Optical Clocks. Tanja E. Mehlstäubler. Physikalisch-Technische Bundesanstalt & Center for Quantum Engineering and Space Time Research

Transcription

1 Optical Clocks Physikalisch-Technische Bundesanstalt & Center for Quantum Engineering and Space Time Research

2 QUEST at PTB Experimental Quantum Metrology Head of Group: Piet O. Schmidt Quantum Sensors with Cold Ions Head of Group: Sub-Hz lasers and high performance cavities Project Leader: Thomas Kessler Task Groups: Variations of Fundamental Constants, Transportable Ultra-Stable Clocks

3 Outline Definition and Measurement of Time Time and Frequency Metrology Ingredients of an Optical Clock - Today s State of the Art - Natural Reference - Candidates - Atom/Ion Traps - Local Oscillator - Frequency Comb Applications and Future Developments

4 Definition and Measurement of Time Greenwich Mean Time - global standard since s = 1 / of the mean solar day Mechanical Clocks Δt ~ 1 s/d

5 Definition and Measurement of Time Greenwich Mean Time - global standard since s = 1 / of the mean solar day Mechanical Clocks Δt ~ 1 s/d Quartz Clocks (f res ~ MHz) s: Δt ~ 1 ms /d Scheibe and Adelsberger, PTR Berlin

6 Definition and Measurement of Time Greenwich Mean Time - global standard since s = 1 / of the mean solar day Mechanical Clocks Δt ~ 1 s/d Ephemeris Time - adopted by the CGPM in s = 1 / 31,556, of the tropical year of 0. January 1900 at 12 h UT Quartz Clocks (f res ~ MHz) s: Δt ~ 1 ms /d Atomic Cs-Clocks (f res = 9.2 GHz) 1955 Essen s clock: Δt ~ 10 µs /d today: Δt < 1 ns /d

7 Definition and Measurement of Time Greenwich Mean Time - global standard since s = 1 / of the mean solar day Mechanical Clocks Δt ~ 1 s/d Ephemeris Time - adopted by the CGPM in s = 1 / 31,556, of the tropical year of 0. January 1900 at 12 h UT Quartz Clocks (f res ~ MHz) s: Δt ~ 1 ms /d TAI (Temps Atomique International) - since 1967 Duration of periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the 133 Cs atom Atomic Cs-Clocks (f res = 9.2 GHz) 1955 Essen s clock: Δt ~ 10 µs /d today: Δt < 1 ns /d

8 Definition and Measurement of Time Mechanical Clocks Δt ~ 1 s/d Quartz Clocks (f res ~ MHz) s: Δt ~ 1 ms /d Atomic Cs-Clocks (f res = 9.2 GHz) 1955 Essen s clock: Δt ~ 10 µs /d today: Δt < 1 ns /d Optical Clocks (f res ~ 1000 THz)

9 Clock Operation (optical) Trapped ion or atoms (long term reference) Local Oscillator to Cs-fountain or 2nd optical clock Frequency Comb f ~ 1000 THz Laser Fluorescence signal 10 Hz linewidth Frequency detuning ULE cavity (Flywheel)

10 Time & Frequency Metrology

11 Uncertainty of Quantities in today s Metrology Chemistry, Biology Voltage, Resistance, Capacity, Mass, Length, Time & Frequency Optical Clocks from BIPM Summer School of Metrology 2007

12 Time and Frequency Metrology Frequency Stability Frequency Accuracy δν/ν 0 ν 0 ν 0 Time Time Example: Zielscheiben aus Riehle??? Riehle: Frequency Measurements (2004)

13 Allan variance Fractional frequency instability as a function of averaging time τ Fractional frequency: y = f ( t) f 0 f 0 σ 1 2 ( y y ) 2 2 y ( τ ) = i 1 i where t + τ i 1 y = i y( t) dt τ t i

14 Allan variance Fractional frequency instability as a function of averaging time τ Fractional frequency: y = f ( t) f 0 f 0 1 Tc σ y ( τ ) = S K Q τ N 1/ 2 quality factor: ν Q = 0 Δν

15 Allan variance Fractional frequency instability as a function of averaging time τ Fractional frequency: y = f ( t) f 0 f 0 1d Stability needed to measure ν 0 with this precision BUT: Is it accurate?

