Highly precise clocks to test fundamental physics M. Abgrall, S. Bize, A. Clairon, J. Guéna, M. Gurov, 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, M. Zawada et al. Journées Systèmes de Référence Spatio-Temporels 2011 September 19 th 2011 Vienna, Austria 1
Outline 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 ti potential ti Prospects 2
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 output correction atoms interrogation ε : fractional frequency offset Accuracy: overall uncertainty on ε y(t) : fractional frequency fluctuations ti Stability: statistical properties of y(t), characterized by the Allan variance σ 2 y2 (τ) Can be done with microwave or optical frequencies, with neutral atoms, ions or molecules 3
Atomic Transitions and Fundamental Constants Atomic transitions and fundamental constants Hyperfine transition n 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 4
Atomic Transitions and Fundamental Constants m p, g (i) are not fundamental parameters of the Standard Model m p, g (i), can be related to fundamental parameters of the Standard Model (m q /Λ QCD, m s /Λ QCD, m q =(m u +m d )/2) It is often assumed that : δ ( m ( m / Λ / Λ QCD ) ) δ ( m = ( m V. V. Flambaum et al., PRD 69, 115006 (2004) s s QCD q q / Λ / Λ QCD QCD ) ) Recent, accurate calculations have been done for some relevant trans t ons transitions V. V. Flambaum and A. F. Tedesco, PRC 73, 055501 (2006) Any atomic transition (i) has a sensitivity to one particular combination of only 3 parameters (α, m e /Λ QCD, m q /Λ QCD ) Alternatively, l one can use (α, µ=m e /m p, m q /m p ) 5
Sensitivity coefficients K a K q K e Rb hfs 2.34-0.064 1 Cs hfs 2.83-0.039 1 K α, K e : accuracy at the percent level or better K q : accuracy? H opt 0 0 0 Yb + opt 0.88 0 0 Hg + opt -3.2 0 0 Dy comb. 1.5 10 7 0 0 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 E. Peik and Chr. Tamm, Europhys. Lett.61, 181 (2003) E. Peik et al., arxiv:0812.3548v2 S. G. Porsev et al., PRL 105, 182501 (2010) 6
3 types of searches Variation with time Repeated measurements between clock A and clock B over few years Variation with gravitation potential Annual modulation of the Sun gravitation potential at the Earth : ~1.6 10-10 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 7
LNE-SYRTE ATOMIC CLOCK ENSEMBLE H-maser H, µw FO1 fountain Cryogenic sapphire Osc. Macroscopic oscillator Phaselock loop τ~1000 s Optical lattice clock Cs, µw Hg, opt FO2 fountain Optical lattice clock FOM transportable fountain Sr, opt Rb, Cs, µw Cs, µw 8
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, 40 Ca + in Innsbruck) Fundamental physics testst PRL 92, 230802 (2004) PRL 84, 5496 (2000) PRL 102, 023002 (2009) J. Phys. B 38, S44 (2005) C.R. Physique 5, 829 (2004) PRL 90, 150801 (2003) Local Lorentz invariance in photon sector (CSO vs H-maser) and in the matter sector (Zeeman transitions in Cs fountain) Stability of fundamental constants t with time (Rb vs Cs, H(1S-2S) vs Cs, Sr vs Cs) and gravitation potential (Sr vs Cs) PRL 100, 053001 (2008) PRL 90, 060402 (2003) Gen. Rel. Grav. 36, 2351 (2004) PR D 70, 051902(R) (2004) Development of Sr and Hg optical lattice clock PRA 68, 030501 (2003) PRA, 72, 033409 (2005) PHARAO/ACES cold Cs atom space clock Support the development of the project Ground segment of PHARAO/ACES mission PRL 96, 060801 (2006) PRD 81, 022003 (2010) PRL 101, 183004 (2008) PRL 100, 140801 (2008) PRA 79, 053829 (2009) PRL 97, 130801 (2006) Eur. Phys. J. D 48, 11-17 (2008) Appl Phys B 99, 41 (2010) PRL 96, 103003 (2006) PRA 79, 061401 (2009) Opt. Lett. 35, 3078 (2010) PRL 106, 073005 (2011) 9
Atomic fountain clocks 133 Cs levels ( 87 Rb similar) 1.0 0.8 0.6 Ramsey fringes 1.0 0.8 0.6 0.4 0.94 Hz 0.2 00 0.0-1.0-0.5 0.0 0.5 1.0 0.4 0.2 0.0-100 -50 0 50 100 detuning (Hz) Atomic quality factor: Best frequency stability (~ Quantum Projection Noise limited): 1.6x10 16 10-14 @1s Best accuracy: 2.6x10-16 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, ) 10 with an accuracy a few 10-15 and <10-15 for a few of them.
