ATOMIC POLARIZABILITIESATOMIC POLARIZABILITIESmsafrono/Talks/ICCMSE2010.pdfATOMIC DIPOLE POLARIZABILITYATOMIC DIPOLE POLARIZABILITY The advent of cold-atom physics owes its existence

ATOMIC POLARIZABILITIESATOMIC POLARIZABILITIESATOMIC POLARIZABILITIESATOMIC POLARIZABILITIESATOMIC POLARIZABILITIESATOMIC POLARIZABILITIESATOMIC POLARIZABILITIESATOMIC POLARIZABILITIES

ICCMSE 2010, KOS, GREECEICCMSE 2010, KOS, GREECEICCMSE 2010, KOS, GREECEICCMSE 2010, KOS, GREECEICCMSE 2010, KOS, GREECEICCMSE 2010, KOS, GREECEICCMSE 2010, KOS, GREECEICCMSE 2010, KOS, GREECE

October 4, 2010

Marianna Marianna Marianna Marianna Marianna Marianna Marianna Marianna SafronovaSafronovaSafronovaSafronovaSafronovaSafronovaSafronovaSafronova

• Atomic Dipole Polarizability

• Applications

• Atomic clocks

• Cooling and trapping of atoms

• Other applications

• Methods for calculation of atomic polarizabilities

• Summary of high-precision results

• How to determine theoretical uncertainties

• Development of combined CI + RLCCSD(T) method

OUTLINEOUTLINEOUTLINEOUTLINEOUTLINEOUTLINEOUTLINEOUTLINE

ATOMIC DIPOLE POLARIZABILITYATOMIC DIPOLE POLARIZABILITYATOMIC DIPOLE POLARIZABILITYATOMIC DIPOLE POLARIZABILITYATOMIC DIPOLE POLARIZABILITYATOMIC DIPOLE POLARIZABILITYATOMIC DIPOLE POLARIZABILITYATOMIC DIPOLE POLARIZABILITY

The advent of cold-atom physics owes its existence to the ability to manipulate

groups of atoms with electromagnetic

fields.

Many topics in the area of field-atom

interactions have recently been the subject of considerable interest and

heightened importance.

Electric-dipole polarizability governs the first-order response of an atom to an applied electric field.

( )U α λ∝

ATOMIC DIPOLE POLARIZABILITYATOMIC DIPOLE POLARIZABILITYATOMIC DIPOLE POLARIZABILITYATOMIC DIPOLE POLARIZABILITYATOMIC DIPOLE POLARIZABILITYATOMIC DIPOLE POLARIZABILITYATOMIC DIPOLE POLARIZABILITYATOMIC DIPOLE POLARIZABILITY

The interaction of field E directed along z-axis with the atom

is described by the Hamiltonian

ext ij i j

ij

H e z a a++++= −= −= −= − ∑∑∑∑E

First-order correction to the wave function satisfies

(((( )))) (1)

0 extH V E H+ − Ψ = − Ψ+ − Ψ = − Ψ+ − Ψ = − Ψ+ − Ψ = − Ψ

where . (((( ))))0H V E+ Ψ = Ψ+ Ψ = Ψ+ Ψ = Ψ+ Ψ = Ψ

(2) (1) 2 21

2ext

E H e αααα= Ψ Ψ = −= Ψ Ψ = −= Ψ Ψ = −= Ψ Ψ = − E

SUMSUMSUMSUM----OVEROVEROVEROVER----STATES METHODSTATES METHODSTATES METHODSTATES METHODSUMSUMSUMSUM----OVEROVEROVEROVER----STATES METHODSTATES METHODSTATES METHODSTATES METHOD

(((( ))))0 2

gn

nn g

f

E Eαααα ====

−−−−∑∑∑∑

Example: scalar static electric-dipole polarizability

Absorption oscillator strength

Mixed approach:

(1) Get polarizability by direct solution method

(2) Extract the most important terms using the sum over states

(3) Replace these terms using the most accurate available data

APPLICATIONS OF APPLICATIONS OF APPLICATIONS OF APPLICATIONS OF

ATOMIC POLARIZABILITIESATOMIC POLARIZABILITIESATOMIC POLARIZABILITIESATOMIC POLARIZABILITIES

(1) Atomic clocks

(2) Cooling & trapping of atoms

(3) Other applications

APPLICATIONS OF APPLICATIONS OF APPLICATIONS OF APPLICATIONS OF


(1) Atomic clocks

(2) Cooling & trapping of atoms

(3) Other applications

ATOMIC CLOCKSATOMIC CLOCKSATOMIC CLOCKSATOMIC CLOCKSATOMIC CLOCKSATOMIC CLOCKSATOMIC CLOCKSATOMIC CLOCKS

Microwave

Transitions

Optical

Transitions

Blackbody Radiation Shifts and Theoretical Contributions to Atomic Clock Research, M. S. Safronova, Dansha Jiang, Bindiya Arora, Charles W. Clark, M. G. Kozlov, U. I. Safronova, and W. R. Johnson, Special Issue of IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control 57, 94 (2010).