16 Accuracy / Systematic Errors Sytematic Shifts can be due to: Example 1e - atom: S = 1/2 nuclear spin: I = 1/2 2 P 3/2 2 P 1/2. Magnetic Fields Electric Fields / Blackbody radiation Collisions Doppler shifts Lock servo errors e.g. 121 nm in H (= THz) F = 1-1, 0, 1 = m F 2 S 1/2 ~ GHz spin - orbit coupling (fine-structure) J = L ± S F = 0 HF-structure F = I ± J 0 magnetic sublevels

17 Improvement through Optical Clocks Accuracy Δν/ν 0 Systematic shifts proportional to ν 0 : Systematic shifts with absolute order of magnitude: 1st and 2nd order Doppler shift 1st and 2nd order Zeemann shift, Stark shifts (blackbody, light shift, etc ) Stability Allan Standard Deviation: σ = 1 π S / N 1 Q Tc τ with ν Q = 0 Δν quality factor of transition ν 0 = Hz ν 0 ~ Hz

18 Ingredients of an Optical Clock

19 (A) Suitable Atoms

20 Atomic Transitions 4(2πυ0) γ ( e g) = 3 3c α e d forbidden transitions 3 g Example 199 Hg + But how to detect γ ~ 2 Hz Quantum Jumps (e - - shelving) fluorescence time

21 Atomic Transitions 1e - Systems 2e - Systems 199 Hg +, 171 Yb +, etc 87 Sr, 27 Al +, 115 In + 1 P 1 γ ~ 20 MHz Ion Clocks Neutral Atom Clocks γ ~ mhz 3 P 0 Clock Laser 698 nm 1 S 0

22 Clocks

23 (B) Atom / Ion Traps

24 Laser Cooling of Atoms Nobel price 1997 "for development of methods to cool and trap atoms with laser light" Steven Chu Claude Cohen- Tannoudji William D. Phillips

25 Laser Cooling of Atoms Doppler cooling: red detuned laser beams on strong transition γ ~ 1-80 MHz laser v laser 1000 K K T temperature scale of laser cooling atomic beam v ~ 700 m/s 300 K: room temperature v ~ some 100 m/s Doppler cooling: mk T Dopp ~1 mk v ~ 1 m/s µk sub-doppler-cooling: v ~ 1 cm/s nk Evaporation

26 Optical Dipole Traps for Neutral Atoms Laser light distorts atomic energy levels loading of Sr atoms into 1D lattice Trap Depth ~ 50 µk

27 The Optical Lattice Clock magic wavelength (*) ground and excited state experience same Stark shift (*) Takamoto et al., Nature 435, 321 (2005)

28 The Optical Lattice Clock Stark-Shift of 1 S 0 and 3 P 1,0 magic wavelength (*) ground and excited state experience same Stark shift (*) Takamoto et al., Nature 435, 321 (2005)

29 Ion Traps Paul trap endcap trap single Yb + -ion

30 Ion Traps Charged ions interact strongly with environment trap with electric fields? BUT: Non-Trapping Theorem φ = r E r = ρ = ε 0 0 Trap Depth ~ 10 4 K Ψ = e 2 E 4mΩ Ponderomotive Potential 2 2 credit: W. Lange

31 Ion versus Neutral Atom Clocks Optical Lattice Clocks with Neutrals atoms: high S/N collisions short servo times higher order effects in lattice high stability polarization dependence of lattice nm ν sec Single Ion Optical Clocks ions are trapped in minimum of EM-field high level control of single ion no collisions storage times up to days/months limited short term stability higher need for ultra-stable laser

32 Today s State of the Art Comparison of 2 ion clocks ( 27 Al + / 27 Al + ): inaccuracy = stability σ ~ in 1s Best resolved atomic resonance ( 87 Sr): Chou et al., PRL 104, (2010) NIST and now at PTB (see P. Schmidt s talk) Sr/Ca comparison (JILA/NIST): inaccuracy = stability ~ in 1s Paris, Boulder, Tokyo, Braunschweig, London, Florence, Moscow, A. Ludlow et al. Science 319, 1805 (2008)

33 (C) Local Oscillator

34 The Reference Cavity Ultra-low expansion (ULE) glass: - Coefficient of thermal expansion < 20 ppb/k - Zero crossing close to room temperature Spacer: 10 cm length Optically contacted mirrors with Finesse F > 100,000 Linewidth: Δf = FSR/ F ~ 15 khz

35 The Reference Cavity Ultra-low expansion (ULE) glass: - Coefficient of thermal expansion < 20 ppb/k - Zero crossing close to room temperature Spacer: 10 cm length 1 Hz laser width: σ ν /ν 0 = σ L = m Optically contacted mirrors with Finesse F > 100,000

