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Fundamental Physics Tests using the LNE-SYRTE Clock Ensemble. M. Abgrall, S. Bize , A. Clairon, J. Guéna, P. Laurent, Y. Le Coq, P. Lemonde, J. Lodewyck, L. Lorini, S. Mejri, J. Millo, J.J. McFerran, P. Rosenbusch, D. Rovera, G. Santarelli, M.E. Tobar, P. Westergaard, P. Wolf, L. Yi, et al.

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fundamental physics tests using the lne syrte clock ensemble
Fundamental Physics Tests using the LNE-SYRTE Clock Ensemble

M. Abgrall, S. Bize, A. Clairon, J. Guéna, P. Laurent, Y. Le Coq, P. Lemonde, J. Lodewyck,

L. Lorini, S. Mejri, J. Millo, J.J. McFerran, P. Rosenbusch, D. Rovera, G. Santarelli, M.E. Tobar, P. Westergaard, P. Wolf, L. Yi, et al.

Rencontres de Moriond and GPhyS colloquium 2011

March 25th 2011

La Thuile, Aosta valley, Italy

  • Atomic clocks and fundamental constants
  • Rb vs Cs in atomic fountain clocks
  • Some optical clock comparisons
  • Constraints to variation of constants with time and gravitation potential
  • Prospects
principle of atomic clocks
Principle of atomic clocks

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

macroscopic oscillator

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 y2()




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


Atomic Transitions and Fundamental Constants

  • Atomic transitions and fundamental constants
    • Hyperfine transition
    • Electronic transition
    • Molecular vibration
    • Molecular rotation
  • Actual measurements: ratio of frequencies
  • Electronic transitions test α alone (electroweak interaction)
  • Hyperfine and molecular transitions bring sensitivity to the strong interaction

Atomic Transitions and Fundamental Constants

  • mp , g(i) are not fundamental parameters of the Standard Model
  • mp , g(i), can be related to fundamental parameters of the Standard Model (mq/ΛQCD, ms/ΛQCD, mq=(mu+md)/2)
  • Recent, accurate calculations have been done for some relevant transitions
  • Any atomic transition (i) has a sensitivity to one particular combination of only 3 parameters (, me/ΛQCD, mq/ΛQCD)
  • Alternatively, one can use (, µ=me/mp, mq/mp)

It is often assumed that :

V. V. Flambaum et al., PRD 69, 115006 (2004)

V. V. Flambaum and A. F. Tedesco, PRC 73, 055501 (2006)


Sensitivity coefficients

K, Ke : accuracy at the percent level or better

Kq : accuracy ?

PR C73, 055501 (2006)

Note: if a variation is detected, these coefficients provide a way to have a clear evidence from experiments with multiple clocks

Dysprosium : RF transition between 2 accidentally degenerated electronic states of different parity

Dzuba et al., Phys. Rev. A 68, 022506 (2003)

In some diatomic molecules: cancellation between hyperfine and rotational energies also leads to large (2-3 orders of magnitude enhancement)

Flambaum, PRA 73, 034101 (2006)

Highly charged ions

Flambaum, PRL 105, 120801 (2010)

Thorium 229 : nuclear transition in the optical domain (163nm) between 2 nearly degenerated nuclear states

S. G. Porsev et al., PRL 105, 182501 (2010)

E. Peik and Chr. Tamm, Europhys. Lett. 61, 181 (2003)

E. Peik et al., arXiv:0812.3548v2


3 types of searches

  • Variation with time
    • Repeated measurements between clock A and clock B over few years
  • Variation with gravitation potential
    • Several measurements per year, search for a modulation with annual period and phase origin at the perihelion
  • Variation with space
    • Several measurements per year, search modulation with annual period and arbitrary phase

Annual modulation of the Sun gravitation potential at the Earth :

~1.6 10-10




H, µW

FO1 fountain

Cryogenic sapphire Osc.

Phaselock loop

~1000 s

Optical lattice clock

Macroscopic oscillator

Hg, opt

Cs, µW

FO2 fountain

Optical lattice clock

FOM transportable fountain

Sr, opt

Rb, Cs, µW

Cs, µW


Applications of LNE-SYRTE clock ensemble

  • Time and frequency metrology
    • Fountain comparisons: accuracy ~4x10-16
    • Secondary definition the SI second based on Rb hfs
    • Calibration of international time (LNE-SYRTE: ~50% of all calibrations)
    • Absolute frequency measurement of optical frequencies in the lab (Sr) and abroad (H(1S-2S) at MPQ, 40Ca+ in Innsbruck)
  • Fundamental physics tests
    • Local Lorentz invariance in photon sector (CSO vs H-maser) and in the matter sector (Zeeman transitions in Cs fountain)
    • Stability of fundamental constants with time (Rb vs Cs, H(1S-2S) vs Cs, Sr vs Cs) and gravitation potential (Sr vs Cs)
  • Development of Sr and Hg optical lattice clock
  • PHARAO/ACES cold Cs atom space clock
    • Support the development of the project
    • Ground segment of PHARAO/ACES mission

J. Phys. B 38, S44 (2005)

C.R. Physique 5, 829 (2004)

PRL 90, 150801 (2003)

PRL 92, 230802 (2004)

PRL 84, 5496 (2000)

PRL 102, 023002 (2009)

PRL 96, 060801 (2006)

PRL 100, 053001 (2008)