MOTIATION: NEXT MOTIATION: NEXT MOTIATION: NEXT MOTIATION: NEXT

GENERATION ATOMIC CLOCKSGENERATION ATOMIC CLOCKSGENERATION ATOMIC CLOCKSGENERATION ATOMIC CLOCKS

MOTIATION: NEXT MOTIATION: NEXT MOTIATION: NEXT MOTIATION: NEXT

GENERATION ATOMIC CLOCKSGENERATION ATOMIC CLOCKSGENERATION ATOMIC CLOCKSGENERATION ATOMIC CLOCKS

Next - generation ultra precise atomic clock

Atoms trapped by laser light

http://CPEPweb.org

The ability to develop more precise optical frequency

standards will open ways to improve global positioningsystem (GPS) measurements and tracking of deep-space

probes, perform more accurate measurements of the physical constants and tests of fundamental physics such as

searches for gravitational waves, etc.

ATOMIC CLOCKS AND VARIATION OF ATOMIC CLOCKS AND VARIATION OF ATOMIC CLOCKS AND VARIATION OF ATOMIC CLOCKS AND VARIATION OF

FUNDAMENTAL CONSTANTS FUNDAMENTAL CONSTANTS FUNDAMENTAL CONSTANTS FUNDAMENTAL CONSTANTS

ATOMIC CLOCKS AND VARIATION OF ATOMIC CLOCKS AND VARIATION OF ATOMIC CLOCKS AND VARIATION OF ATOMIC CLOCKS AND VARIATION OF

FUNDAMENTAL CONSTANTS FUNDAMENTAL CONSTANTS FUNDAMENTAL CONSTANTS FUNDAMENTAL CONSTANTS

(1) Astrophysical constraints on variation of α: 4σ4σ4σ4σ!

Study of quasar absorption spectra

Changes in isotopic abundances mimic shift of α

(2) Laboratory atomic clock experiments:

Compare rates of different clocks over long

period of time to study time variation of

fundamental constants

Need: ultra precise clocks!

ATOMIC CLOCKS AND POLARIZABILITYATOMIC CLOCKS AND POLARIZABILITYATOMIC CLOCKS AND POLARIZABILITYATOMIC CLOCKS AND POLARIZABILITYATOMIC CLOCKS AND POLARIZABILITYATOMIC CLOCKS AND POLARIZABILITYATOMIC CLOCKS AND POLARIZABILITYATOMIC CLOCKS AND POLARIZABILITY

(1) Magic Wavelengths

(2) Blackbody Radiation Shift

MAGIC WAVELENGTHMAGIC WAVELENGTHMAGIC WAVELENGTHMAGIC WAVELENGTHMAGIC WAVELENGTHMAGIC WAVELENGTHMAGIC WAVELENGTHMAGIC WAVELENGTH

Atom in state A sees potential UA

Atom in state Bsees potential UB

( )U α λ∝

Magic wavelength λmagic is the wavelength for which the optical potential U experienced

by an atom is independent on its state

Magic wavelength λmagic is the wavelength for which the optical potential U experienced

by an atom is independent on its state

m agicλλλλ

wavelength

αα αα(λ

)(λ

)(λ

)(λ

)

State B

State A

LOCATING MAGIC WAVELENGTHLOCATING MAGIC WAVELENGTHLOCATING MAGIC WAVELENGTHLOCATING MAGIC WAVELENGTHLOCATING MAGIC WAVELENGTHLOCATING MAGIC WAVELENGTHLOCATING MAGIC WAVELENGTHLOCATING MAGIC WAVELENGTH

BLACKBODY RADIATION SHIFTBLACKBODY RADIATION SHIFTBLACKBODY RADIATION SHIFTBLACKBODY RADIATION SHIFTBLACKBODY RADIATION SHIFTBLACKBODY RADIATION SHIFTBLACKBODY RADIATION SHIFTBLACKBODY RADIATION SHIFT

T = 300 KT = 300 KT = 300 KT = 300 K

CLOCKCLOCKCLOCKCLOCK

TRANSITIONTRANSITIONTRANSITIONTRANSITION

LEVEL ALEVEL ALEVEL ALEVEL A

LEVEL BLEVEL BLEVEL BLEVEL B

∆BBRT = 0 KT = 0 KT = 0 KT = 0 K

Transition frequency should be corrected to account for the effect of the black body radiation at T=300K.

