AC Fundamental Constants

AC Fundamental Constants

Savely G Karshenboim

Pulkovo observatory (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.

[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 (, 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 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 (, 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 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 model-independent constraints reliable model-independent constraints on a possible time variation of constants.on a possible time variation of constants.

Outline Are fundamental constants: fundamental?

constants? Various fundamental constants Origin of the constants in modern physics

Measurements and fundamental constants Fundamental constants & units of physical quantities Determination of fundamental constants

Precision frequency measurements & variation of constants

Clocks for fundamental physics Advantages and disadvantages of laboratory searches Recent results in frequency metrology

Current laboratory constraints

Introduction Physics is an experimental science and the

measurements is the very base of physics. However, before we perform any measurements we have to agree on certain units.



Our way of understanding of Nature is a quantitive understanding, which takes a form of certain laws.




These laws themselves can provide no quantitive predictions. Certain quantitive parameters enter the expression of these laws. Some enter very different equations from various fields.

Introduction Physics is an experimental science and the measurements

is the very base of physics. However, before we perform any measurements we have to agree on certain units.


These laws themselves can provide no quantitive predictions. Certain quantitive parameters enter the expression of these laws. Some enter very different equations from various fields.

Such universal parameters are recognized as fundamental physical constants. The fundamental constants are a kind of interface to apply these basic laws to a quantitive description of Nature.

Fundamental constants & various physical phenomenaFirst universal parameters appeared centuries ago.G and g entered a big number of various problems.

Fundamental constants & various physical phenomenaFirst universal parameters appeared centuries ago.G and g entered a big number of various problems.

Just in case:

G is the gravitaiton constant;g is acceleration of free fall.

Fundamental constants & various physical phenomenaFirst universal parameters appeared centuries ago.G and g entered a big number of various problems.G is still a constant,

Fundamental constants & various physical phenomenaFirst universal parameters appeared centuries ago.G and g entered a big number of various problems.G is still a constant, g is not anymore.


Universality: theoretical point of view: really fundamental ones are such as

G, h, c



G, h, c practical point of view: constants which are really necessary

for various measurements (Bohr magneton, cesium HFS ...)





Most fundamental constants in physics: G, h, c – properties of space-time





Most fundamental constants in physics: G, h, c – properties of space-time – property of a universal interaction





Most fundamental constants in physics: G, h, c – properties of space-time – property of a universal interaction Just in case:

is the fine structure constant:which is e2/40ħc.





Most fundamental constants in physics: G, h, c – properties of space-time – property of a universal interaction me, mp – properties of individual elementary particles


Universality: theoretical point of view: really fundamental ones are such as G,

h, c practical point of view: constants which are really necessary for

various measurements (Bohr magneton, cesium HFS ...)

Most fundamental constants in physics: G, h, c – properties of space-time – property of a universal interaction me, mp – properties of individual elementary particles cesium HFS, carbon atomic mass – properties of specific

compound objects

Lessons to learn:

A variation of certain constants already took place according to the inflation model.

is likely the most fundamental of phenomenological constants (the masses are not!) accessible with high accuracy.

Lessons to learn:

A variation of certain constants already took place according to the inflation model.

is likely the most fundamental of phenomenological constants (the masses are not!) accessible with high accuracy.

The only reason to be sure that a certain `constant´is

a constant is to trace its origine and check.

Units

Physics is based on measurements and a measurement is always a comparison.

Still there is a substantial difference between

a relative measurement (when we take advantage of some relations between two values we like to compare) and

an absolute measurements (when a value to compare with has been fixed by an agreement – e.g. SI).

Fundamental constants & units for physical quantitiesEarly time: units are determined by humans (e.g. foot) Earth (e.g. g = 9.8 m/s, day) water (e.g. = 1 g/cm3; Celsius temperature scale) Sun (year)Now we change most of our definitions but keep size of the

units!

The fundamental scale is with atoms and particles and most of constants are » 1 or « 1.

Fundamental constants & units for physical quantitiesEarly time: units are determined by humans (e.g. foot) Earth (e.g. g = 9.8 m/s, day) water (e.g. = 1 g/cm3; Celsius temperature scale) Sun (year)Now we change most of our definitions but keep size of the

units!

The fundamental scale is with atoms and particles and most of constants are » 1 or « 1.

An only constant ~ 1 isRy ~ 13.6 eV

(or IH ~ 13.6 V) since all electric potentials were linked to atomic and molecular energy.

Towards natural units Kilogram is defined via an old-fashion way: an artifact. Second is defined via a fixed value of cesium HFS

f = 9 192 631 770 Hz (Hz = 1/s). Metre is defined via a fixed value of speed of light

c = 299 792 458 m/s .If we consider 1/f as a natural unit of time, and c as a

natural unit of velocity, then their numerical values play role of conversion factors:

1 s = 9 192 631 770 × 1/f,1 m/s = (1/299 792 458) × c.

Those numerical factors are needed to keep the values as they were introduced a century ago what is a great a great illusion of SIillusion of SI.

The fundamental constants serve us both as natural units and as conversion factors.

