Searching for variations of fundamental constants using the atomic clocks ensemble at LNE-SYRTE

Systèmes de référence Temps-Espace Searching for variations of fundamental constants using the atomic clocks ensemble at LNE-SYRTE Luigi De Sarlo, M Favier, R Tyumenev, R Le Targat, J Lodewyck, P Wolf, J Guéna, S Bize PSAS 2016 Jerusalem, Israel

Einstein s equivalence principle Universality of free fall: cannonball and feather fall the same way as do Rb and Cs atoms Local position invariance: coupling constants independent on (space-)time EEP! α Local Lorentz invariance: constants independent on gravitational potential α α

Can we test this in the lab? Violation of local position invariance: coupling constants depend on (space-)time Violation of local Lorentz invariance: coupling constants depend on gravitational potential R XY = X Y = f(,m p /m e,m q / 3 ) so do atomic frequencies ratios! Two examples: d ln R Rb/Cs = 0.49 d ln 0.021d ln(m q / 3 ) d ln R Hg/Sr =0.81d ln T.H. Dinh, et al., PRA 79 054102 (2009) E. J. Angstmann, et al., PRA 70 014102 (2004)

Comparisons are the key Local oscillator Useful signal: to be compared! Correction Atomic reference t Rabi = 100 ms ω clock E b E a Interrogation Two families of frequency comparisons: local, distant.

The clock ensemble at SYRTE GNSS GNSS Telecom GPS LAB 1 LAB 2

The clock ensemble at SYRTE GNSS GNSS Telecom GPS LAB 1 LAB 2 Cs beam UTC(OP) H-maser

The clock ensemble at SYRTE GNSS GNSS Telecom GPS LAB 1 LAB 2 Cs beam UTC(OP) H-maser FO1 Cs fountain Cryo DRO FO2 dual Rb & Cs fountain FOM transportable Cs fountain Microwave clocks

The clock ensemble at SYRTE GNSS GNSS Telecom GPS LAB 1 LAB 2 Cs beam UTC(OP) Optical frequency measurement Optical frequency combs H-maser Spectral hole burning FO1 Cs fountain Cryo DRO FO2 dual Rb & Cs fountain FOM transportable Cs fountain Microwave clocks

The clock ensemble at SYRTE GNSS GNSS Telecom Coherent optical fiber links Fiber-based TF dissemination GPS LAB 1 LAB 2 1.5um ultrastable laser Cs beam UTC(OP) Optical frequency measurement Optical frequency combs H-maser Spectral hole burning FO1 Cs fountain Cryo DRO FO2 dual Rb & Cs fountain FOM transportable Cs fountain Microwave clocks

The clock ensemble at SYRTE GNSS GNSS Telecom Coherent optical fiber links GPS Fiber-based TF dissemination 1.5um ultrastable laser LAB 1 LAB 2 UTC(OP) Cs beam Optical frequency measurement Optical frequency combs Spectral hole burning H-maser Optical clocks FO1 Cs fountain 698 nm ultrastable laser Cryo DRO FOM transportable Cs fountain 1062.5 nm ultrastable laser FO2 dual Rb & Cs fountain Microwave clocks Sr optical lattice clocks Hg optical lattice clock

Outline 1. Experiments with atomic fountains 1. Variation of fundamental constants 2. Searching for dark matter candidates 2. The mercury optical lattice clock at SYRTE 1. Why mercury 2. Experimental setup 3. Error budget 3. Optical clock comparisons 1. Sr/Cs local comparisons 2. Sr/Sr distant comparisons 3. Hg/Sr local comparison 4. Perspectives

