ac fundamental constants - göteborgs...

AC Fundamental Constants

Savely G Karshenboim

D.I. Mendeleev Institute for Metrology (St. Petersburg)and Max-Planck-Institut für Quantenoptik (Garching)

Astrophysics, Clocks andFundamental Constants

Astrophysics, Clocks andFundamental ConstantsWhy astrophysics?

Cosmology: changing universe.Inflation: variation of constants.Pulsars: astrophysical clocks.Quasars: light from a very remote past.

Why clocks?

Frequency: most accurately measured.Different clocks: planetary motion, pulsars, atomic, molecular and nuclear clocks – different dependence on the fundamental constants.

Astrophysics, Clocks andFundamental ConstantsWhy astrophysics?

Cosmology: changing universe.Inflation: variation of constants.Pulsars: astrophysical clocks.Quasars: light from a very remote past.

Why clocks?

Frequency: most accurately measured.Different clocks: planetary motion, pulsars, atomic, molecular and nuclear clocks – different dependence on the fundamental constants.

But:But:everything related to astrophysics is everything related to astrophysics is model dependent and not transparent.model dependent and not transparent.

Atomic Clocks andFundamental Constants

The next ACFC meeting will take place

in 2007 in Bad Honnef

[Optical] Atomic Clocks andFundamental ConstantsWhy atomic clocks?

Frequency measurements are most accurate up to date.Different atomic and molecular transitions differently depend on fundamental constants (α, me/mp, gp etc).

Why optical?

Optical clocks have been greatly improved and will be improved further.They allow a transparent model-independent interpretation in terms of α variation.

Atomic Clocks andFundamental ConstantsWhy atomic clocks?

Frequency measurements are most accurate up to date.Different atomic and molecular thansitions differently depend on fundamental constants (α, me/mp, gp etc).

Why optical?

Optical clocks have been greatly improved and will be improved further.They allow a transparent model-independent interpretation in terms of α variation.

Up to now the optical measurements Up to now the optical measurements are the only source for accurate and are the only source for accurate and reliable modelreliable model--independent constraints independent constraints on a possible time variation of constants.on a possible time variation of constants.

Outline

Precision frequency measurements & variation of constants

Clocks for fundamental physicsAdvantages and disadvantages of laboratory searchesRecent results in frequency metrology

Current laboratory constraints

Optical frequency measurements

Clocks used to be related to RF because of accurate frequency comparisons and conventional macroscopic and electromagnetic frequency range.

Length measurements are related to optics since RF has too large wave lengths for accurate measurements.




Now: clocks enter optics and because of more oscillations in a given period they are potentially more accurate.





That is possible because of frequency comb technology which offers precision comparisons optics to optics and optics to RF.

Optical frequency measurements & α variations




That is possible because of frequency comb technology which offers precision comparisons optics to optics and optics to RF.Meantime comparing various optical transitions

to cesium HFS we look for their variation at the level of few parts in 1015 per a year.







I regret to inform you that the result for the variations is negative.








I am sorry!








I am really sorry!

Atomic Clocks andFundamental Constants

ClocksAtomic and molecular transitions:

their scaling with α, me/mp etc.Advantages and disadvantages of clocks to search the variations.Recent progress.

Atomic Clocks

Caesium clock

Primary standard:

Locked to an unperturbed atomic frequency.All corrections are under control.

Atomic Clocks

Caesium clock

Primary standard:


Clock frequency =atomic frequency

Atomic Clocks

Caesium clock

Primary standard:


Hydrogen maser

An artificial device designed for a purpose.

The corrections (wall shift) are not under control.Unpredictable drift –bad long term stability.

Clock frequency =atomic frequency

Atomic Clocks

Caesium clock

Primary standard:


Hydrogen maser



Clock frequency =atomic frequency Clock frequency ≠

atomic frequency

Atomic Clocks

Caesium clock

Primary standard:


Hydrogen maser




atomic frequencyIf we like to look for a variationof natural constants we have to deal with standards similarto caesium clock.

