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![Page 1: Blackbody radiation shifts and magic wavelengths for atomic clock research IEEE-IFCS 2010, Newport Beach, CA June 2, 2010 Marianna Safronova 1, M.G. Kozlov.](https://reader035.fdocuments.net/reader035/viewer/2022062516/56649d375503460f94a0fcb2/html5/thumbnails/1.jpg)
Blackbody radiation shifts and magic wavelengths for atomic clock
research
Blackbody radiation shifts and magic wavelengths for atomic clock
research
IEEE-IFCS 2010, Newport Beach, CA IEEE-IFCS 2010, Newport Beach, CA June 2, 2010
Marianna SafronovaMarianna Safronova11, M.G. Kozlov, M.G. Kozlov1,21,2, , Dansha JiangDansha Jiang11, and U.I. Safronova, and U.I. Safronova33
1University of Delaware, USA2PNPI, Gatchina, Russia
3University of Nevada, Reno, USA
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• Black-body radiation shifts
• Microwave vs. Optical transitions
• BBR shift in Rb frequency standard• How to calculate its uncertainty?
• Development of new methodology for precision
calculations of Group II-type system properties
• Polarizabilities
• Magic wavelengths
OutlineOutline
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Blackbody radiation shiftsBlackbody radiation shifts
T = 300 K
Clocktransition
Level A
Level B
BBRT = 0 K
Transition frequency should be corrected to account for the effect of the black body radiation at T=300K.
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atomic clocksblack-body radiation ( BBR ) shift
atomic clocksblack-body radiation ( BBR ) shift
Motivation:
BBR shift gives large contribution into uncertainty budget for some of the atomic clock schemes.
Accurate calculations are needed to achieve ultimate precision goals.
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BBR shift and polarizabilityBBR shift and polarizability
BBR shift of atomic level can be expressed in terms of a scalar static polarizability to a good approximation [1]:
[1] Sergey Porsev and Andrei Derevianko, Physical Review A 74, 020502R (2006)
42
BBR 0
1 ( )(0)(831.9 / ) (1+ )
2 300
T KV m
Dynamic correction is generally small. Multipolar corrections (M1 and E2) are suppressed by 2 [1].
Vector & tensor polarizability average out due to the isotropic nature of field.
Dynamic correctionDynamic correction
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microWave transitionsmicroWave transitions optical transitionsoptical transitions
4d5/2
Sr+
Lowest-order polarizability
2
0 1
3(2 1)vnv n v
n D v
j E E
5s1/2
Cs
6s F=3
6s F=4
In lowest (second) order the polarizabilities of ground hyperfine 6s1/2 F=4 and F=3 states are the same.
Therefore, the third-order F-dependent polarizability F (0) has to be calculated.
(1) (1) (1) 2, ,DDT DT D T D terms
2D term
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BBR shifts for microwave transitionsBBR shifts for microwave transitions
Atom Transition Method Ref. 7Li 2s (F=2 – F=1) LCCSD[pT] [1] -0.5017 10-14 23Na 3s (F=2 – F=1) LCCSD[pT] [7] -0.5019 10-14
39K 4s (F=2 – F=1) LCCSD[pT] [2] -1.118 10-14
87Rb 5s (F=2 – F=1) CP [3] -1.26(1) 10-14
133Cs 6s (F=3 – F=4) LCCSD[pT] [4] -1.710(6) 10-14
CP [3] -1.70(2) 10-14
Experiment [5] -1.710(3) 10-14
137Ba+ 6s (F=2 – F=1) CP [3] -0.245(2) 10-14
171Yb+ 6s (F=1 – F=0) CP [3] -0.0983 10-14
MBPT3 [6] -0.094(5) 10-14
137Hg+ 6s (F=1 – F=0) CP [3] -0.0102(5) 10-14
[1] W.R. Johnson, U.I. Safronova, A. Derevianko, and M.S. Safronova, PRA 77, 022510 (2008)[2] U.I. Safronova and M.S. Safronova, PRA 78, 052504 (2008)[3] E. J. Angstmann, V.A. Dzuba, and V.V. Flambaum, PRA 74, 023405 (2006)[4] K. Beloy, U.I. Safronova, and A. Derevianko, PRL 97, 040801 (2006)[5] E. Simon, P. Laurent, and A. Clairon, PRA 57, 426 (1998)[6] U.I. Safronova and M.S. Safronova, PRA 79, 022510 (2009)[7] M. S. Safronova et al., IEEE - TUFFC 57, 94 (2010).