• The temperature-dependent electric field

created by the blackbody radiation is described

by (in a.u.) :

BBR SHIFT OF A LEVELBBR SHIFT OF A LEVELBBR SHIFT OF A LEVELBBR SHIFT OF A LEVELBBR SHIFT OF A LEVELBBR SHIFT OF A LEVELBBR SHIFT OF A LEVELBBR SHIFT OF A LEVEL

32 8( )

exp( / ) 1

dE

kT

α ω ωω

π ω=

−

2

BBR ( ) ( ) v A E dα ω ω ω∆ = − × ∫

Dynamic polarizability

• Frequency shift caused by this electric field is:

BBR SHIFT AND POLARIZABILITYBBR SHIFT AND POLARIZABILITYBBR SHIFT AND POLARIZABILITYBBR SHIFT AND POLARIZABILITYBBR SHIFT AND POLARIZABILITYBBR SHIFT AND POLARIZABILITYBBR 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)

4

2

BBR 0

1 ( )(0)(831.9 / ) (1+ )

2 300

T KV mν α η

∆ = −

Dynamic correction is generally small.

Multipolar corrections (M1 and E2) are suppressed by a2 [1].

VECTOR & TENSOR POLARIZABILITY AVERAGE

OUT DUE TO THE ISOTROPIC NATURE OF FIELD.

Dynamic correctionDynamic correction

BLACKBODY RADIATION SHIFTS IN BLACKBODY RADIATION SHIFTS IN BLACKBODY RADIATION SHIFTS IN BLACKBODY RADIATION SHIFTS IN

OPTICAL FREQUENCY STANDARDS:OPTICAL FREQUENCY STANDARDS:OPTICAL FREQUENCY STANDARDS:OPTICAL FREQUENCY STANDARDS:

(1) (1) (1) (1) MONOVALENTMONOVALENTMONOVALENTMONOVALENT SYSTEMSSYSTEMSSYSTEMSSYSTEMS

(2) DIVALENT SYSTEMS(2) DIVALENT SYSTEMS(2) DIVALENT SYSTEMS(2) DIVALENT SYSTEMS

(3) OTHER, MORE COMPLICATED SYSTEMS(3) OTHER, MORE COMPLICATED SYSTEMS(3) OTHER, MORE COMPLICATED SYSTEMS(3) OTHER, MORE COMPLICATED SYSTEMS

BLACKBODY RADIATION SHIFTS IN BLACKBODY RADIATION SHIFTS IN BLACKBODY RADIATION SHIFTS IN BLACKBODY RADIATION SHIFTS IN

OPTICAL FREQUENCY STANDARDS:OPTICAL FREQUENCY STANDARDS:OPTICAL FREQUENCY STANDARDS:OPTICAL FREQUENCY STANDARDS:

(1) (1) (1) (1) MONOVALENTMONOVALENTMONOVALENTMONOVALENT SYSTEMSSYSTEMSSYSTEMSSYSTEMS

(2) DIVALENT SYSTEMS(2) DIVALENT SYSTEMS(2) DIVALENT SYSTEMS(2) DIVALENT SYSTEMS

(3) OTHER, MORE COMPLICATED SYSTEMS(3) OTHER, MORE COMPLICATED SYSTEMS(3) OTHER, MORE COMPLICATED 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)

S1/2

P1/2

D5/2

Quantum

bit

Quantum Computer

(Innsbruck)

StateStateStateState----insensitive cooling insensitive cooling insensitive cooling insensitive cooling

and trapping for and trapping for and trapping for and trapping for

quantum information quantum information quantum information quantum information

processingprocessingprocessingprocessing

COOLING AND TRAPPING OF COOLING AND TRAPPING OF COOLING AND TRAPPING OF COOLING AND TRAPPING OF

NEUTRAL ATOMSNEUTRAL ATOMSNEUTRAL ATOMSNEUTRAL ATOMS

COOLING AND TRAPPING OF COOLING AND TRAPPING OF COOLING AND TRAPPING OF COOLING AND TRAPPING OF

NEUTRAL ATOMSNEUTRAL ATOMSNEUTRAL ATOMSNEUTRAL ATOMS

Atom in state A sees potential UA

Atom in state Bsees potential UB

λ λ λ λ (nm)

925 930 935 940 945 950 955

αα αα (a.u.)

