Search for temporal variations of fundamental constants

Transcription

1 Schladming School 2010: Masses and Constants Lecture II Search for temporal variations of fundamental constants Ekkehard Peik Physikalisch-Technische Bundesanstalt Time and Frequency Department Braunschweig, Germany

2 Lecture I The International System of units SI Units based on fundamental constants Routes towards a new definition of the kilogram A new generation of atomic clocks Lecture II Variations of fundamental constants: Motivation Search in geo- and astrophysics Search for new physics in precision experiments with atomic clocks

3 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?

4 Early proposals on variable constants (1930ies): Zwicky, Chalmers, Dirac, Jordan Dirac s Large Number Hypothesis (Nature 139, 323 (1937)) Ruled out by arguments from stellar evolution!

5 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). The SI system has fixed certain quantities by definition: speed of light: c= m/s Cs hyperfine frequency: f Cs = Hz 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) Problem in devising a test: Isolate variability of one fundamental constant if we have to expect all of them to vary.

6 The Oklo natural nuclear reactor Discovered in 1972 in Gabon in uranium mining via a U-235 deficiency. Reactor was active 2 billion years ago. Sm-149 was depleted via a neutron capture resonance at 0.1 ev: Isotope ratios indicate that the cross section for this process did not change significantly in the yr since the activity. Photo: Y. Fujii Canbeusedto infera (model-dependent) limit on the change of α (Shlyakhter (1976), Damour&Dyson,...) in the range:

7 Y. Fujii et al., astro-ph/ Find two branches of possible solutions: The analysis depends on the temperature in the reactor. Effects of electromagnetic and strong interaction on the resonance cross sections are difficult to separate.

8 Evidence for a varying 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.

9 Result: >4σ evidence for α-variation. Linear fit:

10 Measurements from other groups with a different instrument, different selections of quasars and absorption lines are consistent with Δα=0. R. Srianand et al., Phys. Rev. Lett. 92, (2004) 3σ 1σ Murphy,Webb data The controversy is still open. Maybe both teams underestimate the uncertainty of their data analysis?

11 Different search strategies for variations of α: Astrophysical and geophysical observations (QSO, Oklo reactor): + cover cosmological time scale evaluation is complicated or model-dependent Laboratory experiments with frequency standards: time scale of a few years only + parameters can be varied and systematics studied

12 Scaling of transition frequencies with fundamental constants H spectroscopy M. Savedoff, 1956 Cs + Rb fountain clocks R. Thompson, 1975 From: S. G. Karshenboim, E. Peik (eds.) Astrophysics, Clocks and Fundamental Constants, Lect. Notes in Physics 648 (2004) J. Prestage, 1995 V. Flambaum et al. Optical clocks with heavy ions or atoms

13 Precision comparisons of atomic frequency standards: IEN 1993 Mg FS / Cs HFS JPL 1995 Hg + HFS / H HFS BNM-SYRTE 2003 Rb HFS / Cs HFS NIST 2003 Hg + opt. / Cs HFS MPQ 2003 H opt. / Cs HFS PTB 2003 Yb + opt. / Cs HFS NIST 2008 Hg + opt. / Al + opt. FS: fine structure HFS: hyperfine structure Opt.: optical (gross structure) Comparisons with hyperfine frequencies involve a combination of electromagnetic and strong interactions, making it impossible to isolate the influence of α in a single measurement. Frequency measurements with molecules are somewhat lacking behind in precision.

