Stationary 87 Sr optical lattice clock at PTB ( Accuracy, Instability, and Applications)

Stationary 87 Sr optical lattice clock at PTB ( Accuracy, Instability, and Applications) Ali Al-Masoudi, Sören Dörscher, Roman Schwarz, Sebastian Häfner, Uwe Sterr, and Christian Lisdat

Outline Introduction Stationary clock Local comparison (Yb + ) Remote comparison (Paris) Summary 2

Atomic clocks interrogation T i oscillator ν osc t atomic reference ν 0 clock cycle correction detection frequency offset Δν stable frequency output 3

polarisability / arb. u. 87 Sr lattice clock (5s6s) 3 S 1 1 S 0-3 P 0 clock transition (ν 0 429 THz). Γ 2π 1 mhz in fermionic 87 Sr (I = 9/2). (5s5p) 1 P 1 Optical lattice at magic wavelength: Differential light shift cancelled. Shifts due to atomic motion suppressed (Lamb Dicke regime). (5s5p) 3 P J 698 nm (clock) J = 2 J = 1 J = 0 3 P 0 3 D 1 3 P 0 3 S 1 (5s 2 ) 1 S 0 magic wavelength (λ m 813 nm) lattice frequency / THz 4

Stationary clock (5s6s) 3 S 1 (5s5p) 1 P 1 200 ms Zeeman slower 1 st stage MOT (461 nm) 90 ms 50 ms 2 nd stage MOT (689 nm) 3 rd stage MOT (689 nm) 461 nm J = 2 65 ms transfer to 1D lattice & state preparation (m F = ±9/2) 689 nm J = 1 J = 0 (5s5p) 3 P J 600 ms interrogation (698 nm) 698 nm (clock) detection n = n 0 ± dn (5s 2 ) 1 S 0 Lattice orientation: horizontal (θ 0.12 ) Atom number: < 1000 Temperature: < 1 µk (ax.) / < 2 µk (rad.) Cycle duration: ca. 1 s 5

Sr-1: Systematic uncertainty u syst 2 10-17 Limiting factors: Temperature gradients (blackbody radiation) Lattice orientation (tunnelling vs. light shifts) effect correction (in 10-17 ) uncertainty (in 10-17 ) BBR, ambient 492.78 1.26 BBR, oven 0.94 0.94 lattice, scalar+tensor -0.69 0.89 lattice, E2/M1 pol. 0 0.34 lattice, hyperpol. -0.39 0.18 tunneling 0 0.21 AOM efficiency 0 0.20 servo error 0 0.18 Zeeman, 2 nd order 3.61 0.15 cold collisions -0.01 0.13 DC Stark shift 0 0.034 probe light 0.002 0.002 line pulling 0 0.0003 optical path length 0 0.0001 total 496.3 1.9 6

temperature / C Blackbody radiation shift 4 6 8 T T T n BBR n dc( T0 ) n ( 4 dyn T0 ) O 6 8 T 0 T0 T0 atomic response to BBR BBR (Temperature) Uncertainty Temperature gradient n dc ( T 0 ) 5 600 mk 19 10 17 22.0 1.26 10 n dyn ( T 0 ) 1.5 10 18 21.5 T. Middelmann, et al., Phys. Rev. Lett., 109, 263004 (2012) T. Nicholson, et al., Nature Com. 6, 6896, (2015) 06:00 12:00 18:00 00:00 06:00 12:00 time 21.0 7

Blackbody radiation shift ylindrical copper Parameters: Copper Outer diameter= 32 mm Inner diameter = 10 mm Length = 83.2 mm Orifice radius = 0.5 mm Graphite tube BK7 Glass Graphite Outer diameter = 10 mm length = 50 mm 20mm 8

Blackbody radiation shift Transport distance = ( 40 50 ) mm Transport time = 350 ms 20mm 9

frequency shift (MOT - CF) / Hz Blackbody radiation shift 0 Accuracy 8-9 * 10-18 possible -1-2 11:00 14:00 17:00 20:00 time 10

