High Accuracy Strontium Ion Optical Clock

Transcription

1 High Accuracy Strontium Ion Optical Clock Helen Margolis, Geoff Barwood, Hugh Klein, Guilong Huang, Stephen Lea, Krzysztof Szymaniec and Patrick Gill T&F Club 15 th April 2005

2 Outline Optical frequency standards and optical clocks based on trapped ions Strontium ion trap standard at NPL Results of recent measurements and future prospects

3 A bit of history 50 years ago the definition of the second was based upon the movement of the earth. 1955: First caesium atomic clock produced at NPL, accurate to 1 part in : Caesium clock adopted as the basis for the international definition of time. The second is currently defined as the duration of periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom.

4 The NPL caesium fountain Accuracy (1 ) (with several days averaging time) 1.0 transition probability microwave frequency [Hz] Szymaniec et al. Metrologia (2005)

5 Optical clocks instability f 1 f (S/N) Based on forbidden optical transitions in atoms or ions Frequencies 10 5 times higher than microwave frequencies Q-factor (or even higher) + + Reference (Single trapped ion) Oscillator (Ultra-stable laser) Counter (Femtosecond comb)

6 Trapped ion optical frequency standards or optical clocks Laser-cooled single trapped ion High-Q optical clock transitions (10 15 or higher) Low perturbation environment

7 Quantum jumps short-lived ( 10 ns) strong cooling transition long-lived ( 1 s) weak reference ( clock ) transition Quantum Jumps ground state Fluorescence (photons/second) Time (seconds)

8 Advantages of ion trap based optical standards No 1 st -order Doppler shift (Lamb Dicke regime) Minimum 2 nd -order Doppler shift Field perturbations minimised at trap centre Background collision rate low Electron shelving technique - quantum jumps give high detection efficiency

9 Laser Cooling ħk Laser Mv z h L ~h 0 Atom or ion is Doppler-shifted into resonance k Laser = ω/c= 2π/λ laser For each photon absorption and emission the ion velocity is reduced dv = ħk / M v(thermal) ~ few x 100 metres per sec dv ~ few cm per sec 10 4 scattering events to reach mk level. Laser 0 Frequency Spectral profile for a Doppler-broadened absorption

10 Trapped ion optical clock candidates Ion Transition Linewidth Freq Laboratory Theory Expt uncert Sr nm 2 S 1/2-2 D 5/2 0.4 Hz 70 Hz 1.5 Hz NPL, NRC 199 Hg nm 2 S 1/2-2 D 5/2 1.7 Hz 7 Hz 1.5 Hz * NIST 171 Yb nm 2 S 1/2-2 D 3/2 3 Hz 30 Hz 6 Hz PTB 115 In nm 1 S 0-3 P 0 1 Hz 170 Hz 230 Hz MPQ 171 Yb nm 2 S 1/2-2 F 5/2 0.5 nhz 180 Hz 600 Hz NPL 43 Ca nm 2 S 1/2-2 D 5/ Hz 1 khz - Uibk, CRL 27 Al nm 1 S 0 3 P 0,2 0.5 mhz - - NIST * (unpublished)

11 88 Sr + term scheme 422 nm cooling laser 2 P 1/2 +1/2-1/ nm repumping laser 2 S 1/2 +1/2-1/2 2 D 5/2 674 nm clock transition +3/2 2 +1/2 D 3/2-1/2-3/2 natural linewidth 0.4 Hz m J +5/2 +3/2 +1/2-1/2-3/2-5/2

12 Zeeman structure of the 88 Sr + clock transition 20 m = Number of jumps in 40 Interrogations Laser Frequency (khz)

13 Strontium endcap trap V mm V ac cos t V 2 = 17.8 MHz V ac ~ 260 V V 1, V 2 ~ few V Allows monitoring of ion motion along all three axes via rf-photon correlation 3D micromotion control

14 Experimental arrangement PMT 844 nm extended cavity diode laser KNbO 3 crystal in build-up cavity 422 nm cooling radiation AOM1 Sr + trap 1092 nm DBR diode laser EOM polarization modulator 1092 nm repumper 674 nm probe laser AOM2 674 nm clock laser

15 674 nm probe laser system vibration-isolation platform current supply FM sideband lock to laser PZT APD /4 PBS ULE highfinesse etalon 674 nm extended cavity diode laser optical isolator phase modulator fibre link to femtosecond comb to ion trap PBS AOM /4

16 Probe laser linewidth Number of quantum jumps in 40 interrogations Hz ~50 Hz FWHM (scanning against cavity drift) Offset frequency 100 Hz 100 Hz Broadened to 200 Hz for absolute frequency measurements (probe pulse length 5 ms) Scan across one component of clock transition in 88 Sr + : Number of quantum jumps in 240 interrogations linewidth 70 Hz Frequency offset from line centre (Hz)

17 Locking the probe laser to the clock transition Number of quantum jumps f 1 f 2 f 3 f 4 Servo scheme uses two Zeeman components symmetrically placed about line centre 10 khz 674 nm probe laser frequency Applied correction combines proportional control f = Number of quantum jumps is sampled at four frequencies f 1 to f 4 Error signals N 2 -N 1 and N 4 -N 3 are generated G (N 2 -N 1 ) (N 1 +N 2 ) with feed-forward drift compensation to reduce servo errors

18 Femtosecond optical frequency comb Time domain E(t) 2 t Frequency domain 1 f rep = I(f) f 0 2 f 0 = f rep f rep 0 f n = n f rep + f 0 f

