Experimental Tests with Atomic Clocks

Transcription

1 418. WE-Heraeus-Seminar: Models of Gravity in Higher Dimensions, Bremen, Experimental Tests with Atomic Clocks Ekkehard Peik Physikalisch-Technische Bundesanstalt Time and Frequency Department Braunschweig, Germany

2 Outline Measuring Time with Atomic Clocks Tests of Relativity with Clocks Search for Variations of Fundamental Constants Proposed Experiments with Clocks in Space

3 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.

4 Accuracy of primary cesium clocks and of optical frequency standards prepared by P. Gill, NPL

5 Uncertainties in the Realization of the SI Base Units Second 6*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

6 Schematic of an (optical) Atomic Clock Atom Laser f Detektor S Frequenzkamm f 0 Regelungselektronik Fehlersignal ds df f 0 f f 0 f Absorptionssignal

7 Stability and Accuracy of Atomic Frequency Standards Ideal atomic clock: realization of unperturbed atomic transition frequency ν o (at v=0, T=0) transition probability 1 Δp Δν Δν: linewidth, ideally Fourier limited ~1/T c, requires stable atomic levels, long interaction time, narrow oscillator for interrogation Δp: measurement noise, ideally projection noise limited ~1/ N N: atom number, white spectrum Stability: normalized two-sample Allan variance ν o Accuracy: ν out -ν o / ν o for a primary clock: based on evaluation of the uncertainty

8 Stability of Atomic Frequency Standards -12 log σ y H maser Cs fountain log ( τ / s ) Single Ion Optical 1 d High stability is a necessary condition for high accuracy. Strategies for improved clocks: reduce Δν with slow or trapped atoms (laser cooling) increase ν o (microwave optical)

9 The Caesium Fountain Early fountain experiments: 1953 Zacharias, MIT (hot Cs, failed) 1989 Chu, Stanford (cold Na) 1991 ENS/LPTF (cold Cs) PTB s fountain clock CSF1 S. Weyers R. Wynands A. Bauch U. Hübner R. Schröder Chr. Tamm D. Griebsch

10 1 pair of vertical laser beams launching height clock output microwave cavity detection laser ν = Hz ± Δ microwave synthesis quartz oscillator electronics for detection and control photodetector 2 pairs of horizontal laser beams cold atoms: T = 1-2 µk launching velocity = 4 m/s

11 Optical Frequency Standards with a Laser-Cooled Ion in a Paul Trap miniature Paul trap ~ Quadrupole Electrodes 5 Yb + ions Lamb-Dicke confinement with small trap shifts unlimited interaction time single ion: no collisions stability: use high-q transition

12 Optical Frequency Standard with a Laser-Cooled Ion in a Paul Trap Very low uncertainty is possible (to ) proposed by Hans Dehmelt in 1975 Ions under study: Hg + (NIST), Yb + (PTB, NPL), Sr + (NRC, NPL), In + (MPG, U Wash.), Ca + (Mars., Innsb.,...), Al + (NIST), Ba + (U Wash.)... Measurements of optical transition frequencies using caesium fountains and femtosecond-laser frequency combs: 199 Hg + S 1/2 -D 5/2 : (97) Hz NIST 171 Yb + S 1/2 -D 3/2 : (1.4) Hz PTB 88 Sr + S 1/2 -D 5/2 : (1.5) Hz NPL CIPM proposed these standards as secondary representations of the second in the optical frequency domain. Measurement of an optical frequency ratio: f(al + )/f(hg + ): (55) NIST

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

14 Yb + Single Ion Optical Frequency Standard

15 High resolution spectroscopy of the quadrupole transition at 688 THz Pi-Pulse τ(pulse)=1 ms 1 khz linewidth standard operation τ(pulse)=30 ms 30 Hz linewidth Close to the resolution limit τ(pulse) = 90 ms 2 τ(yb + ) 10 Hz linewidth

16 Three tasks in optical frequency metrology absolute measurement comparison of an optical frequency and a Cs frequency standard relative measurement comparison of two optical frequencies as difference or ratio frequency division generation of a microwave frequency from an optical reference, optical clockwork

