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

• 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

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.

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.

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

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

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).

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).

BBR shift in RbBBR shift in Rb

= -1.255(4) 10-14

Uncertainty estimateUncertainty estimate

How to determine theoretical uncertainty?

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

(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

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.

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)

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.

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)

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

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.

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).

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)

( )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

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)

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

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.