0

2000

4000

6000

8000

10000

6S1/26P3/2

932 nm

938 nm

a0- a2

a0+ a2

λλλλmagic

0 2vα α αα α αα α αα α α= += += += + MJ = ±3/2

MJ = ±1/20 2vα α αα α αα α αα α α= −= −= −= −

Other*Other*

λλλλmagic around 935nm

* Kimble et al. PRL 90(13), 133602(2003)

MAGIC WAVELENGTH FOR CSMAGIC WAVELENGTH FOR CSMAGIC WAVELENGTH FOR CSMAGIC WAVELENGTH FOR CSMAGIC WAVELENGTH FOR CSMAGIC WAVELENGTH FOR CSMAGIC WAVELENGTH FOR CSMAGIC WAVELENGTH FOR CS

Magic wavelengths for the ns-np transitions in alkali-metal atoms, Bindiya Arora,

M.S. Safronova, and C. W. Clark, Phys. Rev. A 76, 052509 (2007).

OTHER APPLICATIONSOTHER APPLICATIONSOTHER APPLICATIONSOTHER APPLICATIONSOTHER APPLICATIONSOTHER APPLICATIONSOTHER APPLICATIONSOTHER APPLICATIONS

• Quantum computing with Rydberg atoms

• Cold degenerate gases

• Study of fundamental symmetries

• Thermometry and other macroscopic standards

• Benchmark tests of theory and experiment

• Atomic transition rate determinations

CURRENT STATUS OF CURRENT STATUS OF CURRENT STATUS OF CURRENT STATUS OF

THEORY AND EXPERIMENTTHEORY AND EXPERIMENTTHEORY AND EXPERIMENTTHEORY AND EXPERIMENT

ATOMIC DIPOLE POLARIZABILITIESATOMIC DIPOLE POLARIZABILITIESATOMIC DIPOLE POLARIZABILITIESATOMIC DIPOLE POLARIZABILITIES

CURRENT STATUS OF CURRENT STATUS OF CURRENT STATUS OF CURRENT STATUS OF

THEORY AND EXPERIMENTTHEORY AND EXPERIMENTTHEORY AND EXPERIMENTTHEORY AND EXPERIMENT

ATOMIC DIPOLE POLARIZABILITIESATOMIC DIPOLE POLARIZABILITIESATOMIC DIPOLE POLARIZABILITIESATOMIC DIPOLE POLARIZABILITIES

JPB TOPICAL REVIEW (2010):

Theory and applications of atomic and ionic polarizabilities,

J. Mitroy, M.S. Safronova, and Charles W. Clark, in press

SUMMARY OF THEORY METHODS FOR SUMMARY OF THEORY METHODS FOR SUMMARY OF THEORY METHODS FOR SUMMARY OF THEORY METHODS FOR




• Configuration interaction (CI)

• CI calculations with a semi-empirical core potential (CICP)

• Density functional theory• Correlated basis functions (Hyl.,ECG)

• Many-body perturbation theory (MBPT)• Coupled-cluster methods (CCSDT)

• Correlation - potential method

• Configuration interaction + second-order MBPT (CI+MBPT)

• Configuration interaction + coupled-cluster method*

*under development

ATOMIC POLARIZABILITIES:ATOMIC POLARIZABILITIES:ATOMIC POLARIZABILITIES:ATOMIC POLARIZABILITIES:ATOMIC POLARIZABILITIES:ATOMIC POLARIZABILITIES:ATOMIC POLARIZABILITIES:ATOMIC POLARIZABILITIES:

HOW ACCURATE ARE THEORY VALUES HOW ACCURATE ARE THEORY VALUES HOW ACCURATE ARE THEORY VALUES HOW ACCURATE ARE THEORY VALUES HOW ACCURATE ARE THEORY VALUES HOW ACCURATE ARE THEORY VALUES HOW ACCURATE ARE THEORY VALUES HOW ACCURATE ARE THEORY VALUES ??

c vc vα α α αα α α αα α α αα α α α= + += + += + += + +

Core term

Valence term

(dominant)