17 Femtosecond laser as optical frequency comb generator T. Hänsch, MPQ, J. Hall, JILA NIST PTB ILP... ΔΦ gpo time Δt = 1/f rep ν(m) f rep ν=0 frequency ν ceo ν(m) = ν ceo + m f rep Measurement of ν ceo and f rep fixes the frequencies of all modes

18 Measurement of optical frequency ratios Maser Yb + (871nm) vs Nd:YAG (1064nm) Nd:YAG (532nm) vs Nd:YAG (1064nm) ν SH / ν 0 = ( 1 ± ) J. Stenger et al. Phys. Rev. Lett. 88, (2002)

19 Setup for absolute optical frequency measurements Cs fountain Yb+ trap 5 MHz ν Yb+ in units of SI Hertz 688 THz (435.5 nm) Laser frequency servo, time constant: s H Maser Femtosecond frequency comb generator Clock laser Σ Reference cavity 100 MHz 344 THz (871 nm) 200 fib li k

20 Results of absolute frequency measurements f Yb Hz Yb + S 1/2 -D 3/2 : (1.4) Hz Day of Measurement (MJD) Main contributions to the uncertainty budget of the measurements in 2005 and 2006: u A =0.40 Hz (continuous measurements up to 36 h) u B (Cs)=0.83 Hz u B (Yb + )=1.05 Hz (quadrupole shift, blackbody AC Stark shift)

21 Tests of Relativity with Clocks Measurement of the gravitational red shift (GP-A,,geodesy) Pulsartiming Very Long Baseline Interferomety (light deflection) Tracking of interplanetary spacecraft (Cassini, Pioneer, ) Sagnac effect and travelling clocks in rotating frame Isotropy of the one-way speed of light (GPS, ) Lunar laser ranging

22 Search for annual frequency variations as a test of Local Position Invariance Solar gravitational potential on the geoid shows relative annual variation by ± because of the ellipticity of the earth orbit. Search for a frequency difference in gravitational red-shift between dissimilar clocks Null gravitational red-shift experiment : J. P. Turneaure et al., 1983

23 y x MJD Cs fountain vs. H masers Δβ < A. Bauch,S. Weyers Phys. Rev. D 65, (2002) Cs fountains vs. H masers Δβ < N. Ashby et al. Phys. Rev. Lett. 98, (2007) Cs fountain vs. Hg + optical clock Δβ = T. Fortier et al. Phys. Rev. Lett. 98, (2007)

24 Lunar Laser Ranging - Observations cover 37 years - Uncertainty in the cm-range (today) - Measures + Earth-Moon dynamics + relativistic parameters (test of EEP Δa/a<10-13 ) Wettzell Apollo 11 J. Müller, LUH Hannover

25 Testing the Constancy Of Fundamental Constants 20 f Yb Hz Day of Measurement (MJD)

26 Fundamental Constants are constant!? Conservation laws (energy, momentum, ) Undistinguishability of elementary particles Einstein s Equivalence Priniciple Metrology with quantum standards: atomic clocks, single electron devices, Adiabatic changes would be possible Is it a universally applicable concept? Does it hold for Quantum Gravity?

27 Why should fundamental constants be variable? Cosmology: The early universe went through a phase transition that determined particle properties (Inflation). Maybe remnants are still observable in later epochs.

28 Why should fundamental constants be variable? Theories of Grand Unification contain: Energy dependence of the coupling constants Additional dimensions; maybe the true constants are defined there, while we only observe projections.

29 Importance of dimensionless numbers If variations in a dimensional quantity (c, ħ, etc.) would be detected, there is no clear way to distinguish between a change of the quantity and a change of the unit (or meter). Most important test cases in a search for variations: Sommerfeld s fine structure constant α=1/ (94) (electromagnetic force; relativistic contributions to atomic and molecular energies) Mass ratio of proton and electron μ= (80) (sensitive to quark masses, strong force)

30 Evidence for variations of the fine structure constant on a cosmological time scale? Analysis of absorption spectra in the light from quasars, J. Webb, M. Murphy, V. Flambaum et al., Univ. New South Wales, Sydney Many Multiplet Method: transition frequencies in MgI, MgII, FeII, CrII etc. have different dependence on α because of relativistic contributions.

