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1 Patrick Gill Geoff Barwood, Hugh Klein, Kazu Hosaka, Guilong Huang, Stephen Lea, Helen Margolis, Krzysztof Szymaniec, Stephen Webster, Adrian Stannard & Barney Walton National Physical Laboratory, UK Advances in Precision Tests & Experimental Gravitatition in Space Galileo Galilei Institute, Arcetri, Firenze 28 th Sept 2006
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3 # $ Frequency ~ 10 5 times higher Linewidth determined by interrogation time (limited either by natural decay or probe interaction time) better stability in optical v N T int τ : Frequency of clock transition : Number of atoms / ions : Ramsey interrogation time : Sampling time Allan Deviation Frequency Instability: σ ( τ) = Cs fountain (9.2 GHz) Yb + ion (642 THz) 2πv Sr + ion (445 THz) Hour Day Month int τ τ [sec] Assuming: Cs fountain: T int = 1 sec Sr + ion: T int = 0.4 sec Yb + ion: T int = 10 sec 1 NT Cs fountain (9.2 GHz)
4 1.0E E-10 Essen's Cs clock iodine-stabilised HeNe Fractional uncertainty 1.0E E E E E E-16 Cs redefinition of the second Microwave atomic clocks Optical frequency standards H Hg +,Yb +,Ca Cs fountain clocks Year H Ca H fs combs Sr + Yb + Hg +
5 #% & & '(( ) $ *! ++ *! ',' -" *!./ *! * * &! $!! -"!) $ 0" 1 2 0" 1
6 Femto-second Comb comparison L-S Ma et al, Science 2004 Uncertainty between combs locked to the same optical reference: 1.4 x 10-19
7 # Single cold trapped ion (atomic reference) Ultra-stable probe laser (local oscillator) 191 Hg +, 88 Sr +, 171 Yb +, 40 Ca +, 115 In +, 27 Al + Femtosecond comb (counter) Optical clocks future redefinition of the second? Fundamental constants and tests of physics Satellite ground station clocks? Future satellite navigation and ranging??
8 # Trapped ion optical clock natural linewidths & frequency uncertainties Ion λ Transition Theory Expt Freq uncert. Laboratory Hg nm 2 S 1/2-2 D 5/ Hz Hz 7 Hz Hz NIST 88 Sr nm 2 S 1/2-2 D 5/2 0.4 Hz 9 Hz, 5Hz Hz NPL, NRC 171 Yb nm 2 S 1/2-2 D 3/2 3 3 Hz Hz 10 Hz Hz Hz PTB 40 Ca nm 2 S 1/2-2 D 5/ Hz 1 khz - - UIBK, CRL 115 In nm 1 S 0-3 P Hz Hz 170 Hz 230 Hz MPQ/Erlangen 171 Yb nm 2 S 1/2-2 F 5/2 0.5 nhz 180 Hz 600 Hz NPL 27 Al nm 1 S 0 3 P 0 8 mhz 20 Hz - - NIST
9 '(( ) $ * $!4 # ) ~ 40 Hz T probe = 20 ms ~ 6.5 Hz Atomic line ~ 1.8 Hz State detection by electron shelving Small blackbody shift static quadrupole shift can be minimized f 282 (Hz) T probe = 120 ms
10 * 5) $ * 6 3 $ seconds of data τ -1/2 Hg vs Maser (AVAR) Hg vs Al (AVAR) Hg vs Al (THEO1) ν/ ν x time [seconds]
11 '(( ) $ * "$ Effect Parameter Hg + shift [ x ] Hg + Uncert [ x ] Blackbody shift Micromotion 2 nd order Doppler Micromotion AC Stark Operating temperature RF field RF field negligible Negligible Secular 2 nd order Doppler Secular temperature nd order Zeeman magnetic field AC Zeeman RMS field AOM phase chirp Drive power Background gas collisions Collision period Total
12 -" * $789/ 0#31 Chr. Tamm, D. Engelke, V. Bühner, Phys. Rev. A 61, (2000)
13 ',' -" * & 2: " Quantum jump probability τ(pulse) = 90 ms 2 τ(yb + ) Hz Detuning at nm (Hz) σ y of difference frequency 4x x x x x x10-16 #: 7" E. Peik, T. Schneider, Chr. Tamm, T [s] J. Phys. B: At. Mol. Opt. Phys 39,145 (2006) #:7 ;; 1,2,3: systems of orthogonal axes