Compensation term

2

0 1

3(2 1)v

nv n v

n D v

j E Eαααα ====

+ −+ −+ −+ −∑∑∑∑

Example:Scalar dipole polarizability

Electric-dipole reduced matrix element

POLARIZABILITY OF AN ALKALI ATOM IN A STATEPOLARIZABILITY OF AN ALKALI ATOM IN A STATEPOLARIZABILITY OF AN ALKALI ATOM IN A STATEPOLARIZABILITY OF AN ALKALI ATOM IN A STATE vSum-over-states approach

POLARIZABILITY OF AN ALKALI ATOM IN A STATEPOLARIZABILITY OF AN ALKALI ATOM IN A STATEPOLARIZABILITY OF AN ALKALI ATOM IN A STATEPOLARIZABILITY OF AN ALKALI ATOM IN A STATE vSum-over-states approach

HOW TO ESTIMATE UNCERTAINTY OF HOW TO ESTIMATE UNCERTAINTY OF HOW TO ESTIMATE UNCERTAINTY OF HOW TO ESTIMATE UNCERTAINTY OF HOW TO ESTIMATE UNCERTAINTY OF HOW TO ESTIMATE UNCERTAINTY OF HOW TO ESTIMATE UNCERTAINTY OF HOW TO ESTIMATE UNCERTAINTY OF

A MATRIX ELEMENT A MATRIX ELEMENT A MATRIX ELEMENT A MATRIX ELEMENT A MATRIX ELEMENT A MATRIX ELEMENT A MATRIX ELEMENT A MATRIX ELEMENT ??

THEORY: EVALUATION OF THE THEORY: EVALUATION OF THE THEORY: EVALUATION OF THE THEORY: EVALUATION OF THE

UNCERTAINTYUNCERTAINTYUNCERTAINTYUNCERTAINTY

THEORY: EVALUATION OF THE THEORY: EVALUATION OF THE THEORY: EVALUATION OF THE THEORY: EVALUATION OF THE

UNCERTAINTYUNCERTAINTYUNCERTAINTYUNCERTAINTY

HOW TO ESTIMATE WHAT YOU DO NOT KNOW?HOW TO ESTIMATE WHAT YOU DO NOT KNOW?

I. Ab initio calculations in different approximations:

(a) Evaluation of the size of the correlation corrections

(b) Importance of the high-order contributions(c) Distribution of the correlation correction

II. Semi-empirical scaling: estimate missing terms

EXAMPLE:EXAMPLE:EXAMPLE:EXAMPLE:

QUADRUPOLEQUADRUPOLEQUADRUPOLEQUADRUPOLE MOMENT OF MOMENT OF MOMENT OF MOMENT OF

3D3D3D3D5/25/25/25/2 STATE IN CSTATE IN CSTATE IN CSTATE IN Ca++++

EXAMPLE:EXAMPLE:EXAMPLE:EXAMPLE:

QUADRUPOLEQUADRUPOLEQUADRUPOLEQUADRUPOLE MOMENT OF MOMENT OF MOMENT OF MOMENT OF

3D3D3D3D5/25/25/25/2 STATE IN CSTATE IN CSTATE IN CSTATE IN Ca++++

Electric quadrupole moments of metastable states of Ca+, Sr+, and Ba+, Dansha Jiang and Bindiya Arora and

M. S. Safronova, Phys. Rev. A 78, 022514 (2008)

Lowest order

2.451

3D3D3D3D5/25/25/25/2 QUADRUPOLE MOMENT IN CAQUADRUPOLE MOMENT IN CAQUADRUPOLE MOMENT IN CAQUADRUPOLE MOMENT IN CA++++3D3D3D3D5/25/25/25/2 QUADRUPOLE MOMENT IN CAQUADRUPOLE MOMENT IN CAQUADRUPOLE MOMENT IN CAQUADRUPOLE MOMENT IN CA++++

Third order

1.610

Lowest order

2.451


All order (SD)

1.785

Third order

1.610

Lowest order

2.451


All order (SDpT)

1.837

All order (SD)

1.785

Third order

1.610

Lowest order

2.451


Coupled-cluster SD (CCSD)

1.822

All order (SDpT)

1.837

All order (SD)

1.785

Third order

1.610

Lowest order

2.451


Coupled-cluster SD (CCSD)

1.822

All order (SDpT)

1.837

All order (SD)