Instability Instability 11

y ( ) Instability 10-15 ( ) y n n 1 N T C 10-16 10-17 10-18 10 0 10 1 10 2 10 3 10 4 averaging time (s) 12

Allan deviation Instability 10-14 Cs fountain clock 10-15 Yb + single ion 10-16 few s 10 3 s 10 6 s 10-17 Sr lattice clock 10-18 10 0 10 1 10 2 10 3 10 4 10 5 averaging time (s) 13

Noise analysis: total Allan deviation Instability Detection limited by QPN for > 130 atoms. Aliased laser noise still dominant (Dick effect). Predicted interleaved instability matches observation. Best published instability for normal operation! σ y (τ) = 1.6 10-16 (τ/s) -1/2 A. Al-Masoudi et al., Phys. Rev. A 92, 063814 (2015) excitation probability noise pe 0.1 0.01 10-16 QPN Electronic noise All without laser noise Shot noise 10 100 1000 g + e 2o (counts) 10-17 10-18 10 0 10 1 10 2 10 3 10 4 averaging time (s) 14

excitation Probability excitation probability excitation Probability Instability From Rabi to Ramsey 1.0 1.0 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0.0-300 -200-100 0 100 200 300 Scan Hz Δν 0.0-200 -150-100 -50 0 50 100 150 200 scan Hz 1.0 0.8 0.6 0.4 0.2 0.0-10 -8-6 -4-2 0 2 4 6 8 10 scan Hz 15

sensitivity function g(t) Instability Multi Ramsey Normal Ramsey 1 p g( t) n ( t) t 2 1.0 Normal Ramsey Multi Ramsey 0.8 0.6 0.4 0.2 0.0 0 50 100 150 200 250 300 350 time (ms) 16

excitation probability excitation Probability Instability Multi Ramsey Normal Ramsey 1.0 Theory Data 1.0 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0.0-75 -50-25 0 25 50 75 scan (Hz) 0.0-10 -8-6 -4-2 0 2 4 6 8 10 scan Hz 17

excitation probability Instability Multi Ramsey Normal Ramsey 1.0 0.8 0.6 0.4 0.2 0.0-3 -2-1 0 1 2 3 applied frequency (Hz) 18

reconstructed phase ( ) sensitivity function g(t) Instability Multi Ramsey Normal Ramsey 1.5 1.0 1.0 Multi Ramsey Normal Ramsey 0.5 0.8 0.0 0.6-0.5 0.4-1.0 0.2-1.5-2 -1 0 1 2 3 applied frequency step (Hz) 0.0 0 50 100 150 200 250 300 350 400 t / ms 19

Applications Applications 20

Local clock comparison: 171 Yb + / 87 Sr PTB s 171 Yb + single-ion clock: Electric-octupole (E3) transition ( 2 S 1/2 2 F 7/2, ν 0 642 THz) 3.9 10-18 systematic uncertainty Instability of 5.3 10-15 (τ/s) -1/2 N. Huntemann, High-Accuracy Optical Clock Based on the Octupole Transition in 171 Yb +, PhD thesis, LU Hannover (2014) Frequency ratio sensitive to variations of α: 171 Yb + clock highly sensitive. 87 Sr clock insensitive. ΔR/R -6 Δα/α V.V. Flambaum and V.A. Dzuba, Can. J. Phys. 87, 25 (2009) 21

Local clock comparison: 171 Yb + / 87 Sr Measurement in 2015: > 80 h of data acquired. Instability of 4.4 10-15 (τ/s) -1/2. Statistical uncertainty 1.3 10-17. Total uncertainty 2.4 10-17. PRELIMINARY 22