Experiment with atomic fountains: testing EEP with clocks

Experiments with atomic fountains Cryo Sapphire Ocillator (with UWA) Atomic quality factor: Typical performances: Stability: Cs: 6 x 10-14 @ 1s Rb: 4.5 x 10-14 @ 1s J Guéna et al., IEEE TUFFC 59, 391 (2012) J Guéna et al., Metrologia 51, 108 (2014) the LNE-SYRTE reference hydrogen maser condary Frequency Standard from October is H-maser 1400XXX in the BIPM clock correspond to interruptions of FO2-Rb for efurbishing the set-up. Fig. 7. Fractional frequency instability characterized in terms of the Allan standard deviation observed with the FO2-Rb Secondary Frequency Standard and the metrology chain of Fig. 5. Red squares: Instability obtained with FO2-Rb operated at high atom number. The first points reflect the dynamics of the digital servo system locking the 6.8 GHz microwave signal to the atomic transition. For > 1000 s, the phase lock loop of the ultra-stable reference to the H-maser is effective. Therefore, data reflects the behavior of the H-maser Uncertainty: Cs: 2.1 x 10-16 Rb: 3.2 x 10-16

Variation of fundamental constants J Guéna et al., Phys. Rev. Lett. 109, 080801 (2012) M Abgral et al., C. R. Phys. 16, 461 (2015) d ν ln( ν d dt Rb Cs ν ln( ν Rb Cs ) 17 = ( 10.7 ± 4.9) 10 yr 16 ) = C + (0.8 ± 0.9) 10 cos[ Ω ( t t 1 perihelion )] c² d du ν ln( ν Rb Cs ) = ( 4.7 ± 5.3) 10 7 Differential redshift test β ( 87 Rb) β ( 133 Cs) = ( 4.7 ± 5.3) 10 7 Variation of constants with gravity d dt ln( α 0.49 ( m q / Λ QCD ) 0.021 ) = ( 4.7 ± 5.3) 10 17 yr 1

Searching for Dark matter candidates using hyperfine freq. comparisons arxiv:1604.8514 Simplest version of post-gr model (scalar tensor theory) : c 2 V ( )=2 m 2 2 L int = d e F 2 ~ 4µ 0 self-interaction coupling to EM Non-zero mass implies oscillation at Compton frequency: +3H +! 2 = 4 G c 2 L int! = m c 2 /~ and no pressure (candidate for DM). We can fix φ0 DM.

Analysing 6 years of Cs vs. Rb arxiv:1604.8514 We look for oscillation in the Cs/Rb frequency ratio: Log(P) Fit to data (LS + Bayes MC): A + S sin(! t)+c cos(! t) Compute power and its variance: P = N(C 2 + S 2 )/(4 2 ) Log(ω/rad s -1 ) No detection, but limit to coupling as a function of mass: Log(d e +0.043(d m -d g )) Log(m ϕ c 2 /ev) - Plot with full coupling. - Complementary to WEP violation - When limited to EM coupling this is the most stringent test. K. Van Tilburg, et al., PRL 115, 011802 (2015) A. Arvanitaki,et al. PRL 116, 031102 (2016)

t Rabi = 260 ms FWHM: 3.4 Hz Beyond atomic fountains: Optical lattice clocks

The mercury optical lattice clock - Fermionic isotope 199 Hg has I=1/2 - Weak sensitivity to black body radiation shift (Sr/30, Yb/15) - Clock transition frequency sensitive to time variation of α - Excellent prospects for 10-18 reproducibility at room T H. Katori et al., Phys. Rev. Lett. 91, 173005 (2003) Hachisu et al., Phys. Rev. Lett. 100, 053001 (2008) L. Yi et al., Phys. Rev. Lett. 106 073005 (2011) A. Ludlow et al., Rev. Mod. Phys. 87, 637 (2015)

The mercury optical lattice clock - Fermionic isotope 199 Hg has I=1/2 - Weak sensitivity to black body radiation shift (Sr/30, Yb/15) - Clock transition frequency sensitive to time variation of α - Excellent prospects for 10-18 reproducibility at room T t Rabi = 260 ms FWHM: 3.4 Hz Rabi Spectroscopy : FWMH 3.4 Hz @ 266 nm Q at 3.4 10 14 H. Katori et al., Phys. Rev. Lett. 91, 173005 (2003) Hachisu et al., Phys. Rev. Lett. 100, 053001 (2008) L. Yi et al., Phys. Rev. Lett. 106 073005 (2011) A. Ludlow et al., Rev. Mod. Phys. 87, 637 (2015)

Experimental setup: UV challenge 1. Cooling 2. Trapping 3. Selection 4. Interrogation 5. detection PC DAQ 3D MOT Pumping Hg reservoir