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BBR shifts for microwave transitionsBBR shifts for microwave transitions
Atom Transition Method Ref. 7Li 2s (F=2 – F=1) LCCSD[pT] [1] -0.5017 10-14 23Na 3s (F=2 – F=1) LCCSD[pT] [7] -0.5019 10-14
39K 4s (F=2 – F=1) LCCSD[pT] [2] -1.118 10-14
87Rb 5s (F=2 – F=1) CP [3] -1.26(1) 10-14
LCCSD[pT] Present -1.255(4) 10-14
133Cs 6s (F=3 – F=4) LCCSD[pT] [4] -1.710(6) 10-14
CP [3] -1.70(2) 10-14
Experiment [5] -1.710(3) 10-14
137Ba+ 6s (F=2 – F=1) CP [3] -0.245(2) 10-14
171Yb+ 6s (F=1 – F=0) CP [3] -0.0983 10-14
MBPT3 [6] -0.094(5) 10-14
137Hg+ 6s (F=1 – F=0) CP [3] -0.0102(5) 10-14
[1] W.R. Johnson, U.I. Safronova, A. Derevianko, and M.S. Safronova, PRA 77, 022510 (2008)[2] U.I. Safronova and M.S. Safronova, PRA 78, 052504 (2008)[3] E. J. Angstmann, V.A. Dzuba, and V.V. Flambaum, PRA 74, 023405 (2006)[4] K. Beloy, U.I. Safronova, and A. Derevianko, PRL 97, 040801 (2006)[5] E. Simon, P. Laurent, and A. Clairon, PRA 57, 426 (1998)[6] U.I. Safronova and M.S. Safronova, PRA 79, 022510 (2009)[7] M. S. Safronova et al., IEEE - TUFFC 57, 94 (2010).
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BBR shift in RbBBR shift in Rb
= -1.255(4) 10-14
Uncertainty estimateUncertainty estimate
How to determine theoretical uncertainty?
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BBR shift in RbBBR shift in Rb
(3) (3) 10 22 1
1(0) (0) 1.240(4) 10 Hz/(V/m)
2s F Fk
= -1.255(4) 10-14
Scalar Stark shift coefficient
Uncertainty estimateUncertainty estimate
How to determine theoretical uncertainty?4
3 0
0
4( )
15 s
Tk
v
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(3) (0) ( , , ) 2F vC j F I T C R
The third-order static scalar electric-dipole polarizability of the hyperfine level F can be written as:
Coefficient Each term involves sums with two electric-dipole and one hyperfine matrix element. The summations in these terms range over core, valence bound and continuum states.
Third-order polarizability calcualtionThird-order polarizability calcualtion
(1)
5 5 5
5 5
( )( )n m mp s ns s
s D mp mp D ns ns T sT A
E E E E
Electric-dipole matrix elements Hyperfine matrix elements
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Sources of uncertaintiesSources of uncertainties
Strategy: dominant terms (m, n=5-12) are calculated with ``best set’’ matrix elements and experimental energies. The remaining terms are calculated in Dirac-Hartree-Fock approximation.
Uncertainty calculation:
(1) Uncertainty of each of the157 matrix elements contributing to dominant terms is estimated.
(2) Uncertainties in all remainders are evaluated.
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157 “Best-set” matrix elements157 “Best-set” matrix elements
Relativistic all-order matrix elements or experimental data
(1)
(1)
, 5 12, 5 12
5 , 5 12
, 5 7, 5 7
j
jj
mp D ns m n
ns T s n
mp T np m n
Transition Value Transition Value Transition Value
5s – 5p1/2 4.231(3) 5s – 6p1/2 0.325(9) 5s – 7p1/2 0.115(3)
6s – 5p1/2 4.146(27) 6s – 6p1/2 9.75(6) 6s – 7p1/2 0.993(7)
7s – 5p1/2 0.953(2) 7s – 6p1/2 9.21(2) 7s – 7p1/2 16.93(9)
8s – 5p1/2 0.502(2) 8s – 6p1/2 1.862(8) 8s – 7p1/2 16.00(2)
9s – 5p1/2 0.331(1) 9s – 6p1/2 0.936(5) 9s – 7p1/2 3.00(2)
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Uncertainty of the remainders: Term T Uncertainty of the remainders: Term T
5m 5
()n m
T
fast convergence
6n
slow convergence
6 12
5 12
n
m
13n 15% of the term T
DHF approximation is determined to be accurate to 4% by comparing accurate results for main terms with DHF values.
