Transcript Atomic Physics and Search for Variation of Fundamental

Variation of
Fundamental Constants
from Big Bang to Atomic
Clocks
V.V. Flambaum
School of Physics, UNSW, Sydney, Australia
Co-authors:
Atomic calculations V.Dzuba,M.Kozlov,E.Angstmann,J.Berengut,M.Marchenko,Cheng
Chin,S.Karshenboim,A.Nevsky
Nuclear and QCD calculations E.Shuryak,V.Dmitriev,D.Leinweber,A.Thomas,R.Young,A.Hoell,
P.Jaikumar,C.Roberts,S.Wright,A.Tedesco,W.Wiringa
Cosmology J.Barrow
Quasar data analysis J.Webb,M.Murphy,M.Drinkwater,W.Walsh,P.Tsanavaris,S.Curran
Quasar observations C.Churchill,J.Prochazka,A.Wolfe, thanks to W.Sargent,R.Simcoe
Motivation
• Extra space dimensions (Kaluza-Klein, Superstring and
M-theories). Extra space dimensions is a common feature
of theories unifying gravity with other interactions. Any
change in size of these dimensions would manifest itself in
the 3D world as variation of fundamental constants.
• Scalar fields . Fundamental constants depend on scalar
fields which vary in space and time (variable vacuum
dielectric constant e0 ). May be related to “dark energy” and
accelerated expansion of the Universe..
• “ Fine tuning” of fundamental constants is needed for
humans to exist. Example: low-energy resonance in
production of carbon from helium in stars (He+He+He=C).
Slightly different coupling constants — no resonance –- no
life.
Variation of coupling constants in space provide natural
explanation of the “fine tuning”: we appeared in area of the
Universe where values of fundamental constants are
suitable for our existence.
Search for variation of
fundamental constants
•Big Bang Nucleosynthesis
|Dc|>0?
•Quasar Absorption Spectra 1
|Dc|>0?
•Oklo natural nuclear reactor
|Dc|>0?
•Atomic clocks 1
1 Based
on analysis of atomic spectra
Which Constants?
Since variation of dimensional constants
cannot be distinguished from variation of units,
it only makes sense to consider variation of
dimensionless constants.
• Fine structure constant a=e2/hc=1/137.036
• Electron or quark mass/QCD strong interaction
scale, me,q/LQCD
a strong (r)=const/ln(r LQCD /ch)
Variation of fine structure constant
a
Quasar absorption spectra
Gas cloud
Earth
Light
a
Quasar
Quasar absorption spectra
Gas cloud
Earth
Quasar
Light
a
One needs to know
E(a2) for each line to
do the fitting
Use atomic calculations to find w(a).
For a close to a0
w = w0 + q(a2/a02-1)
q is found by varying a in computer codes:
q = dw/dx = [w(0.1)-w(-0.1)]/0.2, x=a2/a02-1
a =e2/hc=0 corresponds to non-relativistic
limit (infinite c).
Methods of Atomic Calculations
Nve
Relativistic Hartree-Fock +
Accuracy
1
All-orders sum of dominating
diagrams
0.1-1%
2-6
Configuration Interaction +
1-10%
Many-Body Perturbation Theory
2-15 Configuration Interaction
10-20%
These methods cover all periodic system of elements
They were used for many important problems:
• Test of Standard Model using Parity Violation in Cs, Tl…
• Predicting spectrum of Fr (accuracy 0.1%), etc.
Fine structure anomalies and level crossing
Energies of “normal” fine structure
triplets as functions of a2
DE=A(Za)2
0
(a/a0)2
1
Problem: level pseudo crossing
Energy levels of Ni II as functions of a2
Values of q=dE/da2
are sensitive to
the position of
level crossing
Solution:
matching
experimental gfactors
0
(a/a0)2
1
Results of calculations (in cm-1)
Negative shifters
Anchor lines
w0
Atom
Atom
q
w0
q
Mg I
35051.217
86
Ni II
57420.013
-1400
Mg II
35760.848
211
Ni II
57080.373
-700
Mg II
35669.298
120
Cr II
48632.055
-1110
Si II
55309.3365
520
Cr II
48491.053
-1280
Si II
65500.4492
50
Cr II
48398.862
-1360
Al II
59851.924
270
Fe II
62171.625
-1300
Al III
53916.540
464
Al III
53682.880
216
Ni II
58493.071
-20
Also, many transitions in Mn II, Ti II,
Si IV, C II, C IV, N V, O I, Ca I, Ca II,
Ge II, O II, Pb II
Different signs and magnitudes of
q provides opportunity to study
systematic errors!