Experimental setup: UV challenge 1. Cooling 2. Trapping 3. Selection 4. Interrogation 5. detection PC DAQ 3D MOT Pumping Hg reservoir Sat absorption Enh SHG BBO 254 nm Seed ECDL 1015 nm Simple SHG ppln 507 nm Fiber ampli 15 W

Experimental setup: UV challenge 1. Cooling 2. Trapping 3. Selection 4. Interrogation 5. detection PC Enh SHG LBO 326 nm Ti:Sa laser 725 nm Wavemeter unc. 10 MHz DAQ 3D MOT Pumping Hg reservoir Sat absorption Enh SHG BBO 254 nm Seed ECDL 1015 nm Simple SHG ppln 507 nm Fiber ampli 15 W

Experimental setup: UV challenge 1. Cooling 2. Trapping 3. Selection 4. Interrogation 5. detection PC Enh SHG LBO 326 nm Ti:Sa laser 725 nm Wavemeter unc. 10 MHz DAQ Lattice build-up cavity 3D MOT Pumping Hg reservoir Sat absorption Enh SHG BBO 254 nm Seed ECDL 1015 nm Simple SHG ppln 507 nm Fiber ampli 15 W

Experimental setup: UV challenge 1. Cooling 2. Trapping 3. Selection 4. Interrogation 5. detection PC Enh SHG LBO 326 nm Ti:Sa laser 725 nm Wavemeter unc. 10 MHz DAQ USC 3 x 10-16 flicker Lattice build-up cavity 3D MOT Pumping Hg reservoir PDH Fiber laser 1062.5 nm Sat absorption Enh SHG BBO 254 nm Seed ECDL 1015 nm Simple SHG ppln 507 nm Fiber ampli 15 W

Experimental setup: UV challenge 1. Cooling 2. Trapping 3. Selection 4. Interrogation 5. detection PC Enh SHG LBO 326 nm Ti:Sa laser 725 nm Wavemeter unc. 10 MHz DAQ USC 3 x 10-16 flicker Lattice build-up cavity 3D MOT Pumping Hg reservoir PDH Fiber laser 1062.5 nm FIBER COMB (for comparison) Enh SHG BBO 266 nm Enh SHG ppslt 531nm Sat absorption Enh SHG BBO 254 nm Seed ECDL 1015 nm Simple SHG ppln 507 nm Fiber ampli 15 W

Experimental setup: UV challenge 1. Cooling 2. Trapping 3. Selection 4. Interrogation 5. detection PC Enh SHG LBO 326 nm Ti:Sa laser 725 nm Wavemeter unc. 10 MHz DAQ USC 3 x 10-16 flicker EM CCD Lattice build-up cavity 3D MOT Pumping Hg reservoir PDH Fiber laser 1062.5 nm FIBER COMB (for comparison) Enh SHG BBO 266 nm Enh SHG ppslt 531nm Sat absorption Enh SHG BBO 254 nm Seed ECDL 1015 nm Simple SHG ppln 507 nm Fiber ampli 15 W

Mercury clock: uncertainty budget Corr. (10-17 ) Unc. (10-17 ) Second order Zeeman 8.2 4.8 Cold collisions 5.2 6.4 Background gas 0 2.0 Lattice light shift linear 4 13.8 Lattice light shift non- -6 4 BBR 16.1 2.2 Probe light shift 0 0.1 AOM chirp 0.2 0.4 y/yold 1 (10 15 ) 6 4 2 0-2 -4-6 2012 2016 TOTAL 27.7 16.7 Most accurate: 3.6 x 10-16 -Light shift is dominant -Some systematics are limited by statistics -For a few effects only theoretical estimation available -Best clocks in the 10-18 : room for improvement!