36 Cavity Designs Thermal Noise PTB horizontally mounted cavity Nazarova et al. Vibration-insensitive reference cavity for an ultra-narrowlinewidth laser Appl. Phys. B 83, 531 (2006) calculation Th. Legero, PTB JILA vertical cavity Notcutt et al. Compact, thermal-noise-limited optical cavity for diode laser stabilization at 1x10-15 Optics Lett. 32, 641 (2007) NPL cut-out cavity Webster et al. Vibration insensitive optical cavity PRA 75, (R) (2007)

37 Sub-Hz Lasers? QUEST RP Reduction of thermal noise in high performance optical reference cavities Silicon as resonator material Alternative mirror concepts Material Q T 0 (K) dα/dt (K -2 ) Opt. transp Si IR Si ULE VIS

38 Sub-Hz Lasers? QUEST RP Reduction of thermal noise in high performance optical reference cavities Silicon as resonator material Alternative mirror concepts σ y thermal noise (120 K) Ca master laser 1 μg/sqrt(hz) Seismic noise 20 khz/g sensitivity /s drift τ (s)

39 Experimental Setup

40 (D) Frequency Combs

41 Optical Frequency Combs Nobel price 2005 "for their contributions to the development of laser-based precision spectroscopy, including the optical frequency comb technique" John L. Hall Theodor W. Hänsch

42 Optical Frequency Combs Mode locked Ti:Sapphire or Er-Fiber Lasers pulse duration 1-10 fs f rep = 100 MHz 1 GHz

43 Optical Frequency Combs f probe = m f rep ± f 0 ± f beat m measured with wavemeter f rep locked to Cs-fountain f 0 by beating ground & 2nd harmonic

44 Optical Frequency Combs Required accuracy and stability for optical clock comparison has been demonstrated! Ma et al., IEEE J. Quant. Electron. 43, 139 (2007)

45 Optical Frequency Combs

46 Applications and Future Developments

47 Clocks and Navigation Optical Clock in Ground Stations: Deep space missions Master Clock in Space: GNSS - improved location resolution - integrity of space segment, smaller prediction errors Simulations by Institute of Communications & Navigation (DLR) ESA study contract 19837/06/F/VS

48 Clocks and Navigation 1997: Lift-off of Cassini - Huygens probe Saturn (2004) 4 Swingbys near Venus, Jupiter, Earth at 300 km distance Required accuracy: ±25 km

49 Are fundamental constants really constant? TG 4 Equivalence Principle: fundamental constants need to be constant in time Reinhold et al., PRL 96, (2006) Murphy et al., Mon. Not. R. Astron. Soc. 345, 609 (2003)

50 Laboratory Tests TG 4 Al + /Hg + Hg + Yb + Present status: Dzuba et al. PRL 82 (1999) Al+/Hg+: T. Rosenband et al., Science 319, 1808 (2008) lnα = ( 2.4 ± 2.7) 10 t ln Ry = (0.0 ± 3.2) 10 t yr yr 1-1

51 Gravitational Redshift Shift of clock transition: Z Δυ = υ ΔU c ( 1+ ε ) 2 non-zero if local position invariance doesn t hold ε tested to be < Einstein Gravity Explorer (EGE) could provide test at the level Schiller, Tino, Gill, Salomon et al. (2007)

52 Geodesy at Direct measurement of earth s geopotential Current uncertainty: cm resolve height difference of 1 cm Tracking tectonic plate movement 2-20 cm/yr Δv ~ 1 cm/yr

53 Future Challenges Reliability (compact, portable clocks) Non destructive detection in optical lattice Can we use more than one ion? new ion trap designs Entangled atoms / ions? Quantum logic clocks Δ υ Quad E Θ = 0 linear trap

54 Scalable Chip Traps Laser cutting with pulsed 10ns tripled YAG at 355nm Low RF-loss AlN / sapphire wafer Au, Nb, Mo metalization First test with ns-pulsed YAG-laser at PTB l = 40mm l = 20mm onboard filtering mounted on compact chip carrier

55 First Prototype (Rogers 4350B) laser cut electrodes low pass 110 Hz stack of glued PC boards with laser cut electrodes onboard RF-filtering with soldered SMD parts, connection of DC-electrodes via bonding of 30µm Au wire

56 Ions in Chip Trap Coulomb crystals of ytterbium-172 ions:

57 Ions in Chip Trap

58 Optical Clock Groups at PTB: T.E.M. Jonas Keller Norbert Herschbach David Meier Karsten Pyka Uwe Sterr Christian Tamm Piet Schmidt Ekkehard Peik