Gen. Rel. Grav. 36, 2351 (2004)

PR D 70, 051902(R) (2004)

PRD 81, 022003 (2010)

PRL 90, 060402 (2003)

PRL 101, 183004 (2008)

PRA 79, 053829 (2009)

Appl Phys B 99, 41 (2010)

Opt. Lett. 35, 3078 (2010)

PRL 106, 073005 (2011)

PRL 100, 140801 (2008)

PRL 97, 130801 (2006)

PRA 68, 030501 (2003)

Eur. Phys. J. D 48, 11-17 (2008)

PRA, 72, 033409 (2005)

PRL 96, 103003 (2006)

PRA 79, 061401 (2009)


Atomic fountain clocks

133Cs levels (87Rb similar)

Ramsey fringes

Atomic quality factor:

Best frequency stability (~ Quantum Projection Noise limited): 1.6x10-14 @1s

Best accuracy: 4x10-16

Real-time control of collision shift with adiabatic passage: Phys. Rev. Lett. 89, 233004 (2002)

More than 10 fountains in operation (LNE-SYRTE, PTB, NIST, USNO, JPL, NICT, NMIJ, METAS, INRIM, NPL, USP,…)

with an accuracy a few 10-15 and <10-15 for a few of them.


LNE-SYRTE FO2: a dual Rb and Cs fountain

Cs 9.192..GHz

Rb 6.834…GHz

  • Dichroic collimators co-located optical molasses
  • Dual Ramsey microwave cavity
  • Synchronized and yet flexible computer systems with two independent optical tables
  • Almost continuous dual clock operation since 2009

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


Example of a Rb vs Cs measurement (2007/2008)

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

S. Bize et al., J. Phys. B: At. Mol. Opt. Phys. 38, S44 (2005)

S. Bize et al., C.R. Physique 5, 829 (2004)

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)

16 Nov 2007-30 Jan 2008: 51 effective days of synchronous data

Resolution 6x10-17 at 50 days (assuming white noise)

(FO2-Rb) (2007) =6 834 682 610.904 309 (8) Hz

Total uncertainty1.1x10-15

Investigation of the Distributed Cavity Phase shift reduces this uncertainty to <10-16

Collaboration with K. Gibble (PennState Univ., USA)

PRL to appear in 1 or 2 weeks

measurements of the rb hyperfine splitting vs time

Weighted least square fit gives:

Measurements of the Rb hyperfine splitting vs time


(1.7 standard deviation)

Improvement by 5.8 wrt PRL 90, 150801 (2003)

With QED calculations:

J. Prestage, et al., PRL (1995), V. Dzuba, et al., PRL (1999)


With QCD calculations:

V. V. Flambaum and A. F. Tedesco, PR C73, 055501 (2006)


Note: 87Rb hyperfine transition was the first secondary representation of the SI second. BIPM CCTF recommended value (based on LNE-SYRTE 2002 data):

Rb(CCTF)= 6 834 682 610.904 324 (21) Hz


Rb vs Cs: Search for annual terms

  • Variation of with gravitation potential
  • Variation with space

Optical clocks

  • The clock transition is in the optical domain allowing improved accuracy (talk by P. Lemonde)
  • Confinement into the Lamb-Dicke regime is used to dramatically reduce the effects of external motion
    • Mandatory to gain over µWave clocks:

Trapped ion clocks

Spectroscopy in the Lamb-Dicke regime

Lattice clocks

Carrier transition, essentially unaffected by external motion


Frequency ratio of Al+ and Hg+ single ion clocks at NIST

Fractional uncertainty: 5.2x10-17

in units of 10-18

Since then improved to 8.6x10-18

Chou et al., PRL 104, 070802 (2010)

T. Rosenband et al., Science 319, 1808 (2008)


Strontium optical lattice clock’s absolute frequency

  • Measurements against Cs fountains at JILA, Tokyo Univ. and SYRTE

Eur. Phys. J. D 48, 11 (2008)

  • 3 independent measurements in excellent agreement to within a few 10-15
  • Very different trap depths (150 kHz to 1.5 MHz) and geometries
  • Close to fountain accuracy limit

Phys. Rev. Lett. 100, 140801 (2008)


Overview of recent measurements

LNE-SYRTE (2011)


Tokyo, JILA, LNE-SYRTE, (PRL 2008)

NIST, (PRL 2007)

Berkeley, (PRL 2007)

PTB, (PRL 2004), (arXiv 2006)

NIST, (Science 2008)

Least squares fit



Constraint to a variation of constants with gravity

SYRTE (2011)


PRL 98, 070802 (2007)


PRL 100, 140801 (2008)


PRL 98, 070801 (2007)


PRA 76, 062104 (2007)

Least squares fit



Summary and Prospects

  • Atomic clocks provide high sensitivity measurements of present day variation of constants
    • Clock tests are independent of any cosmological model
    • Complement tests at higher redshift (geological and cosmological time scale)
    •  Inputs for developing unified theories
  • Improvements in these tests will come from:
    • Improvements in clock accuracy
      • As fast as in the last decade ?
    • Improvements in remote comparison methods
      • Coherent optical fiber links
      • Use PHARAO/ACES mission on ISS (talk by L. Cacciapuoti),
      • In the future, mission like USTAR dedicated to satellite remote comparisons
    • New atomic and molecular systems with enhanced sensitivities
      • Molecules
      • Highly charged ions
      • Nuclear transition in 229Th