19 Self-referenced optical frequency comb f probe = m f rep f 0 Trapped ion probe laser I(f) Offset frequency f rep Hydrogen-maser (Cs) referenced repetition rate f 0 0 f n 1 f rep + f 0 x 2 2n 1 f rep + 2f 0 n 2 f rep + f 0 beat = f 0 if n 2 = 2n 1

20 Femtosecond optical frequency comb mode-locked Ti:sapphire laser, f rep 88 MHz tilt dispersioncompensating prisms translation 532 nm pump laser microstructure fibre f rep grating f 0 SHG 1060 nm /2 PBS delay line 530 nm PBS /2 grating 88 Sr + probe laser (fibre link) f Sr = m f rep f 0

21 Stability of frequency measurements s counter gate time (Frequency values not corrected for maser offset from 10 MHz) (Measured frequency ) / Hz Time (s) Allan deviation at 10 s Allan deviation 1E-12 1E-13 1E Averaging time (s)

22 Electric quadrupole shift Due to the interaction between the electric quadrupole moment of the 4d 2 D 5/2 state with any residual electric field gradient at the position of the ion. Frequency shift of the 4d 2 D 5/2 state with magnetic quantum number m j is: 35 2 A m 3 cos 2 j 12 1 where A = 3 Q dc (D,5/2) / 10 h = angle between quadrupole field axis and magnetic field Q dc = quadrupole field gradient (D,5/2) = quadrupole moment of 4d 2 D 5/2 state h = Planck s constant Q dc is determined from measurements of the trap secular frequencies and minimized by adjusting the voltages on the outer endcap electrodes. The 4d 2 D 5/2 state quadrupole moment was measured see: G. P. Barwood et al., Phys. Rev. Lett. 93, (2004)

23 Nulling the quadrupole shift Method A: Select a particular pair of Zeeman components Carry out frequency measurements for three mutually orthogonal magnetic field directions Average quadrupole shift is zero 35 2 A m 3 cos 2 j 12 1 Method B: Carry out frequency measurements for three different pairs of Zeeman components, corresponding to m j = 1/2, 3/2, and 5/2 Average quadrupole shift is zero independent of magnetic field direction

24 88 Sr + frequency measurements: method A (Measured frequency ) / Hz April 25 April 29 April 3 May 7 May Date Measurements carried out relative to the NPL caesium fountain Quadrupole shift nulled by measuring in 3 orthogonal B-field directions 6 days of data, statistical uncertainty 1.3 Hz f Sr = (1.9) Hz

25 88 Sr + frequency measurements: method B (Measured frequency ) / Hz July 26 July 27 July 28 July 29 July 30 July 31 July Date Measurements carried out relative to the NPL caesium fountain Quadrupole shift nulled by measuring for 3 different values of m j 5 days of data, statistical uncertainty 1.2 Hz f Sr = (1.6) Hz

26 Uncertainty estimate Source Statistics Quadrupole shift 2 nd order Doppler shift (micromotion) 2 nd order Doppler shift (secular motion) Stark shift (micromotion) Stark shift (secular motion) Blackbody Stark shift 1092 nm ac Stark shift 422 nm ac Stark shift Servo errors Maser reference frequency Gravitational shift Total Method A Shift (Hz) Uncertainty (Hz) < < < Method B Shift (Hz) Uncertainty (Hz) <0.01 < < <

27 Comparison with previous results (Measured frequency ) / Hz NPL (2003) NRC (2003) (1.5) Hz NRC (2004) NPL (2004) NPL (2003): Margolis et al., Phys. Rev. A 67, (2003) NRC (2003): Madej et al., Phys. Rev. A 70, (2004) NRC (2004): Dubé et al., CPEM 2004 book of abstracts NPL (2004): Margolis et al., Science 306, 1355 (2004)

28 Stability Allan deviation Active H-maser Allan Deviation 1.0E E E E E E-17 NPL CsF1, short term NPL CsF1 alternating mode Ion trap projected Hg ion trap NIST NPL Sr ion trap (limited by synthesiser) 1.0E Averaging Time (seconds)

29 674 nm probe laser linewidth improvements Beat between two probe lasers Hz Beat frequency amplitude (arbitrary units) Hz sidebands (mains frequency) Frequency

30 Allan deviation of beat between two probe lasers Relative frequency stability Probe laser stability Averaging time (seconds)

31 Conclusion A measured absolute frequency of f Sr = (1.5) Hz Relative standard uncertainty Within a factor of three of the NPL caesium fountain standard Accurate enough to put forward as a secondary representation of the second

32 What next? Improvements in 422 nm extinction ratio (reduced ac Stark shift) Reductions in probe laser linewidth and drift (reduced servo errors) Additional AOM giving a drift-free source for frequency measurements Second endcap trap to enable trap comparisons Frequency measurements using a second (higher repetition rate) femtosecond comb Our aim: A 88 Sr + optical frequency standard with stability and reproducibility exceeding that of the caesium fountain primary frequency standard

33 With thanks to Witold Chalupczak and Dale Henderson (Cs fountain) John Davis, Peter Stacey and Peter Whibberley (masers and NPL timescale) Neil Moore (electronics support) Fiona Auty (media coverage) and other members of the Time and Quantum Detection Team

34 Applications of atomic frequency standards Realisation of SI units Time and length Fundamental physics Tests of QED, general relativity Measurements of fundamental constants Laboratory searches for time-variation of fundamental constants Satellite navigation and ranging GPS, Galileo and deep space Telecommunications Astronomy and survey Gravity wave detection Star and planetary survey using very deep baseline interferometry

35 Optical clock Science (3 August 2001)