1.785

Third order

1.610

Lowest order

2.451


Estimateomittedcorrections

All order (SD), scaled 1.849All-order (CCSD), scaled 1.851All order (SDpT) 1.837All order (SDpT), scaled 1.836

Third order

1.610

Final results: 3d5/2 quadrupole momentFinal results: 3d5/2 quadrupole moment

Lowest order

2.454

1.849 (13)1.849 (13)

All order (SD), scaled 1.849All-order (CCSD), scaled 1.851All order (SDpT) 1.837All order (SDpT), scaled 1.836

Third order

1.610

Final results: 3d5/2 quadrupole momentFinal results: 3d5/2 quadrupole moment

Lowest order

2.454

1.849 (13)1.849 (13)

Experiment1.83(1)

Experiment1.83(1)

Experiment: C. F. Roos, M. Chwalla, K. Kim, M. Riebe, and R. Blatt, Nature 443, 316 (2006).

DEVELOPMENT OF HIGHDEVELOPMENT OF HIGHDEVELOPMENT OF HIGHDEVELOPMENT OF HIGH----PRECISION PRECISION PRECISION PRECISION

METHODSMETHODSMETHODSMETHODS

PRESENT STATUS OF THEORY ANDPRESENT STATUS OF THEORY ANDPRESENT STATUS OF THEORY ANDPRESENT STATUS OF THEORY AND

NEED FOR FURTHER DEVELOPMENTNEED FOR FURTHER DEVELOPMENTNEED FOR FURTHER DEVELOPMENTNEED FOR FURTHER DEVELOPMENT

DEVELOPMENT OF HIGHDEVELOPMENT OF HIGHDEVELOPMENT OF HIGHDEVELOPMENT OF HIGH----PRECISION PRECISION PRECISION PRECISION

METHODSMETHODSMETHODSMETHODS

PRESENT STATUS OF THEORY ANDPRESENT STATUS OF THEORY ANDPRESENT STATUS OF THEORY ANDPRESENT STATUS OF THEORY AND

NEED FOR FURTHER DEVELOPMENTNEED FOR FURTHER DEVELOPMENTNEED FOR FURTHER DEVELOPMENTNEED FOR FURTHER DEVELOPMENT

Coupled-clusterCorrelation potential

CI+MBPT

Polarizabilities of excited states

• Atomic clocks

• Study of parity violation (Yb)

• Search for EDM (Ra)

• Degenerate quantum gases,

alkali-group II mixtures

• Quantum information

• Variation of fundamental constants

MOTIVATION: MOTIVATION: MOTIVATION: MOTIVATION:

STUDY OF GROUP II STUDY OF GROUP II STUDY OF GROUP II STUDY OF GROUP II –––– TYPE SYSTEMSTYPE SYSTEMSTYPE SYSTEMSTYPE SYSTEMS

MOTIVATION: MOTIVATION: MOTIVATION: MOTIVATION:

STUDY OF GROUP II STUDY OF GROUP II STUDY OF GROUP II STUDY OF GROUP II –––– TYPE SYSTEMSTYPE SYSTEMSTYPE SYSTEMSTYPE SYSTEMS

Divalent ions:Divalent ions:Divalent ions:Divalent ions:AlAlAlAl++++, In, In, In, In++++, etc., etc., etc., etc.Divalent ions:Divalent ions:Divalent ions:Divalent ions:AlAlAlAl++++, In, In, In, In++++, etc., etc., etc., etc.

Mg Mg Mg Mg Ca Ca Ca Ca SrSrSrSrBaBaBaBaRaRaRaRaZnZnZnZnCdCdCdCdHgHgHgHgYbYbYbYb

Mg Mg Mg Mg Ca Ca Ca Ca SrSrSrSrBaBaBaBaRaRaRaRaZnZnZnZnCdCdCdCdHgHgHgHgYbYbYbYb





• Configuration interaction (CI)

• CI calculations with a semi-empirical core potential (CICP)

• Density functional theory• Correlated basis functions (Hyl.,ECG)

• Many-body perturbation theory (MBPT)• Coupled-cluster methods (CCSDT)

• Correlation - potential method

• Configuration interaction + second-order MBPT (CI+MBPT)

• Configuration interaction + all-order (RLCCSD(T) coupled-cluster) method*

*under development

CONFIGURATION INTERACTION +CONFIGURATION INTERACTION +CONFIGURATION INTERACTION +CONFIGURATION INTERACTION +

ALLALLALLALL----ORDER METHOD ORDER METHOD ORDER METHOD ORDER METHOD

CONFIGURATION INTERACTION +CONFIGURATION INTERACTION +CONFIGURATION INTERACTION +CONFIGURATION INTERACTION +

ALLALLALLALL----ORDER METHOD ORDER METHOD ORDER METHOD ORDER METHOD

CI works for systems with many valence electrons

but can not accurately account for core-valence

and 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.