Main systematic: lattice light shift - Differential Measurement Uref = 56 ER (5.5W @ 362nm) U 1 from 56 to 25 E R LLS = 1/2[ + (U L ) + (U REF )+ + (U L ) (U REF )] - Magic wavelength determination ν magic = 826 855 539 (21) MHz Good agreement with RIKEN group Yamanaka et al., PRL 114, 230801 (2015) - Correction at operating point of the clock (56 E R ) (4 ± 13.8) x 10-17 from linear term (-6 ± 3.6) x 10-17 from computed unresolved non linear contributions Katori et al., PRA 91, 052503 (2015)

Absolute frequency of the Sr clock transition 4 2015 2016 ν Sr /Hz - 429228004229870 3.5 3 2.5 2 54000 54500 55000 55500 56000 56500 57000 MJD 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 The future of clock-based tests: Optical to optical clock comparisons

Clock comparisons at SYRTE CSO + H-maser + Fountains USC 1550 nm Fiber comb f 0 mixed-out AOM AOM Hg USC 1062 nm Sr USC 698 nm

International measurements of Sr/Cs Latest measurement at SYRTE: arxiv:1605.03878 ν Sr /Hz - 429228004229870 4 3.5 3 2.5 2 54000 54500 55000 55500 56000 56500 57000 MJD 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 SYRTE PTB JILA Univ. Tokyo NICT NMIJ NIM - Excellent level of reproducibility at the international level - Agreement between the two best measurements at a few 10-16 - Large level arm (> 10 years) for testing EEP (mid 10-17 /year) - Optical/Microwave ratio limited by the accuracy of atomic fountains

All-optical remote clock comparison SYRTE, LPL, PTB collaboration 1E-15 total Allan deviation σ y (τ) 1E-16 1E-17 1 10 100 1000 10000 100000 averaging time τ (s) C Lisdat et al., arxiv:1511.07735 (2015)

All-optical remote clock comparison SYRTE, LPL, PTB collaboration 1E-15 total Allan deviation σ y (τ) 1E-16 1E-17 1 10 100 1000 10000 100000 averaging time τ (s) - First long distance or international clock comparison with a fibre link - 10 times more resolution, and orders of magnitude faster than satellite comparison (2 10-17 resolution after a few 1000 s) - record agreement between distant clocks (4±5) 10-17 - first link of a future backbone of fibre links in France/Europe C Lisdat et al., arxiv:1511.07735 (2015)

Mercury vs Sr: arxiv:1603.02026 Comparison stability (10-15 ): Best run: 2.7 @ 1s Avg over 10 days: 4.3 @ 1s Fract. Unc. (units of 10-17 ) Sr clock 4.1 Hg clock 16.7 Optical-to-optical frequency ratio Link + Comb 1 U B (syst. total) 18 Fractional uncertainty: 1.8x10-16 U A (stat.) 5.0

v Hg /v Sr : best reproduced physical quantity? Tuymenev et al., arxiv:1603.02026 (2016) 2015 Yamanaka et al., PRL 114, 230801 (2015) - Completely independent measurement - Beyond (slightly) current SI second 2016 - Great reproducibility at 10-16 level: - similar to Sr/Cs - better than Yb/Sr - Can and will be used for testing GR

Summary & Perspectives

Perspectives - Fountains have >10 more years of data taking for TAI - Redefinition of the SI second - Exploiting optical clocks for fundamental physics tests - Towards 10-18 accuracy Hg remains an excellent candidate for a reproducible 10-18 room temperature frequency standard Measurement of non-linear lattice shifts (limitation?) - Valuable Hg/ frequency ratios Local Plenty of yet unmeasured frequency ratios are now available via optical fiber link networks in Europe (Hg/Yb + (E2), Hg/Yb + (E3), Hg/Sr + ) ACES

People & bibliography - Atomic fountains: M Abgrall, J Guéna, S Bize J Guéna et al., IEEE TUFFC 59, 391 (2012) J Guéna et al., Metrologia 51, 108 (2014) - Theory and GR tests: P Wolf, P Delva A Hees et al., arxiv:1604.8514 (2016) J Guéna et al., Phys. Rev. Lett. 109, 080801 (2012) M Abgral et al., C. R. Phys. 16, 461 (2015) - Optical to optical comparisons: Combs: Y Le Coq, R Le Targat Strontium: J Lodewyck, R Le Targat Mercury: L De Sarlo, S Bize C Lisdat et al., arxiv:1511.07735 (2015) R Tyumenev et al., arxiv:1603.02026 (2016)

Thank you for your attention!