Positive shifters
Atom
w0
q
Fe II
62065.528
1100
Fe II
42658.2404
1210
Fe II
42114.8329
1590
Fe II
41968.0642
1460
Fe II
38660.0494
1490
Fe II
38458.9871
1330
Zn II
49355.002
2490
Zn II
48841.077
1584
ω = ω0 + q (α2/α02 – 1)
Laboratory
Measurements
(London, NIST,
Lund, etc.)
w0
Quasar
Observations
(Keck, VLT)
w
Analysis
(J.Webb,
M.Murphy, et al.)
Da
q
Atomic
Calculations
(V.A. Dzuba,
V.V. Flambaum, et al.)
Results of the analysis
• Murphy et al, 2003: Keck telescope, 143 systems, 23
lines, 0.2<z<4.2
Da/a=-0.543(116) x 10-5
• Quast et al, 2004: VLT telescope, 1 system, Fe II, 6
lines, 5 positive q-s, one negative q, z=1.15
Da/a=-0.4(1.9)(2.7) x 10-6
• Srianand et al, 2004: VLT telescope, 23 systems, 12
lines, Fe II, Mg I, Si II, Al II, 0.4<z<2.3
Da/a=-0.06(0.06) x 10-5
Systematic effect or spatial variation?
No explanation by systematic
effects have been found so far
Spatial variation (C.L.Steinhardt)
10 5 Da/a
Murphy et al
• North hemisphere
• South (close to North)
Strianand et al (South)
-0.66(12)
-0.36(19)
-0.06(06)
Variation of strong interaction
Grand unification models (Marciano; Calmet,
Fritzch;Langecker,Segre Strasser;Dent)
D(m/LQCD)/(m/LQCD)=35Da/a
1. Proton mass Mp=3LQCD , measure me/Mp
2. Nuclear magnetic moments m=g eh/4Mpc
g=g(mq/ LQCD)
3. Nuclear energy levels
Dependence on quark mass
• Dimensionless parameter is mq/LQCD . It is
convenient to assume LQCD =const, i.e. measure
mq in units of LQCD
• mp is proportional to (mqLQCD)1/2
Dmp/mp=0.5Dmq/mq
• Other meson and nucleon masses remains finite
for mq=0.
Dm/m=K Dmq/mq
Coefficients K are calculated for p,n,r,w,s.
mu + md
mq =
 5 MeV , LQCD = 350 MeV  K = 0.02 - 0.06
2
Strange quark mass ms = 120 MeV
Nuclear magnetic moments
depends on p-meson mass mp
p
n
p
p
n
p
p
Nucleon
magnetic
moment
Spin-spin interaction
between valence and
core nucleons
Nucleon magnetic moment
m = m0 (1 + amp + ...) = m0 (1 + b mq + ...)
Nucleon and meson masses
M = M0 + amq
QCD calculations: lattice, chiral perturbation
theory,cloudy bag model, Shwinger-Dyson
equation, semiempirical.
Nuclear calculations: meson exchange theory
of strong interaction.
Measurements me / Mp or me / LQCD
• Tsanavaris,Webb,Murphy,Flambaum,
Curran PRL 2005
Hyperfine H/optical , 8 quasar absorption systems
with Mg,Ca,Mn,C,Si,Zn,Cr,Fe,Ni
Measured X=a2 gp me / Mp
DX/X=1.17(1.01)10-5 No variation
• Reinhold,Bunnin,Hollenstein,Ivanchik,
Petitjean PRL 2006 , H2 molecule, 2 systems
D(me / Mp )/ (me / Mp)=-2.4(0.6)10-5 Variation 4 s !
Systematics or space-time variation?
Oklo natural nuclear reactor
n+Sm capture cross section is dominated by
Er =0.1 eV resonance
Shlyakhter;Damour,Dyson;Fujii et al
Limits on variation of alpha
Flambaum, Shuryak PRD 2003
DEr = 170 MeV DX/X + 1 MeV Da/a
X=ms/ LQCD , enhancement 170 MeV/0.1 eV=1.7x109
Lamoreax,Torgerson PRD(2004) DEr =-0.58(5) eV
DX/X=-0.34(3) 10-9 two billion years ago
Atomic clocks
Cesium primary frequency standard:
F=4
HFS of 6s:
n = 9 192 631 770 Hz
F=3
Also: Rb, Cd+, Ba+, Yb+, Hg+, etc.
E.g. n(Hg+) = 40 507 347 996.841 59(14)(41) Hz
(D. J. Berkeland et al, 1998).