14 ++ * 2 P 3/2 422 nm cooling laser 2 +1/2 P 1/2-1/ nm repumping laser 2 D 5/2 674 nm clock transition (natural linewidth 0.4 Hz) Number of jumps in 40 Interrogations m J +5/2 +3/2 +1/2-1/2-3/2-5/2 +3/2 2 +1/2 D 3/2-1/2-3/ m = Laser Frequency (khz) +1/2 2 S 1/2-1/2 0.4 s lifetime, no HFS but linear Zeeman shift
15 PMT 844 nm extended cavity diode laser 1092 nm DBR diode laser 674 nm probe laser 422 nm cooling radiation KNbO 3 crystal AOM1 in build-up cavity Sr + trap 1092 nm repumper EOM polarization modulator 674 nm clock laser AOM2 > : 1033 nm EC diode laser 7 vibration-isolation platform /,8 " ": & < ') =0'7 1 <?) =09@ 1 current supply 674 nm extended cavity diode laser FM sideband lock to laser PZT APD fibre link optical isolator phase modulator to femtosecond comb λ/4 ULE highfinesse etalon AOM
16 3 ": : /,8 " 3s averaging time Relative Frequency Stability drift ~ 0.2 Hz s Frequency (Hz) 2 Hz 30 s averaging time, drift compensation 0.2 Hz s Averaging Time (s) 6.2 Hz Linewidth probably limited by vertical vibrations Frequency (Hz) Frequency (Hz)
17 ++ * /,8 : 0.16 m J = 1/2 m J = 1/2 Zeeman component Probe pulse length: 100ms Frequency step width: 2 Hz 0.2 Hz s -1 drift compensated 4 separate scans combined Transition probability Fitted τ = 107(5) ms corresponds to 8.3 Hz linewidth Frequency (Hz) Consistent with Fourier-transform-limited linewidth of 9 Hz.
18 4 $ ++ * & " Due to interaction between electric quadrupole moment of 4d 2 D 5/2 state and residual electric field gradient at position of ion. Frequency shift of 4d 2 D 5/2 state with magnetic quantum number m j is: ν = Q 10h quadrupole field gradient dc m j 35 Θ( D,5/ 2) 12 quadrupole moment of 4d 2 D 5/2 state ( 3 cos β 1) Measure frequencies of pair of Zeeman components in 3 orthogonal magnetic field directions Average EQS = 0 (NIST) angle between quadrupole field axis & magnetic field Measure frequencies of 3 pairs of Zeeman components m j = 1/2, 3/2, & 5/2 Average EQS = 0 independent of field direction (NRC) f Sr+ = (1.5) Hz Margolis et al., Science 306, 1355 (2004)
19 A ++ * Second order Doppler shifts: due to residual thermal motion (ω/2π ~ 1-2 MHz) and micromotion (Ω/2π ~ 15 MHz) ν T ~ (ω x a / 2c) 2 ν M ~ (Ω x a / 2c) 2 Zeeman Shifts: for T ~ 1 mk for micromotion well-minimised in 3D Linear Zeeman ν z ~ Hz nt -1 for m = 0 components need symmetrical component averaging and mu-metal shielding for typical 1 µt field and few nt noise Quadratic Zeeman ν z ~ 5.6 µhz µt -2 (for m = 0) 6 µhz Blackbody shift ν BBz ~ 40 µhz for BB room temp field of 7 µt 2
20 A* Stark shifts: Micromotion- and thermal-induced interaction with time-averaged fields (eg patch fields) ~ few mhz (10-17 ) with well-minimised micromotion Blackbody Stark shift (relative to 0 K) due to room temp apparatus ~ 300 mhz (6 x ) large due to T 4 temp dependence, but essentially constant 1 K reproducibility of T(apparatus) 10 mhz (2 x ) also large uncertainty (+30 %) for Stark coefficients need better values AC Stark shifts: off-resonant interactions of probe (and other cooling / clear-out) light with coupled transitions out of upper & lower levels of clock transition 422 nm cooling & 1092 nm clear-out not a problem if fully switched off from ion during probe interrogation period 674 nm probe light Stark coefficient: ~ 0.5 mhz (Wm -2 ) ~ 0.15 mhz (<10-18 ) for 30 nw in 300 µm