LNE-SYRTE FO2: a dual Rb and Cs fountain 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 Cs 9192 9.192..GHz Rb 6.834 GHz J. Guéna et al., IEEE Trans. on UFFC 57, 647 (2010) 11
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) Resolution 6x10-17 at 50 days (assuming white noise) 16 Nov 2007-30 Jan 2008: 51 effective days of synchronous data ν(fo2-rb) (2007) =6 834 682 610.904 309 (8) Hz Total uncertainty 1.1x10-15 Investigation of the Distributed Cavity Phase shift reduces this uncertainty to <10-16 Collaboration with K. Gibble (PennState Univ., USA) J. Guéna et al., PRL 106, 130801 (2011) -0.96 ± 0.84 2.6 12
Measurements of the Rb hyperfine splitting vs time Weighted least square fit gives: (-2.0±1.2) (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) (-2.0±1.2) With QCD calculations: V. V. Flambaum and A. F. Tedesco, PR C73, 055501 (2006) (-2.0±1.2) Note: 87 Rb hyperfine transition was the first secondary representation of the SI second. BIPM CCTF recommended value (based on LNE-SYRTE 2002 data): 13 ν 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 14
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 0.4 Lattice clocks Transition prob bability 0.3 0.2 0.1 0.0-200 -100 0 100 200 detuning [khz] Carrier transition, essentially unaffected by external motion 15
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) 16
Strontium optical lattice clock s absolute frequency Measurements against Cs fountains at JILA, Tokyo Univ. and SYRTE F JE? =. A J I A? @ = JJE? A BHA G K A? O? >. Eur. Phys. J. D 48, 11 (2008) 5 H= J I + 5 7 5 + 0 ) 5-4 + 5 0 ) 5-4 BHA G K A? O ) - + ( $ ' & 3 independent measurements in excellent agreement to within a few 10-15 Very different trap depths (150 khz to 1.5 MHz) and geometries Now, accuracy ~1.5x10-16 Phys. Rev. Lett. 100, 140801 (2008) Science 319, 1805 (2008) Phys. Rev. Lett. 106, 210801 (2011) 17
Overview of recent measurements LNE-SYRTE (2011) MPQ + LNE-SYRTE (PRL 2004) Tokyo, JILA, LNE-SYRTE, E, (PRL 2008) NIST, (PRL 2007) Berkeley, (PRL 2007) PTB, (PRL 2004), (arxiv 2006) NIST,,(Science 2008) Least squares fit INDEPENDENT OF COSMOLOGICAL MODELS 18
Constraint to a variation of constants with gravity SYRTE (2011) NIST, SYRTE, PTB, PRL 98, 070802 (2007) SYRTE, Tokyo, JILA, PRL 100, 140801 (2008) NIST, PRL 98, 070801 (2007) Berkeley, PRA 76, 062104 (2007) Least squares fit INDEPENDENT OF COSMOLOGICAL MODELS 19
Summary and Prospects Atomic clocks provide high sensitivity measurements of present day variation of constants nts Clock tests are independent of any cosmological model Complement tests at higher redshift (geological and cosmological time scale) Oklo (~10-17 yr -1, 18 1.8 Gyr), Quasars (~10-16 yr -1, 10 Gyr) 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 In the future, mission like GEOSTAR dedicated to satellite remote comparisons, STE-QUEST New atomic and molecular systems with enhanced sensitivities At SYRTE: use Hg. Recently: first determination of λ magic Molecules l Highly charged ions Nuclear transition in 229 Th? ~ 14 Gyr = 1.4x10 10 yr PRL 106, 073005 (2011) 20