31 Result: >4σ evidence for changing α Linear regression: Observations and analyses of different groups are not consistent.

32 Search for α-variation in optical electronic transition frequencies. Method of Analysis: electronic transition frequency can be expressed as Rydberg frequency in SI hertz numerical constant (function of quantum numbers) dimensionless function of α; describes relativistic level shifts Relative temporal derivative of the frequency: common shift of all transition frequencies specific for the transition under study can be calculated with relativistic Hartree-Fock (Dzuba, Flambaum)

33 Search for variations of the fine structure constant in atomic clock comparisons S. G. Karshenboim physics/ relative frequency drift rate Yb + Hg + H Ca In + Sr + Yb + Ba + relativistic level shift: sensitivity factor A calculations by V. Dzuba and V. Flambaum heavy atoms, light atoms heavy atoms, j g >j e j g <j e

34 Remote comparison of single-ion clocks NIST-PTB, Hg +, S - D at 1064 THz (NIST Boulder) 171 Yb +, S - D at 688 THz (PTB) T. Fortier et al., Phys. Rev. Lett. 98, (2007) A(Yb)= 0.88 A(Hg)= 3.19 E. Peik et al., physics/

35 Limits for Temporal Variations of Fundamental Constants Combining the data from Yb + with those from the Hg + frequency standard at NIST, W. H. Oskay et al., Phys. Rev. Lett. 97, (2006), yields model-independent limits For the fine structure constant: For the Rydberg frequency: d ln Ry / dt (10-15 yr -1 ) Yb d ln α / dt (10-15 yr -1 ) Hg + A=-3.2 A=0.88 E. Peik et al., physics/ Proc. 11th Marcel Grossmann Meeting, Berlin 2006 NIST group: T. Fortier et al., PRL 98, (2007)

36 Combination of available data from optical clocks (spring 2008) Al + /Hg + : T. Rosenband et al., Science 319, 1808 (2008) Sr: S. Blatt et al., Phys. Rev. Lett. 100, (2008)

37 New project: 171 Yb nm octupole transition 2 P 1/2 2 D 3/2 τ ~ 50 ms Resolution only limited by laser linewidth and by heating rate of trapped ion 370 nm cooling and detection 2 S 1/2 F=1 F=0 E2 436 nm E3 467 nm (642 THz) 2 F 7/2 τ ~ 6 yr Single-ion clock of high stability Driven by a frequency doubled diode laser (needed: 1 mw power 0.1 Hz linewidth) ( & repumping at 935 nm, 638 nm, 370 nm HFS ) Pioneering work at NPL: see e.g. P.J. Blythe et al., Phys. Rev. A 67, (2003)

38 171 Yb +, prospects for dα/dt measurements 2 D 3/2 A = Yb + E2 436 nm 2 F 7/2 A = F=1 F=0 2 S 1/2 E3 467 nm - higher ΔA than in any other combination of optical frequency standards (S. Lea, NPL; V. Dzuba and V. Flambaum, UNSW) - can be done in ONE trap - frequency ratio measurement by comb generator; independence from Cs clocks, long-distance transfer,... - measurements with uncertainty, performed over one year, would lead to a sensitivity of (1/α)(dα/dt) / yr

39 Proposed Experiments with Clocks in Space

40 PI: Peter Wolf, LNE-SYRTE, Paris

41 Peter Wolf

42

43 Acknowledgements A. Bauch B. Lipphardt T. Mehlstäubler M. Okhapkin D. Piester H. Schnatz T. Schneider I. Sherstov B. Stein Chr. Tamm S. Weyers R. Wynands K. Zimmermann Funding: DFG FQXi QUEST S. Karshenboim, VNIIM and MPQ