Atomic Clocks

Caesium clock

Primary standard:


Hydrogen maser

An articitial device designed for a purpose.



atomic frequencyIf we like to look for a variationof natural constants we have to deal with standards similarto caesium clock.

To work with such a near primary clock is the same as to measure an atomic frequency in SI or other appropriate units.

Scaling of atomic transitions

Gross structure Ry

Fine structure α2 × Ry

HFS structure α2 × µNucl/µB × Ry

Relativistic corrections × F(α)

Scaling of molecular transitions

Electronic transitions Ry

Vibrational transitions (me/mp)1/2 × Ry

Non-harmonic corrections × F((me/mp)1/4)Rotational transitions me/mp × Ry

Relativistic corrections × F(α)

Scaling of atomic and molecular transitions

Atomic transitionsGross structureFine structureHFS structureRelativistic corrections

Molecular transitionsElectronic transitionsVibrational transitionsRotational transitionsRelativistic corrections



Molecular transitionsElectronic transitionsNon-harmonic correctionsRotational transitionsRelativistic corrections

Up to date the most accurate resultshave been obtained for atomic transitionsrelated to gross and HFS structure.

Others are not competitive.



Molecular transitionsElectronic transitionsNon-harmonic correctionsRotational transitionsRelativistic corrections

Up to date the most accurate resultshave been obtained for atomic transitionsrelated to gross and HFS structure.

Others are not competitive.

That is not so bad because That is not so bad because the relativistic correctionsthe relativistic correctionsare large. are large.

Sometimes Sometimes –– really large.really large.

They are ~ (They are ~ (ZZαα))22..

Best data from frequency measurements

Atom Frequency

[GHz]δf/f

[10-15]∆f/∆t

[Hz/yr]@

H, Opt 2466061 14 -8±16 MPQ

Ca, Opt 455986 13 -4±5 PTB

Rb, HFS 6.8 1 (0±5)×10-6 LPTF

Yb+, Opt 688359 9 -1±3 PTB

Yb+, HFS 12.6 73 (4±4) ×10-4 NML

Hg+, Opt 1064721 9 0±7 NIST

Progress in α variations since ACFC meeting (June 2003)

Method:

f = C0 × c Ry × F(α)

Progress in α variations since ACFC meeting (June 2003): optical measurements

Method:

f = C0 × c Ry × F(α)and thus

d ln{f}/dt = d ln{cRy}/dt

+ A × d lnα/dt.


Method:f = C0 × c Ry × F(α)

d ln{f}/dt = d ln{cRy}/dt+ A × d lnα/dt.

Measurements: Optical transitions in Hg+ (NIST), H

(MPQ), Ca (PTB), Yb+ (PTB) versus Cs HFS;Calcium (NIST), aluminum ion (NIST), strontium ion (NPL) and neutral strontium (JILA and Tokyo) and octupole Yb+ (NPL) are coming.





(MPQ), Ca, Yb+ (PTB) versus Cs HFS;Calculation of relativistic corrections (Flambaum, Dzuba):

A = d lnF(α)/d lnα


Method:d ln{f}/dt = d ln{cRy}/dt

+ A × d lnα/dt.Measurements of optical transitions in Hg+ (NIST), H

(MPQ), Ca, Yb+ (PTB) versus Cs HFS.Calculation of relativistic corrections (Flambaum, Dzuba):

A = d lnF(α)/d lnα

Atom, transition d ln{f}/dt AH, 1s-2s (-3±6)×10-15 yr -1 0.0040Ca, 1S0 - 3P1 (-8±11)×10-15 yr -1 0.03171Yb+, 2S1/2-2D3/2 (-1±4)×10-15 yr -1 0.9199Hg+, 2S1/2-2D5/2 (-0±7)×10-15 yr -1 -3.2





(MPQ), Yb+ (PTB) versus Cs HFS;Ca, Sr+, Sr, Al+ and octupole Yb+

are comingCalculation of relativistic corrections (Flambaum, Dzuba):

A = d lnF(α)/dα







A = d lnF(α)/dα Sr+, Sr, Caoctupole Yb+







A = d lnF(α)/dα

Further constraints

Model independent constraints can be reached for variations of α, {Ry}, and certain nuclear magnetic moments in units the Bohr magneton.