Towards natural units Kilogram is defined via an old-fashion way: an artifact. Second is defined via a fixed value of cesium HFS

f = 9 192 631 770 Hz (Hz = 1/s). Metre is defined via a fixed value of speed of light

c = 299 792 458 m/s .If we consider 1/f as a natural unit of time, and c as a

natural unit of velocity, then their numerical values play role of conversion factors:

1 s = 9 192 631 770 × 1/f,1 m/s = (1/299 792 458) × c.

Those numerical factors are needed to keep the values as they were introduced a century ago what is a great a great illusion of SIillusion of SI.

The fundamental constants serve us both as natural units and as conversion factors.

If the constants are changing the units are changing as well.

Constants & their numerical valuesWe have to distinguish clearly between fundamental

constants and their numerical values. The Rydberg constant is defined via e, h, me, 0 and c.It has no relation to cesium and its hyperfine structure

(nuclear magnetic moment).

While the numerical value of the Rydberg constant2 × {Ry} = 9 192 631 770 / {Cs HFS}At.un.

is related to cesium and SI, but not to Ry.

If e.g. we look for variation of constants suggesting a variation of cesium magnetic moment, the numerical value of Ry will vary, while the constant itself will not.

Progress in determination of fundamental constants

This is the progress for over 30 years. Impressive for some of constants (Ry, me/mp) and moderate for others.



Note: the progress is not necessaryan increase of accuracy,

Lessons to learn:

If fundamental constants are changing, the units are changing as well.

Variation of a dimensional quantity can in principle be detected.

However, it is easier to deal with dimensionless quantities, or numerical values in well-defined units.

Lessons to learn: Fundamental constants have been

measured not so accurately as we need.

We have to look for consequenses of their variations for most precision measured quantities.

One can note from accuracy of the Rydberg constant: those are frequencies.

Optical frequency measurements

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

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




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 & 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 a part in 1015 per a year.

What is the frequency comb? When an optical signal is

modulated by an rf, the results contains ffoptopt+nf+nfrfrf, where n = 0, ±1, ± 2 ...

When the rf signal is very unharmonic, n can be really large.

For the comb one starts with femtosecond pulses.

Each comd line can be presented as ffoffoff+nf+nfreprep.

A measurement is a comparison of an optical frequency f with a comb line, determining their differnce which is in rf domain.

An important issue is an octave, i.e. a spectrum where fmax < 2×fmix.

That is achieved by using special fibers.

With octave one can express ffoffoff in terms of ffreprep.






A measurement is a comparison of an optical frequency F with a comb line, determining their differnce which is in rf domain.

An important issue is an octave, i.e. a spectrum where fmax < 2fmix.








A measurement is a comparison of an optical frequency F with a comb line, determining their differnce which is in rf domain.

An important issue is an octave, i.e. a spectrum where fmax < 2fmix.



Presence of regular reference lines,Presence of regular reference lines,distance between which is in rf domain,distance between which is in rf domain,

across all the visible spectrumacross all the visible spectrum(and a substantial paft of IR and UV)(and a substantial paft of IR and UV)

allows a comparison of two opical lines,allows a comparison of two opical lines,or an optical againts a radio frequency.or an optical againts a radio frequency.






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

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






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


I am sorry!






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


I am really sorry!

Atomic Clocks andFundamental Constants

Clocks Atomic and molecular transitions:

their scaling with , 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.


Atomic Clocks

Caesium clock

Primary standard:



Hydrogen maser





Clock frequency atomic frequency

Atomic Clocks

Caesium clock

Primary standard:



Hydrogen maser






If 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. The corrections





If 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 2 × Ry

HFS structure 2 × Nucl/B × Ry

Relativistic corrections

× F()


Gross structure Ry




× F()

That is what one can easily derive for hydrogen.That is what one can easily derive for hydrogen.

More complicated atoms lead to More complicated atoms lead to more complicated calculation of numerical factors.more complicated calculation of numerical factors.


Gross structure Ry




× F()

Characteristic electron velocity in an atom is Characteristic electron velocity in an atom is c/n. c/n.

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()

Scaling of atomic and molecular transitions

Atomic transitions Gross structure Fine structure HFS structure Relativistic

corrections

Molecular transitions Electronic

transitions Vibrational

transitions Rotational

transitions Relativistic

corrections



corrections


transitions Non-harmonic

corrections Rotational


corrections

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

Others are not competitive.



corrections





corrections



That is not so bad because That is not so bad because the relativistic correctionsthe relativistic correctionsareare large. large.

Sometimes – reallySometimes – really largelarge..

They are ~ (They are ~ (ZZ))22..

Scaling of atomic and molecular transitionsNeutral atom (Rb, Cs) Nucleus

charge: +Ze Electron core

charge -(Z-1)e charge of nucleus +

electron core = e Valent electron

partly penetrates into core

v/c ~ (outside core) v/c ~ Z(inside core)



corrections





corrections



That is not so bad because That is not so bad because the relativistic correctionsthe relativistic correctionsareare large. large.

Sometimes – reallySometimes – really largelarge..

