Optical Clocks and Tests of Fundamental Principles

Transcription

1 Les Houches, Ultracold Atoms and Precision Measurements 2014 Optical Clocks and Tests of Fundamental Principles Ekkehard Peik Physikalisch-Technische Bundesanstalt Time and Frequency Department Braunschweig, Germany

2 Physikalisch-Technische Bundesanstalt: the National Metrology Institute of Germany Metrology: The science of measurement with applications for science, technology, economy, society Metrology Meteorology

3 Clock Hall in Kopfermann-Building of PTB, Braunschweig Legal time for Germany 4 primary caesium clocks Time distribution via long-wave radio DCF77 / internet / telephone Time transfer via satellites for international atomic time scales TAI and UTC Caesium fountain clocks Optical clocks with trapped ions Optical frequency measurements

4 Outline of the Lectures 1.Introduction to atomic clocks 2.Optical clocks with laser-cooled trapped atoms and ions 3.Clocks and relativity

5 Recommended literature: Review article: Optical Atomic Clocks A. D. Ludlow, M. M. Boyd, Jun Ye, E. Peik, P. O. Schmidt arxiv Modern Textbook: C. Audoin, B. Guinot: The Measurement of Time, Cambridge Univ. Press General publications on Time and Frequency from NIST: PTB: General reading (from NIST): J. Jespersen, J. Fitz-Randolph: From Sundials to Atomic clocks

6 Atomic Clocks Principles Clock characteristics Microwave and optical clocks

7 A Brief History of Atomic Time James Clerk Maxwell, 1870: If, then, we wish to obtain standards of length, time, and mass which shall be absolutely permanent, we must seek them not in the dimensions, or the motion, or the mass of our planet, but in the wave-length, the period of vibration, and the absolute mass of these imperishable and unalterable and perfectly similar molecules. Postulate: Atomic energies are natural constants and do not depend on space or time (apart from relativistic effects). (Einstein s Equivalence Principle) 1955: Cs beam clock, Essen and Parry, NPL : Measurement of Cs frequency in terms of the ephemeris second ν= (20) Hz (NPL and USNO) 1967: Definition: The second is 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.

8 Improvement in the Accuracy of Clocks ν /s Optical clocks ν /s ν 10 4 /s ν 1/s from: C. Audoin, B. Guinot: The Measurement of Time

9 Uncertainties in the Realization of the SI Base Units Second 3*10-16 Meter (definition linked to the second) Kilogramm 0 (for prototype, 10-9 for comparisons) Ampere 4*10-8 Kelvin 3*10-7 Candela 10-4 Mol 8*10-8

10 Principle of Atomic Clocks Absorber (ions, atoms, molecules) Atome, Moleküle oder Ionen ν out Oszillator oscillator ν Optical clockwork: femtosecond laser ν 0 Regelungselektronik servo - electronics Detektor detector S ν 0 ν Absorptions- absorption signal signal Fehlersignal error ds dν ν 0 ν

11 Caesium Clocks

12 Caesium Beam Clock with Magnetic State Selection Oven at T 100 o C Magnetic dipole for state selection (Stern-Gerlach configuration) Ramsey interaction region with homogeneous magnetic field. flop-in detection of atoms that have made the hyperfine transition Detection via surface ionsation of caesium

13 Magnetic State Selection In the Paschen-Back region: (F=4,m F =0) atoms are magnetic low-field seekers (F=3,m F =0) atoms are magnetic high-field seekers A lens based on magnetic field gradients (e.g. a hexapole) will focus low-field seekers and defocus high-field seekers.

14 Rabi- and Ramsey-Excitation 2-level system with pulsed excitation. χ: res. Rabi frequency, δ: detuning Excitation probability after the pulse P 2 = (quadatic Fourier transform of the pulse) 1 Pulse (Rabi) P 2 = 2 Pulses (Ramsey)

15 Advantages of Ramsey excitation about 0,5x narrower resonance for the same interaction time Resonance not broadened by perturbations between the interaction zones (like B field inhomogeneity) Influence of the velocity distribution: leads to a distribution in T Central peak: δ=0, therefore δt=0, independent of v Further peaks: phase δt=nπ, will be washed out

16 The Caesium Fountain Early fountain experiments: 1953 Zacharias, MIT (hot Cs, failed) 1989 Chu, Stanford (cold Na) 1991 ENS/LPTF (cold Cs) Use laser cooled atoms instead of a thermal atomic beam PTB s fountain clock CSF1 (1999)

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18 Ramsey fringes in a caesium fountain Instability: a few in 1 s Accuracy: a few (requires 3 days of averaging; central fringe split by factor 10 6 ) Dominant systematic shifts from: Cs-Cs cold collisions, cavity phase shift