21 4 Response to vertical acceleration 250 response / (mhz / micro g) z coordinate of support / mm ++ * /,8 & # 0$: '(( ) $ *! ',' -" * +, 1 B : "7) = " " 7 ".7 " ""
22 ++ * C "D Quantum limited stability for probe times ~ 0.4 s natural decay 6 x τ -1/2 Feed-forward compensation of 0.2 Hz s -1 (5x10-16 s -1 ) ULE cavity drift Black-body Stark shift uncertainty for 1K temp rise 2 x Long single ion storage times possible All-diode-laser driven 1092 nm repumper: DFB now 1033 nm fast clear-out 844 nm cooling ECDL now, DFB? E @'? 7.@.? D1
23 Spectroscopy of 27 Al + 1 P 1 27 Al + I=5/2 3 P 2 1 mhz? 8 mhz linewidth clock transition minimal static quadrupole shift smallest known room temperature blackbody shift no accessible strong transition λ = 167 nm cooling transition? 266 nm 3 P 1 ~ 3 khz 267 nm 3 P nm, ν ~ 8 mhz use 9 Be + for cooling, state preparation & readout RF 1 S 0 Be CE Al D.J. Wineland et. al.,proc. 6th Symp. on Freq Stds and Metrology, EC linear Paul Trap
24 27 Al + Optical Clock I(f) 1070 nm 1070 nm fiber laser 2 W AOM x2 AOM nm line width < 2 Hz x2 Femto-second comb S. Diddams et al. Frequency Counter 200 khz BW 0.1 Hz BW ULE cavity (vibration insensitive) sensitive) x2 x2 Ion trap 534 nm dye laser line width < 5 khz 3 dye lasers (626 nm))
25 4 2 ) =7: F "! : F 9 ' " 09,@ ) =1 $09@ ) =1 2$$ ""! ": D ">$% " :! G '$ 20H.@@'1 9 7$: 2$7$$ : "7λ $ 2$! ' 02 "7 $ 1 ' ) : : 0$1 Optical lattice trapping sites
26 4 2 0-") $ 1!" # $ %&! ' ( ) ((! ( & *!!( & (! &(( +,!( & -(( - &. '.!!(- / λ0 %! & - 1 %! &-
27 & Cold atom optical clock linewidths ( ν ν) & uncertainties Atom λ nm Transition ν (Hz) Absol. Freq Laboratory Theory Expt Uncert. (Hz) Mg 457 nm 1 S 0 3 P Hannover Ca 657 nm 1 S 0 3 P Hz PTB, NIST Sr 698 nm 1 S 0 3 P JILA, 5 Hz Tokyo, SYRTE, PTB Firenze Yb 551 nm 1 S 0 3 P NIST, KRISS Duesseldorf
28 & (! & & System Studied at Value / Hz Relative uncertainty 199 Hg + NIST x Sr + NPL, NRC x Yb + PTB x Sr NMIJ / Toyko, JILA, LNE-SYRTE, PTB, Firenze, (NPL, NRC) x * * included: (4) Hz Tokyo (5.3) Hz SYRTE (4.5) Hz JILA
29 Comparisons of optical standards for fine structure constant variation with time optical caesium MPQ NIST PTB 1 H(2γ) 199 Hg + (E2) 171 Yb + (E2) ln t ln t ln t f f f (H) (Hg + (Yb = + ) ) 1 ( ) ± year = = 1 ( ) ± year SYRTE FOM NIST-F1 1 ( ) ± year PTB-CsF1 Time transfer
30 ',' -" * & 77 α7 Two optical frequency standards in one ion 4f 14 6p 2 P 1/2 369 nm dipole (E1) 4f 14 6s 2 S 1/2 4f 14 5d 2 D 3/2 436 nm quadrupole (E2) 467 nm octupole (E3) 4f 13 6s 2 2 F 7/2 rejection of common mode systematic uncertainties projected uncertainty: α α ν/ν < ν ν after 1 year: ~ year 1
31 # : &! 8 (-& 9: (! 1,!( ). ( & ---,, ( &((- % ; <. &!( (! ( && 8 &!!&(( &( &.!
32 : : $ D =. & %.,>? *>A9- &. (-! 6 B (- & <& - % C7)D* *,%! 8 %!1= : =*+ 9((, ( 9# E9+ E9&C- F -( ) &,(- - &&> --B,9-!%-. - &!. > =,> # %
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