They are ~ (They are ~ (ZZ))22..

Best data from frequency measurements

Atom Frequency

[GHz]

f/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

More even better data from frequency measurements


NIST: quantum logics & direct comparison NIST: quantum logics & direct comparison between two optical clocks between two optical clocks


1D optical lattice

A `direct’ measurement

Progress in variations since the 1st ACFC meeting (June 2003) Method:

f = C0 × c Ry × F()


f = C0 × c Ry × F()

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

+ A × d ln/dt.


f = C0 × c Ry × F() d ln{f}/dt = d ln{cRy}/dt

+ A × d ln/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 (Tokyo, JILA, LNE-SYRTE) and mercury (LNE-SYRTE) and octupole Yb+ (NPL) are coming.



+ A × d ln/dt. Measurements: Optical transitions in Hg+ (NIST),

H (MPQ), Ca, Yb+ (PTB) versus Cs HFS;

Calculation of relativistic corrections (Flambaum, Dzuba):

A = d lnF()/d ln


d ln{f}/dt = d ln{cRy}/dt + A × d

ln/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()/d ln



+ A × d ln/dt. Measurements: Optical transitions in Hg+ (NIST), H

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

octupole Yb+ are coming Calculation of relativistic

corrections (Flambaum, Dzuba):

A = d lnF()/d







A = d lnF()/d

Sr+, Sr, Ca, Al+octupol

e Yb+

Hg







A = d lnF()/d

Further constraints

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

Further constraints


Those are not fundamental.

Further constraints



However, we badly need a universal presentation of all data for a cross check.

Further constraints



However, 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



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 However: Nothing is better!better!

Current laboratory constraints on variations of constants

X Variation d lnX/dt Model

(– 0.3(– 0.3±±2.0)2.0)××1010-15-15 yr yr -1-1 ----

{c Ry}{c Ry} (– 2.1(– 2.1±±3.1)3.1)××1010-15-15 yr yr -1-1 ----

mmee/m/mpp (2.9(2.9±±6.2)6.2)××1010-15-15 yr yr -1-1 Schmidt

model

pp//ee (2.9(2.9±±5.8)5.8)××1010-15-15 yr yr -1-1 Schmidt

model

ggpp (– 0.1(– 0.1±±0.5)0.5)××1010-15-15 yr yr -1-1 Schmidt

model

ggnn (3(3±±3) 3) ××1010-14-14 yr yr -1-1 Schmidt

model



(– 0.3(– 0.3±±2.0)2.0)××1010-15-15 yr yr -1-1 ----

{c Ry}{c Ry} (– 2.1(– 2.1±±3.1)3.1)××1010-15-15 yr yr -1-1 ----


model


model


model


model

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

are improved substantially:

From talk by Ekkehard Peik at Leiden-2009 workshop



(– 0.3(– 0.3±±2.0)2.0)××1010-15-15 yr yr -1-1 ----

{c Ry}{c Ry} (– 2.1(– 2.1±±3.1)3.1)××1010-15-15 yr yr -1-1 ----


model


model


model


model

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.

What are astrophysical data from? Quasars produce light

from very remote past. Travelling to us the light

cross delute clouds. We study absorbsion

lines. The lines are redshifted. To identify lines we

compare various ratios; they should match the laboratory values.

The ratios are sensitive to value of a, me/mp and e/p in different ways.

Small departures from the present-day laboratory results are analized as a possible systematic effect due to a variation of fundamental constant.

Julian A. King et al., arXiv:1202.4758

Consequences for atomic clocks (from Victor Flambaum)

Sun moves 369 km/s relative to CMB cos towards area with larger

This gives average laboratory variation cosper year

Earth moves 30 km/s relative to Sun- 1.6 10 -20cos(tannual modulation


Geochemistry (Oklo & Co):a model-dependent evaluation of data; based on a single element (Oklo); a simplified interpretation in terms of ;contradictions at level of 1×10-17 per a year; separation: 109 yr.

What is `Oklo´? Some time ago French

comission for atomic energy reported on reduction of amount of U-235: the U-deposites (1972) in Oklo (Gabon, West Africa) contains 0.705% instead of 0.712%.

The interpretation was a fossil natural nuclear reactor.

It happens because 2 Gyr ago the uranium was `enriched´.

That was so-called water-water reactor.

The operation lasts from 0.5 to 1.5 Myr.

The fission produces Sm isotopes and Sm-149 has a neutron-capture resonance at 97.3 meV.








Just in case:

Myr = mega-yearMyr = mega-year

Gyr = giga-year Gyr = giga-year

meV = milli-electron-voltmeV = milli-electron-volt







The fission produces Sm isotopes and Sm-149 a neutron-capture resonance at 97.3 meV.

In 1976 Shlyachter suggested In 1976 Shlyachter suggested to examine Sm isotopes to test to examine Sm isotopes to test

variation of the constants.variation of the constants.



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 and {cRy}; reliability; time separation ~ 1-3-10 yr.

Acknowledgments

No fundamental constants have been hurt during preparation of this talk. Neither their variations in the Earth area have been reported to any scientific authority.

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