19 The most important specifications of a clock: Stability and Accuracy bad! problematic: long measuring time, Long evaluation NI tutorial Useful reference if calibrated e.g. hydrogen maser ideal: Primary clock, agrees with an unperturbed reference value

20 Stability analysis using the Allan Deviation - Perform sequence of frequency measurements over time interval τ - Calculate normalized frequencies y k - Calculate variance of differences y k+1 -y k, Allan variance σ y 2 (two-sample variance, named after David Allan, NIST, avoids divergences for drifting sources) - produce double-log plot of σ y (τ) -Slope ρ indicates spectral shape of dominant noise sources

21 Stability analysis using the Allan Deviation -Slope ρ indicates spectral shape of dominant noise sources (Atom) Shot noise, E.g. thermal, 1/f noise Good atomic clock: averages down σ y (τ) like 1/τ 1/2 until it hits the flicker floor

22 Typical Allan deviation curves Commercial Rb Commercial Cs (5071A) CS1 vs. CS2 (8 years) Passive H maser Active H maser Cs fountains (CSF1, FO-2) Sr lattice clock

23 Stability of atomic frequency standards microwave optical frequency ν 0 increases by 5 orders of magnitude An optical single-ion frequency standard with ν=1 Hz provides higher stability than a caesium fountain clock with 10 6 atoms.

24 Measuring population of a two-level system in a single atom yields a random sequence of values 0 and 1 (state projection) Variance for a measurement with N atoms:

25 Optical Frequency Standard / Optical Clock Atomic Reference forbidden transition of atoms in a laser-cooled, trapped sample in the Lamb-Dicke regime Laser locked to atomic resonance, short-term stabilized to passive Fabry-Perot cavity fs-comb Generator optical clockwork, provides radiofrequency output and means for comparison with other optical frequencies

26 Forbidden transitions as reference transitions for the clock Forbidden : based on the selection rules for electric dipole radioation. Photon carries angular momentum: L=1, 2, 3, (not 0!) Atomic electron makes transition: J J J J L J + J L=1 dipole radiation J=0, ±1, not 0 0 L=2 quadrupole radiation J=0, ±1, ±2 not 0 0 L=3 octupole radiation J=0, ±1, ±2, ±3 not 0 0 Etc. An indication on the radiative lifetime of excited states: Power emitted by an antenna of size r in multipole order L: A EL ω (r/λ) 2L r/λ for visible light Dipole decay: nano microseconds Quadrupole: milliseconds seconds Octupole: hours months

27 The Lamb-Dicke Regime R. H. Dicke, Phys. Rev. 89, 472 (1953) The linear Doppler shift may be suppressed if the motion of the emitting or absorbing atom is restrained to a region of size <λ Doppler and recoil free line Emission spectrum of an atom in a box Doppler shift of the free atom Reaching the Lamb-Dicke regime is a prerequisite for a precise atomic clock. It is relatively easy for microwaves, but harder for an optical clock.

28 Heterodyne detection of Fluorescence in a 1D lattice Lamb-Dicke Regime, Transitions between vibrational levels

29 σ+σ : Lamb-Dicke confinement, but no lattice structure

30 Sideband - Strengths Classical harmonic oscillator: Frequency modulated spectrum (via the Doppler effect), Modulation index: kx Bessel functions Lamb-Dicke condition, carrier dominates Quantum harm. Osc.: Lamb-Dicke condition: Emission spectrum in the LD limit: carrier dominates, high frequency sideband vanishes for n 0

31 Lamb-Dicke confinement: recoil-free absorption and emission Harmonic oscillator ground state extension Lamb-Dicke condition for the ground state Recoil energy < 1 oscillator quantum Resonant scattering is elastic and recoil free. But: random momentum transfer is possible in non-resonant scattering events. Close to <n>=0: absorption and emission spectrum are different!

32 After Doppler cooling after sideband cooling Transitions: (A) Doppler cooling (B) Sideband cooling (C) Quench <n>=0.051(12) T=47(3) µk

33 Two systems for optical clocks with atoms in traps Optical lattice with neutral atoms Single ion in an ion trap Optical lattice: Dipole trap at the magic wavelength ~10 6 atoms interrogated simultaneously Storage with minimal perturbation from the trap potential unlimited observation time one ion: no collisional shift g T 2 = 6 ms 8 ms 10 ms 12 ms 14 ms 16 ms Absorption images of trapped Sr atoms and of an expanding cloud of free atoms 5 Yb + Ions

34 Optical clock with trapped neutral atoms Problem for neutral atoms: Trap shifts energy levels. Possible solution: Optical lattice of dipole traps with magic detuning, so that both levels of the reference transition shift by the same amount. (Hidetoshi Katori, 2001) E see: T. Ido, H. Katori, Phys. Rev. Lett. 91, (2003) x

35 The magic wavelength

36 Light shift as a function of the lattice wavlength (Sr clock, SYRTE group Paris) A. Brusch et al. PRL 96, (2006)

37 J=0 0 forbidden in all multipole orders, because of conservation of angular momentum. States with J=0: two-electron systems: Mg, Sr Al +, In + etc. 1 S 0 3 P 0 : favorable reference transition because both states possess high symmetry and are not easily polarized by external E fields (original proposal by H. Dehmelt) J=0 0: (weak) electric dipole transition is possible under loss of rotational symmetry, e.g. from a magnetic field: Internal (nuclear spin, hyperfine interaction) or external field mixes states with different J.