Variations of the fine-structure constant α Measurement in 2015: > 80 h of data acquired. Instability of 4.4 10-15 (τ/s) -1/2. Statistical uncertainty 1.3 10-17. Total uncertainty 2.4 10-17. PRELIMINARY courtesy of: Nils Huntemann Drift measurement: Combine ratio measurements from 2012 and 2015. Uncertainty improved by factor 4! Sr/Yb + @ PTB (preliminary): (1/α) (dα/dt) = (7±5) 10-18 / yr Al + /Hg + @ NIST: (1/α) (dα/dt) = (16±23) 10-18 / yr T. Rosenband et al., Science 319, 1808 (2008) 23

Remote clock comparison Collaboration of PTB with participation of the Réseau National de télécommunications, the Institut für Erdmessung of the Leibniz Universität Hannover, and the Laboratoire Photonique, Numérique et Nanosciences. Paris Braunschweig 24

Remote clock comparison Satellite link (TWSTFT, GPS) Paris Braunschweig 25

Remote clock comparison Satellite link: Few 10-16 uncertainty Long averaging times ( weeks) Difficulties due to satellite motion and atmosphere. Satellite link (TWSTFT, GPS) Paris Braunschweig 26

Remote clock comparison Satellite link: Few 10-16 uncertainty Long averaging times ( weeks) Difficulties due to satellite motion and atmosphere. Satellite link (TWSTFT, GPS) Paris Telecom fibre link Braunschweig 27

Remote clock comparison Satellite link: Few 10-16 uncertainty Long averaging times ( weeks) Difficulties due to satellite motion and atmosphere. Telecom fibre link: Uncertainties far below 1 10-18 Short averaging times ( ~ minutes) Satellite link (TWSTFT, GPS) Paris Telecom fibre link Braunschweig 28

Frequency transfer link across 690 km Ch. Lisdat et al., arxiv:1511.07735 (2015) PTB OP 29

total Allan deviation y ( ) First remote clock comparison Ch. Lisdat et al., arxiv:1511.07735 (2015) 10-15 10-16 10-17 10-18 10-19 1 st campaign 2 nd campaign link 1 10 100 1000 10000 100000 averaging time (s) 3 10-17 precision after 1000 s of averaging. 10 better 10,000 faster 30

total Allan deviation y ( ) First remote clock comparison Ch. Lisdat et al., arxiv:1511.07735 (2015) 10-15 10-16 10-17 10-18 10-19 1 st campaign 2 nd campaign link 1 10 100 1000 10000 100000 averaging time (s) 3 10-17 precision after 1000 s of averaging. 10 better 10,000 faster Uncertainty limited by clocks! Contribution uncertainty (in 10-17 ) systematic, Sr(OP) 4.1 systematic, Sr(PTB) 1.9 statistical 2 fs combs 0.1 link 0.03 gravity potential 0.4 total 5.0 31

total Allan deviation y ( ) Sr PTB / Sr SYRTE 1 First remote clock comparison Ch. Lisdat et al., arxiv:1511.07735 (2015) 10-15 4 10 15 0 4 10 15 10-16 2 10 16 10-17 1 10 16 10-18 10-19 1 st campaign 2 nd campaign link 1 10 100 1000 10000 100000 averaging time (s) 3 10-17 precision after 1000 s of averaging. 10 better 10,000 faster 0 1 10 16 0.2 0.3 85 90 95 100 105 date of measurement (MJD 57092) Agreement within combined uncertainty of clocks (5 10-17 ). First comparison of remote clocks at the 10-17 -level! 32

total Allan deviation y ( ) excitation probability frequency shift (MOT - CF) / Hz Summary 0 Accuracy -1-2 11:00 14:00 17:00 20:00 time 1.0 Instability 0.8 0.6 0.4 0.2 0.0-3 -2-1 0 1 2 3 applied frequency (Hz) 10-15 Applications 10-16 10-17 10-18 More 10-19 1 10 100 1000 10000 100000 averaging time (s) 33

Thank you for your attention. Ali Al-Masoudi Physikalisch-Technische Bundesantalt Working Group 4.32 Optical Lattice Clocks Bundesallee 100 D-38116 Braunschweig Germany phone: +49 531 592-4325 e-mail: ali.al-masoudi@ptb.de web: www.ptb.de 34