14 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)

15 Signature of a varying fine structure constant 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

16 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

17 Yb + single-ion optical frequency standard 171 Yb + level scheme Measurement cycle 40 ms ms Advantages of Yb + all diode laser system long trapping time (months)

18 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

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) fib li k

20 Results of absolute frequency measurements fyb Hz Yb + S 1/2 -D 3/2 : (73) Hz Day of Measurement (MJD) Main contributions to the uncertainty budget of the measurement in 2008: u A =0.30 Hz (continuous measurement over 4 days) u B (Cs)=0.62 Hz (cavity phase shift, cold collisions, ) u B (Yb + )=0.31 Hz (quadrupole shift, blackbody AC Stark shift, ) Chr. Tamm et al., Phys. Rev. A 80, (2009)

21 Remote comparison of single-ion clocks NIST-PTB, Hg +, S - D at 1064 THz (NIST Boulder) A(Yb)= 1.00 A(Hg)= Yb +, S - D at 688 THz (PTB) 20 fyb Hz Day of Measurement (MJD) T. Fortier et al., Phys. Rev. Lett. 98, (2007) First analysis of this kind: E. Peik et al., Phys. Rev. Lett. 93, (2004)

22 The Al + clock (NIST, Boulder) J=0 0 transition with small systematic shifts Sympathetic laser cooling via Be + or Mg + Quantum logic for state readout Anchor transition with A 0 1 P 1 1 S 0 3 P 0 λ=167 nm (!) clock transition λ = nm γ = 2π 8 mhz 27 Al + (I=5/2) partial level scheme Proposed by D. Wineland in 2001 P.O. Schmidt et al., Science, 309, 749 (2005) T. Rosenband et al., Science 319, 1808 (2008)

23 Limits for Temporal Variations of Fundamental Constants: Combination of available data from optical clocks (fall 2008) Al + /Hg + : T. Rosenband et al., Science 319, 1808 (2008) Hg + : T. Fortier et al., Phys. Rev. Lett. 98, (2007) Yb + : Chr. Tamm et al., Phys. Rev. A 80, (2009) 2 Al + /Hg + Optical Frequency Ratio Measurement Hg + d ln Ry / dt (10-15 /year) Yb d ln α / dt (10-15 /year) combined Limit for d lnα/dt more than 20x smaller than from the Webb et al. QSO data. But: measured in a different place and time!

24 Further prospects for dα/dt measurements: Transitions with high sensitivity Yb + electric octupole transition 2 P 1/2 2 D 3/2 τ ~ 50 ms 370 nm cooling and detection 2 S 1/2 F=1 F=0 E2 436 nm E3 467 nm (642 THz) 2 F τ ~ 6 yr 7/2 A= _ + 2 [631] 229m Th Isomer μ=-0.08 μ N A ΔE=7.6 ev M1 transition τ 3000 s Thorium-229 nuclear transition V. Flambaum: Phys. Rev. Lett. 97, (2006) 5_ + 2 [633] μ=0.4 μ N Q e m Th Ground State

25 Coming back to Dirac s hypothesis: Search for dg/dt From timing data on the binary pulsar PSR : d lng/dt= (1.0 ± 2.3) /yr ( < H o ) Th. Damour, G. Gibbons, J. Taylor, Phys. Rev. Lett. 61, 1151 (1988)

26 Test of General Relativity in Lunar Laser Ranging r reflector Apollo 11 July 1969 r EM r station d - transformation between reference systems (Moon, Earth, inertial) - transformation between time systems - orbital motion of the solar system bodies - rotation of Earth and Moon - gravitational time delay (Shapiro) Obs. Wettzell

27 Test of General Relativity in Lunar Laser Ranging - Data available over more than 40 years - Uncertainty in the cm-range (presently) J. Müller, L. Biskupek, Class. Quantum Grav. 24, 4533 (2007) Hawaii McDonald Grasse Wettzell Matera Orrora l Worldwide distribution of observatories

28 Summary of Lecture II Search for variations of fundamental constants: possible experimental window to new physics. Astrophysics: uncertainty Δα/α 10-5 over yr, conclusions still subject to debate. Lunar laser ranging: 1/G dg/dt <10-12 /yr over 40 yr. Laboratory experiments with atomic clocks: 1/α dα/dt<10-16 /yr over 10 years, Sensitivity <10-20 /yr seems accessible in selected systems.