Further constraints


Those are not fundamental.

Further constraintsHowever, we badly

need a universal presentation of all data for a cross check.



Further constraintsHowever, we badly

need a universal presentation of all data for a cross check.

The next step can be done with the help of the Schmidt model.



Further constraints



We badly need a universal presentation of all data for a cross check.


The model is not quite reliable and the constraints are model dependent.

Further constraints

Model independent constraints can be reached for variations of α, Ry, and nuclear magnetic moments in units the Bohr magneton.


We badly need a universal presentation of all data for a cross check.


The model is not quite reliable and the constraints are model dependent.

However: Nothing is better!However: Nothing is better!

Current laboratory constraints on variations of constants

X Variation d lnX/dt Model

αα ((–– 0 .30 .3±±2.0)2.0)××1010--1515 yryr --11 ----

{c Ry}{c Ry} ((–– 2.12.1±±3.1)3.1)××1010--1515 yryr --11 ----

mmee/m/mpp (2.9(2.9±±6.2)6.2)××1010--1515 yryr --11 Schmidt model

µµpp//µµee (2.9(2.9±±5.8)5.8)××1010--1515 yryr --11 Schmidt model

ggpp ((–– 0.10.1±±0.5)0.5)××1010--1515 yryr --11 Schmidt model

ggnn (3(3±±3) 3) ××1010--1414 yryr --11 Schmidt model

Current laboratory constraints on variations of constants

X Variation d lnX/dt Model

αα ((–– 0 .30 .3±±2.0)2.0)××1010--1515 yryr --11 ----

{c Ry}{c Ry} ((–– 2.12.1±±3.1)3.1)××1010--1515 yryr --11 ----

mmee/m/mpp (2.9(2.9±±6.2)6.2)××1010--1515 yryr --11 Schmidt model

µµpp//µµee (2.9(2.9±±5.8)5.8)××1010--1515 yryr --11 Schmidt model

ggpp ((–– 0.10.1±±0.5)0.5)××1010--1515 yryr --11 Schmidt model

ggnn (3(3±±3) 3) ××1010--1414 yryr --11 Schmidt model

At present: dlnX/dt for αα and {c Ry}{c Ry}

are more than twice more accurate!

Various constraintsAstrophysics:contradictions at level of 1 part in 1015 per a year; a non-transperant statistical evaluation of the data; time separation: 1010 yr.


Geochemistry (Oklo & Co):a model-dependent evaluation of data; based on a single element (Oklo); a simplified interpretation in terms of α;contradictions at level of 1×10-17

per a year; separation: 109 yr.




Laboratory (HFS incl.):particular experiments which may be checked; recent and continuing progress; involvment of the Schmidt model; access to gn; time separation ~ 10 yr.




Laboratory (HFS incl.):particular experiments which may be checked; recent and continuing progress; involvment of the Schmidt model; access to gn; time separation ~ 10 yr.

Laboratory (opt. + Cs):particular experiments which may be checked; recent and continuing progress; model-independence; access only to αand {cRy}; reliability; time separation ~ 1-3-10 yr.

AcknowledgmentsNo fundamental constants have been hurt

during preparation of this talk. Neither their variations in the Earth area have been reported to any scientific authority.

The author greatly appreciatea support from RFBR, DFG, PTB, MPQa support from W.E. Heraeus-Stiftung in organizing ACFC meeting in 2003;fruitful and stimulating discussions with L. Okun, E. Peik, and V. Flambaum.

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