38 Two types of lattice clocks: Fermionic isotopes with: half-integer nuclear spin (e.g. 87 Sr) J=0 0: transition induced by hyperfine mixing Collisions (s-wave) suppressed even in 1D lattice with many atoms per site Problem: no m F =0 component (small linear Zeeman shift) Bosonic isotopes without nuclear spin (e.g. 88 Sr) J=0 0: transition induced by external magnetic field Collisions suppressed in 3D lattice with one atom per site Problem: quadratic Zeeman shift from strong external field

39 Optical clocks with trapped ions Paul traps Principle of operation of a single-ion clock Systematic frequency shifts, uncertainty budget Example: Yb +

40 Optical Clock with a Single Laser-Cooled Ion in a Paul Trap The spectroscopist s ideal: an isolated atom at rest in free space Lamb-Dicke confinement with small trap shifts unlimited interaction time no collisions ~ Quadrupole Electrodes Very low uncertainty is possible (to ) proposed by Hans Dehmelt 1975 Experiments with Hg +, Al + (NIST), Yb + (PTB, NPL), In + (U Wash.,NICT), Sr + (NRC, NPL), Ba +, Ca + (Innsbruck, Marseille),...

41 Physics Nobel Laureates from 1989 Hans Dehmelt Wolfgang Paul Norman Ramsey Single electrons and positrons in Penning trap Laser cooling Single-ion optical clock Quadrupole mass spectrometer Paul trap Ramsey spectroscopy Microwave atomic clocks Hydrogen maser

42 The Paul Trap storage in an oscillating quadrupole field

43 highly mass-selective (e/m) operation preferred operation region as a trap

44 Linear Paul trap Open ends: quadrupole mass spectrometer (main commercial application of Paul s idea) Closed ends: linear trap (trap string of ions on field-free line without micromotion)

45 animation: Wolfgang Lange, MPQ

46 Particle trajectories in a Paul trap single particle: secular oscillation with superposed micromotion Coulomb crystal of many particles: particle in center at rest, outer particles with micromotion. R. Wuerker, H. Shelton, R. Langmuir J. Appl. Phys. 30, 342 (1959)

47 Time average over many 1/Ω results in a pseudopotential: (ponderomotive potential) Particles minimize the kinetic energy in the driven micromotion and are driven to regions of low field strength E(r) Quadrupole Paul trap: E(r) r time averaged pseudopotential is harmonic Many other potential shapes are possible.

48 trap electrodes ytterbium oven electron source Paul trap for Yb + d=1.4 mm U=600 V at 16 MHz

49 Ions, atoms and types of transition under study J=0 -- J=0 transition, hyperfine-quenched 27 Al +, 115 In + small field-induced shifts All neutral atom lattice clocks: Sr, Yb, Hg S -- D electric quadrupole transition 40 Ca +, 88 Sr +, 171 Yb +, 199 Hg + convenient laser systems S -- F electric octupole transition 171 Yb + narrow linewidth, dα/dt test case nuclear magnetic dipole transition 229 Th 3+ small field-induced shifts

50 State Detection in a Single Ion via Electron Shelving Cooling transition (dipole allowed) "forbidden" transition Photon Count Rate Time (s) Single ion data (In + ): Observation of a Quantum Jump

51 171 Yb + Single Ion Optical Frequency Standard Measurement cycle

52 171 Yb + Optical Frequency Standard High-resolution spectroscopy of the Yb + quadrupole transition motional sidebands Doppler cooling limit, <n vib > 15 -ν r ν r 2 1 m=0 1-2 Zeeman structure B 1 µt m=0 shift: 0.05 Hz π pulse, τ = 1 ms ~ Fourier-limited π pulse, τ = 30 ms ~ Resolution limit Quantum jump probability 30 Hz All measurements: single scan, 20 cycles/point scan time minutes Detuning at 436 nm

53 High resolution excitation spectrum of the Yb + octupole transition

54 Results of absolute frequency measurements of Yb + transitions with caesium fountain clocks at PTB, Relative uncertainty of recent measurements: (Cs-limited) ν(e2)= (36) Hz ν(e3)= (25) Hz

55 Highly accurate and stable optical clocks Recent rapid progress on a variety of systems! Next: optical frequency ratio measurements for consistency checks and tests of fundamental physics