CONFIGURATION INTERACTION CONFIGURATION INTERACTION CONFIGURATION INTERACTION CONFIGURATION INTERACTION

METHODMETHODMETHODMETHOD


METHODMETHODMETHODMETHOD

i i

i

cΨ = Φ∑ Single-electron valence

basis states

( ) 0effH E− Ψ =

1 1 1 2 2 1 2( ) ( ) ( , )eff

one bodypart

two bodypart

H h r h r h r r

− −

= + +��

Example: two particle system: 1 2

1

−r r


METHOD + ALLMETHOD + ALLMETHOD + ALLMETHOD + ALL----ORDERORDERORDERORDER


METHOD + ALLMETHOD + ALLMETHOD + ALLMETHOD + ALL----ORDERORDERORDERORDER

1 1 1

2 2 2

1 2,

h h

h h

→ + Σ

→ + Σ

Σ Σ

Heff is modified using all-order calculation

are obtained using all-order, RLCCSD(T),

method used for alkali-metal atoms with

appropriate modifications

( ) 0effH E− Ψ =

In the all-order method, dominant correlation corrections are summed to all orders of perturbation theory.

Lowest order Corecorevalence electron any excited orbital

Single-particle excitations

Double-particle excitations

(0)

vΨ

(0)† †

mn m nm

a av vna

vaa a aρ Ψ∑

† (0)

a aa

m mm

va aρ Ψ∑ † (0)

v v vv

m mm

a aρ≠

Ψ∑

† † (0)12 m nmn

mab b v

na

ab

aa aaρ Ψ∑

RLCCSDRLCCSDRLCCSDRLCCSD ATOMIC WAVE FUNCTION ATOMIC WAVE FUNCTION ATOMIC WAVE FUNCTION ATOMIC WAVE FUNCTION RLCCSDRLCCSDRLCCSDRLCCSD ATOMIC WAVE FUNCTION ATOMIC WAVE FUNCTION ATOMIC WAVE FUNCTION ATOMIC WAVE FUNCTION

MONOVALENTMONOVALENTMONOVALENTMONOVALENT SYSTEMS: SYSTEMS: SYSTEMS: SYSTEMS:

VERY BRIEF SUMMARY OF WHAT WEVERY BRIEF SUMMARY OF WHAT WEVERY BRIEF SUMMARY OF WHAT WEVERY BRIEF SUMMARY OF WHAT WE

CALCULATED WITH ALLCALCULATED WITH ALLCALCULATED WITH ALLCALCULATED WITH ALL----ORDER METHODORDER METHODORDER METHODORDER METHOD

MONOVALENTMONOVALENTMONOVALENTMONOVALENT SYSTEMS: SYSTEMS: SYSTEMS: SYSTEMS:

VERY BRIEF SUMMARY OF WHAT WEVERY BRIEF SUMMARY OF WHAT WEVERY BRIEF SUMMARY OF WHAT WEVERY BRIEF SUMMARY OF WHAT WE

CALCULATED WITH ALLCALCULATED WITH ALLCALCULATED WITH ALLCALCULATED WITH ALL----ORDER METHODORDER METHODORDER METHODORDER METHOD

Properties

• Energies• Transition matrix elements (E1, E2, E3, M1) • Static and dynamic polarizabilities & applications

Dipole (scalar and tensor) Quadrupole, OctupoleLight shiftsBlack-body radiation shiftsMagic wavelengths

• Hyperfine constants• C3 and C6 coefficients• Parity-nonconserving amplitudes (derived weak charge and anapole moment)

• Isotope shifts (field shift and one-body part of specific mass shift)• Atomic quadrupole moments• Nuclear magnetic moment (Fr), from hyperfine data