Therefore, we adjust the DHF tail by 4%.Entire adjustment (4%) is taken to be uncertainty in the tail.
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Blackbody radiation shifts in optical frequency standards:
(1) monovalent systems(2) divalent systems(3) other, more complicated systems
Blackbody radiation shifts in optical frequency standards:
(1) monovalent systems(2) divalent systems(3) other, more complicated systems
+1/2 5/2
+1/2 5/2
+1/2 5/2
+1/2 5/2
C (4 3 )
S (5 4 )
B (6 5 )
R (7 6 )
a s d
r s d
a s d
a s d
Mg, Ca, Zn, Cd, Sr, Al+, In+, Yb, Hg ( ns2 1S0
– nsnp 3P)
Hg+ (5d 106s – 5d 96s2)Yb+ (4f 146s – 4f 136s2)
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GOAL of the present project:
calculate properties of group II
atoms with precision comparable
to alkali-metal atoms
GOAL of the present project:
calculate properties of group II
atoms with precision comparable
to alkali-metal atoms
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Configuration interaction +all-order method
Configuration interaction +all-order method
CI works for systems with many valence electrons but can not accurately account for core-valenceand core-core correlations.
All-order (coupled-cluster) method can not accurately describe valence-valence correlation for large systems but accounts well for core-core and core-valence correlations.
Therefore, two methods are combined to Therefore, two methods are combined to acquire benefits from both approaches. acquire benefits from both approaches.
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CI + ALL-ORDER RESULTSCI + ALL-ORDER RESULTS
Atom CI CI + MBPT CI + All-order
Mg 1.9% 0.11% 0.03%Ca 4.1% 0.7% 0.3%Zn 8.0% 0.7% 0.4 %Sr 5.2% 1.0% 0.4%Cd 9.6% 1.4% 0.2%Ba 6.4% 1.9% 0.6%Hg 11.8% 2.5% 0.5%Ra 7.3% 2.3% 0.67%
Two-electron binding energies, differences with experiment
Development of a configuration-interaction plus all-order method for atomic calculations, M.S. Safronova, M. G. Kozlov, W.R. Johnson, Dansha Jiang, Phys. Rev. A 80, 012516 (2009).
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Cd, Zn, and Sr Polarizabilities, preliminary results (a.u.)
Zn CI CI+MBPT CI + All-order
4s2 1S0 46.2 39.45 39.28
4s4p 3P0 77.9 69.18 67.97
Cd CI CI+MBPT CI+All-order
5s2 1S0 59.2 45.82 46.55
5s5p 3P0 91.2 76.75 76.54
*From expt. matrix elements, S. G. Porsev and A. Derevianko, PRA 74, 020502R (2006).
Sr CI +MBPT CI+all-order Recomm.*
5s2 1S0 195.6 198.0 197.2(2)
5s5p 3P0 483.6 459.4 458.3(3.6)
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( )U
Magic wavelength magic is the wavelength for which the optical potential U experienced by an atom is independent on its state
Magic wavelength magic is the wavelength for which the optical potential U experienced by an atom is independent on its state
Atom in state A sees potential UA
Atom in state B sees potential UB
magic wavelengthmagic wavelength
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Cd, Zn, Sr, and Hg magic wavelengths, preliminary results (nm)
Sr Present Expt. [1]813.45 813.42735(40)
PresentCd 423(4)Zn 414(5)
Present Theory [2]Hg 365(5) 360
[1] A. D. Ludlow et al., Science 319, 1805 (2008)[2] H. Hachisu et al., Phys. Rev. Lett. 100, 053001 (2008)
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Summary of the fractional uncertainties due to BBR shift and the fractional error in the absolute transition frequency induced by the BBR shift uncertainty at
T = 300 K in various frequency standards.
M. S. Safronova et al., IEEE - TUFFC 57, 94 (2010).
510-17Present
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ConclusionConclusion
I. New BBR shift result for Rb frequency standard is presented.
The new value is accurate to 0.3%.
II. Development of new method for calculating atomic properties of divalent and more complicated systems is reported (work in progress).
• Improvement over best present approaches is demonstrated.
• Preliminary results for Mg, Zn, Cd, and Sr polarizabilities are presented.
• Preliminary results for magic wavelengths in Cd, Zn, and Hg are presented.