Optical frequency standards:
Z
Atom
Transition
20
Ca
1S - 3P
0
1
38
Sr+
1S - 3P
0
1
434 829 121 311(10) kHz Ferrari et al,
2003
49
In+
1S - 3P
0
0
1 267 402 452 899 920(230) Hz von Zanthier
et al, 2005
70
Yb+
2S - 2F
1/2
7/2
Frequency
455 986 240 494 144(5.3) Hz
Source
Degenhardt
et al, 2005
642 121 496 772 300(600) Hz Hosaka et al,
2005
Also: H, Al+, Sr, Ba+, Yb, Hg, Hg+, Tl+, Ra+, etc.
Accuracy about 10-15 can be further improved to 10-18!
Atomic clocks:
Comparing rates of different clocks
over long period of time can be used to
study time variation of fundamental
constants!
Optical transitions:
a
Microwave transitions: a, (me, mq )/LQCD
Advantages:
• Very narrow lines, high accuracy of
measurements.
• Flexibility to choose lines with larger
sensitivity to variation of fundamental
constants.
• Simple interpretation (local time variation).
Calculations to link change of frequency to
change of fundamental constants:
Optical transitions: atomic calculations (as for
quasar absorption spectra) for many narrow
lines in Al II, Ca I, Sr I, Sr II, In II, Ba II, Dy I,
Yb I, Yb II, Yb III, Hg I, Hg II, Tl II, Ra II .
w = w0 + q(a2/a02-1)
Microwave transitions: hyperfine frequency is sensitive
to nuclear magnetic moments (suggested by
Karshenboim)
We performed atomic, nuclear and QCD calculations of
powers k ,b for H,D,Rb,Cd+,Cs,Yb+,Hg+
V=C(Ry)(me/Mp)a2+k (mq/LQCD)b , Dw/w=DV/V
Results for variation of
fundamental constants
Clock1/Clock2
da/dt/a(10-15 yr-1)
Rb(hfs)/Cs(hfs)
0.05(1.3)a
Hg+(opt)/Cs(hfs)
-0.03(1.2)a
H(opt)/Cs(hfs)
-1.1(2.3)a
Source
Marion et al, 2003
Bize et al,
2003
Fisher et al, 2004
Peik et al,
2004
Yb+(opt)/Cs(hfs)
-0.2(2.0)
Bize et al,
2004
Rb(hfs)/Cs(hfs)
0.1(1)a
aassuming
mq/LQCD = Const
Combined results:
d/dt lna = -0.9(2.9) x 10-15 yr-1
d/dt ln(mq/LQCD) = ...10-15 yr-1
me /Mp or me/LQCD …10-15 yr -1
Dysprosium miracle
Dy: 4f105d6s E=19797.96… cm-1 , q=
6000 cm-1
4f95d26s E=19797.96… cm-1 , q= -23000 cm-1
Interval Dw = 10-4 cm-1
Enhancement factor K = 108 (!), i.e. Dw/w0 = 108 Da/a
Preliminary result (Budker et al, Berkeley)
|dlna/dt| < 4.3 x 10-15 yr-1
Problem: states are not narrow!
Molecular clocks
Cancellations between rotational and
hyperfine intervals in very narrow
microwave transitions in
LaS, LaO, LuS,LuO, etc.
w0 =Erotational -E hyperfine= E hyperfine /100-1000
Enhancement factor K = 102 -103,
Dw/w0 = K Da/a
Nuclear clocks
(suggested by Peik,Tamm 2003)
Very narrow UV transition between first excited
and ground state in 229 Th nucleus
Energy 3-5 eV, width 10-4 Hz
Nuclear/QCD calculation: Enhancement 105 -106,
Dw/w0 = 105 (4 Da/a + DXq/Xq-10DXs/Xs )
Xq=mq/ LQCD , Xs=ms/ LQCD
235 U
energy 76 eV, width 6 10-4 Hz
Ultracold atomic and molecular
collisions (in Bose condensate).
Cheng Chin, Flambaum PRL 2006
Enhancement near Feshbach resonance.
Variation of scattering length
D a/a=K D X/X , K=102 – 1012
X=me/Mp
Conclusions
• Quasar data: MM method provided sensitivity increase
100 times. Anchors, positive and negative shifterscontrol of systematics. Keck- variation of a, VLT-no
variation. Undiscovered systematics or spatial variation.
• me /Mp : hyperfine H/optical – no variation, H2 - variation
4 s . Undiscovered systematics or space-time variation.
• Big Bang Nucleosynthesis: may be interpreted as
variation of ms/ LQCD ?
• Oklo: variation of ms/ LQCD ?