Systems

Li, Na, Mg II, Al III, Si IV, P V, S VI, K, Ca II, In, In-like ions, Ga, Ga-like ions, Rb, Cs, Ba II, Tl, Fr, Th IV, U V, other Fr-like ions, Ra II

http://www.physics.udel.edu/~msafrono


+ + + + ALLALLALLALL----ORDERORDERORDERORDER METHODMETHODMETHODMETHOD


+ + + + ALLALLALLALL----ORDERORDERORDERORDER METHODMETHODMETHODMETHOD

Heff is modified using all-order excitation coefficients

Advantages: most complete treatment of the

correlations and applicable for many-valenceelectron systems

( ) ( )

( ) ( ) L

mnklnmlk

L

mnkl

mnmnmn

ρεεεε

ρεε

−−+=Σ

−=Σ

~~

~

2

1

CI + ALLCI + ALLCI + ALLCI + ALL----ORDER RESULTSORDER RESULTSORDER RESULTSORDER RESULTSCI + ALLCI + ALLCI + ALLCI + ALL----ORDER RESULTSORDER RESULTSORDER RESULTSORDER RESULTS

AtomAtomAtomAtom CI CI CI CI CICICICI + MBPT+ MBPT+ MBPT+ MBPT CI + AllCI + AllCI + AllCI + All----orderorderorderorderMg 1.9%Mg 1.9%Mg 1.9%Mg 1.9% 0.11%0.11%0.11%0.11% 0.03%0.03%0.03%0.03%Ca Ca Ca Ca 4.1%4.1%4.1%4.1% 0.7%0.7%0.7%0.7% 0.3%0.3%0.3%0.3%ZnZnZnZn 8.0%8.0%8.0%8.0% 0.7%0.7%0.7%0.7% 0.4 %0.4 %0.4 %0.4 %SrSrSrSr 5.2%5.2%5.2%5.2% 1.0%1.0%1.0%1.0% 0.4%0.4%0.4%0.4%CdCdCdCd 9.6% 9.6% 9.6% 9.6% 1.4%1.4%1.4%1.4% 0.2%0.2%0.2%0.2%BaBaBaBa 6.4% 6.4% 6.4% 6.4% 1.9%1.9%1.9%1.9% 0.6%0.6%0.6%0.6%HgHgHgHg 11.8%11.8%11.8%11.8% 2.5%2.5%2.5%2.5% 0.5%0.5%0.5%0.5%RaRaRaRa 7.3%7.3%7.3%7.3% 2.3%2.3%2.3%2.3% 0.67%0.67%0.67%0.67%

TwoTwoTwoTwo----electron binding energies, differences with experimentelectron binding energies, differences with experimentelectron binding energies, differences with experimentelectron 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).

SSSSr POLARIZABILITIESPOLARIZABILITIESPOLARIZABILITIESPOLARIZABILITIES

PRELIMINARY RESULTS PRELIMINARY RESULTS PRELIMINARY RESULTS PRELIMINARY RESULTS (a.u.)

* From expt. matrix elements, S. G. Porsev and A. Derevianko, PRA 74, 020502R (2006).

458.3(3.6)459.4483.65s5p 3P0

197.2(2)198.0195.65s2 1S0

Recomm.*CI + all-orderCI +MBPTSr

CONCLUSIONCONCLUSIONCONCLUSIONCONCLUSIONCONCLUSIONCONCLUSIONCONCLUSIONCONCLUSION

Development of new method for calculating atomic properties of divalent systems is reported.

• Improvement over best present approaches is demonstrated.

• Results for group II atoms from Mg to Ra are presented.

Polarizabilities are of significant importance

for various applications ranging from study of fundamental symmetries to development of more precise clocks.

Significant improvement in accuracy is needed for

polarizabilities of systems

with more than one valence electrons.

OTHER COLLABORATIONS:OTHER COLLABORATIONS:OTHER COLLABORATIONS:OTHER COLLABORATIONS:

Michael Kozlov (PNPI, Russia)(Visiting research scholar at the University of Delaware)

Walter Johnson (University of Notre Dame), Charles Clark (NIST)Jim Mitroy (Darwin), Ulyana Safronova (University of Nevada-Reno)

GRADUATEGRADUATEGRADUATEGRADUATE

STUDENTS: STUDENTS: STUDENTS: STUDENTS:

Rupsi Pal*Dansha Jiang*Bindiya Arora*Jenny Tchoukova*Z. ZhuriadnaMatt Simmons

Documents

ATOMIC POLARIZABILITIESATOMIC POLARIZABILITIESmsafrono/Talks/ICCMSE2010.pdfATOMIC DIPOLE POLARIZABILITYATOMIC DIPOLE POLARIZABILITY The advent of cold-atom physics owes its existence