary to tests over cosmological timescales (~10 Gyr)

64

� Variation with timeRepeated measurements between clock A and clock B over few years

� Variation with gravitation potentialAnnual modulation of the Sun gravitation potential at the Earth :

Several measurements per year, search for a modulation with annual period and phase origin at the perihelion

� Variation with space: modulation with arbitrary phase

3 types of searches

~1.6 10-10

65

Stability of constants tested with clocks� Search with Rb and Cs : variation with time and with gravitational potential

� Combining with other species: time variation

� Test separating electroweak and strong interactions

J. Guéna et al., Phys. Rev. Lett. 109, 080801 (2012)

mainly determined with Rb/Cs

Perspectives with the fountains� Systematic effects, Atomic Physics:

■ Measure the microwave lensing shift, never observed : Recent prediction: 7x10-17 pour FO1, FO2

■ Cs/Rb Collisions : with FO2, fine tuning of the collision energy

� Metrology

■ Time scales: TAI, SI, UTC(OP) and generation of an ACES time scale.■ Absolute optical frequency measurements : redefinition of the second ■ Comparisons with other european NMIs via coherent fiber link (1st test by mid-2014)

■ Comparisons via T2L2

� Participation to PHARAO/ACES (launch in 2016, 2 years):Development of the ground segment with a ACES-MLW terminal.

Lecture #7