• Atomic clocks: present time variation of a , ms/ LQCD
• Transitions between narrow close levels in atoms,
molecules and nuclei – huge enhancement!
Publications:
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V. A. Dzuba, V. V. Flambaum, J, K. Webb, PRL 82, 888 (1999).
V. A. Dzuba, V. V. Flambaum, J, K. Webb, PRA 59, 230 (1999).
V. A. Dzuba, V. V. Flambaum, PRA 61, 034502 (2000).
V. A. Dzuba, V. V. Flambaum, M. T. Murphy, J, K. Webb, LNP 570, 564 (2001).
J. K. Webb et al , PRL 87, 091301 (2001).
V. A. Dzuba, V. V. Flambaum, M. T. Murphy, J, K. Webb, PRA 63, 042509 (2001).
M. M. Murphy et al, MNRAS, 327, 1208 (2001).
V. A. Dzuba et al, PRA, 66, 022501 (2002).
V. A. Dzuba, V. V. Flambaum, M. V. Marchenko, PRA 68, 022506 (2003).
E. J. Angstmann, V. A. Dzuba, V. V. Flambaum, PRA 70, 014102 (2004).
J. C. Berengat et al, PRA 70, 064101 (2004).
M. M. Murphy et al, LNP, 648, 131 (2004).
V. A. Dzuba, PRA, 71, 032512 (2005).
V. A. Dzuba, V. V. Flambaum, PRA, 71, 052509 (2005).
V. A. Dzuba, V. V. Flambaum, PRA, 72, 052514 (2005).
V. A. Dzuba, PRA, 71, 062501 (2005).
S. G. Karshenboim et al, physics/0511180.
Alkali Doublet Method
(Varshalovich, Potekhin, Ivanchik, et al)
Fine structure interval
DFS = E(p3/2) - E(p1/2) = A(Za)2
If DZ is observed at red shift Z and D0 is FS
measured on Earth then
Da
a

1  DZ

=
- 1


2  D0

Ivanchik et al, 1999: Da/a = -3.3(6.5)(8) x 10-5.
Murphy et al, 2001: Da/a = -0.5(1.3) x 10-5.
Text
Many Multiplet Method
(Flambaum, Webb, Murphy, et al)
p3/2
p1/2
p3/2
p1/2
w
w
s1/2
a1
dw >> dDFS !
s1/2
a2
Advantages:
•Order of magnitude gain in sensitivity
•Statistical: all lines are suitable for analysis
•Many opportunities to study systematic errors
Atoms of interest
1N
ve
Z
Atom / Ion
Transitions
Nve1
6
C I, C II, C III
p-s
4, 3, 2
8
OI
p-s
4
11
Na I
s-p
1
12
Mg I, Mg II
s-p
2, 1
13
Al II, Al III
s-p
2, 1
14
Si II, Si IV
p-s
3, 1
16
S II
s-p
4
20
Ca II
s-p
1
22
Ti II
s-p, d-p
3
24
Cr II
d-p
5
25
Mn II
s-p, d-p
1
26
Fe II
s-p, d-p
7
28
Ni II
d-p
9
30
Zn II
s-p
1
– number of valence electrons
Fine structure unomalies and level crossing
Energies of “normal” fine structure
doublets as functions of a2
DE=A(Za)2
0
(a/a0)2
1
Fine structure unomalies and level crossing
Energies of strongly interacting states
as functions of a2
1D
DE=A(Za)2
2
3P
0,1,
2
0
(a/a0)2
1
Implications to study of a variation
• Not every fine structure interval can be
used in the analysis based on formula
DE=A(Za)2 (not good!).
• Strong enhancement is possible (good,
but for atomic clocks only).
• Level crossing may lead to instability of
calculations (bad!).
Problem: level pseudo crossing
Energy levels of Ni II as functions of a2
Values of q=dE/da2
are sensitive to
the position of
level crossing
0
(a/a0)2
1
Pb II: g-factors don’t help
Energy levels of Pb II as functions of a2
2D
2D
5/
3/2
2
2S
1/2
4P
5/2
0
2D
Two 3D3/2 states are
strongly mixed,
but g-factors do
not depend on
mixing.
2D
3/2
5/2
4P
3/2
(a/a0)2
Solution: perform
calculations with
extremely high
accuracy.
4P
1/2
1
Microwave transitions
Hyperfine frequency is sensitive to nuclear
magnetic moments (suggested by
Karshenboim)
We performed atomic, nuclear and QCD
calculations of powers k ,b for
H,D,Rb,Cd+,Cs,Yb+,Hg+
V=C(Ry)(me/Mp)a2+k (mq/LQCD)b ,
Dw/w=DV/V