Atomic calculations: recent advances and modern applications

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July 8, 2010
JQI seminar
Atomic calculations recent advances and modern
applications
Marianna Safronova
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Outline

• Selected applications of atomic calculations
• Study of fundamental symmetries
• Atomic clocks
• Optical cooling and trapping and quantum
  information
• Examples magic wavelengths
• Present status of theory
• How accurate are theory values?
• Present challenges
• Development of CIall-order method for group II
  atoms
• Future prospects

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Atomic calculations for study of fundamental
symmetries
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Transformations and symmetries
Translation Momentum conservation Translation
in time Energy conservation Rotation Conservation
of angular momentum C Charge
conjugation C-invariance P Spatial
inversion Parity conservation (P-invariance) T
Time reversal T-invariance CP CPT
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Transformations and symmetries
Translation Momentum conservation Translation
in time Energy conservation Rotation Conservation
of angular momentum C Charge
conjugation C-invariance P Spatial
inversion Parity conservation (P-invariance) T
Time reversal T-invariance CP CPT
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Parity Violation
Parity-transformed world Turn the mirror image
upside down. The parity-transformed world is
not identical with the real world.
Parity is not conserved.
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Parity violation in atoms
Nuclear spin-independent PNC Searches for new
physics beyond the Standard Model
Nuclear spin-dependent PNC Study of PNC In the
nucleus
Nuclear anapole moment
Weak Charge QW
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Standard Model

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Searches for New Physics Beyond the Standard Model
High energies
(1) Search for new processes or
particles directly (2) Study (very
precisely!) quantities which Standard Model
predicts and compare the result with its
prediction
Weak charge QW
Low energies
http//public.web.cern.ch/, Cs experiment,
University of Colorado
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The most precise measurement of PNC amplitude
(in cesium)
C.S. Wood et al. Science 275, 1759 (1997)
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0.3 accuracy
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Stark interference scheme to measure ratio of the
PNC amplitude and the Stark-induced amplitude b
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Parity violation in atoms
Nuclear spin-dependent PNC Study of PNC In the
nucleus
Nuclear spin-independent PNC Searches for new
physics beyond the Standard Model
Nuclear anapole moment
Present status agreement with the Standard Model
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Spin-dependent parity violation Nuclear anapole
moment
Valence nucleon density
Parity-violating nuclear moment
Anapole moment
Nuclear anapole moment is parity-odd,
time-reversal-even E1 moment of the
electromagnetic current operator.
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Constraints on nuclear weak coupling contants
W. C. Haxton and C. E. Wieman, Ann. Rev. Nucl.
Part. Sci. 51, 261 (2001)
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Nuclear anapole momenttest of hadronic weak
interations
The constraints obtained from the Cs experiment
were found to be inconsistent with constraints
from other nuclear PNC measurements, which favor
a smaller value of the133Cs anapole
moment. All-order (LCCSD) calculation of
spin-dependent PNC amplitude k 0.107(16)
1 theory accuracy No significant difference
with previous value k 0.112(16) is found.
Fr, Yb, Ra
NEED NEW EXPERIMENTS!!!
M.S. Safronova, Rupsi Pal, Dansha Jiang, M.G.
Kozlov, W.R. Johnson, and U.I. Safronova,
Nuclear Physics A 827 (2009) 411c
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Why do we need Atomic calculations to study
parity violation?

1. Present experiments can not be analyzed without
   theoretical value of PNC amplitude in terms of
   Qw.
2. Theoretical calculation of spin-dependent PNC
   amplitude is needed to determine anapole moment
   from experiment.
3. Other parity conserving quantities are needed.

Note need to know theoretical uncertainties!
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Transformations and symmetries
Translation Momentum conservation Translation
in time Energy conservation Rotation Conservation
of angular momentum C Charge
conjugation C-invariance P Spatial
inversion Parity conservation (P-invariance) T
Time reversal T-invariance CP CPT
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Permanent electric-dipole moment ( EDM )
Time-reversal invariance must be violated for an
elementary particle or atom to possess a
permanent EDM.
S
d
d
S
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EDM and New physics
Many theories beyond the Standard Model predict
EDM within or just beyond the present
experimental capabilities.
David DeMille, Yale PANIC 2005
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Atomic calculations and search for EDM

• EDM effects are enhanced in some heavy atoms and
  molecules.
• Theory is needed to calculate enhancement
  factors and search for new systems for EDM
  detection.
• Recent new limit on the EDM of 199Hg

d(199Hg) lt 3.1 x 10-29 e cm
Phys. Rev. Lett. 102, 101601 (2009)
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Atomic clocks

Optical Transitions
Microwave 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).
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Atomic calculations more precise clocks

• Prediction of atomic properties required for new
  clock proposals
• New clock proposals require both estimation of
  the atomic properties for details of the
  proposals (transition rates, lifetimes, branching
  rations, magic wavelength, scattering rates,
  etc.) and evaluation of the systematic shifts
  (Zeeman shift, electric quadruple shift,
  blackbody radiation shift, ac Stark shifts due to
  various lasers fields, etc.).
• (2)Determination of the quantities contributing
  to the uncertainty budget of the existing
  schemes.
• In the case of the well-developed proposals, one
  of the main current uncertainty issues is the
  blackbody radiation shift.

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Blackbody radiation shift
Level B
Clock transition
Level A
DBBR
T 300 K
T 0 K
Transition frequency should be corrected to
account for the effect of the black body
radiation at T300K.
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BBR shift and polarizability
BBR shift of atomic level can be expressed in
terms of a scalar static polarizability to a good
approximation 1
Dynamic correction
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.
1 Sergey Porsev and Andrei Derevianko, Physical
Review A 74, 020502R (2006)
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microWave transitions
optical transitions
Sr
Cs
6s F4
4d5/2
5s1/2
6s F3
In lowest (second) order the polarizabilities of
ground hyperfine 6s1/2 F4 and F3 states are
the same. Therefore, the third-order
F-dependent polarizability aF (0) has to be
calculated.
Lowest-order polarizability
term
terms
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Blackbody radiation shifts in optical frequency
standards(1) monovalent systems(2) divalent
systems(3) other, more complicated systems
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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Example BBR shift in sr
Present
a0(5s1/2) 91.3(9)
a0(4d5/2) 62.0(5)
Need precise lifetime measurements
nf tail contribution issue has been resolved
Present Ref.1 Ref. 2
D(5s1/2 ? 4d5/2) 0.250(9) 0.33(12) 0.33(9)
1 A. A. Madej et al., PRA 70, 012507 (2004)
2 H. S. Margolis et al., Science 306, 19 (2004).
1 Dynamic correction, E2 and M1 corrections
negligible
Sr Dansha Jiang, Bindiya Arora, M. S.
Safronova, and Charles W. Clark, J. Phys. B 42
154020 (2010). Ca Bindiya Arora, M.S.
Safronova, and Charles W. Clark, Phys. Rev. A
76, 064501 (2007)
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Summary of the fractional uncertainties dn/n0 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.
5?10-17
Present
M. S. Safronova et al., IEEE - TUFFC 57, 94
(2010).
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Atoms in optical lattices

• Cancellations of ac Start shifts
  state-insensitive optical cooling and trapping
• State-insensitive bichromatic optical trapping
  schemes
• Simultaneous optical trapping of two different
  alkali-metal species
• Determinations of wavelength where atoms will
  not be trapped
• Calculations of relevant atomic properties
  dipole matrix elements,
• atomic polarizabilities, magic wavelengths,
  scattering rates, lifetimes, etc.

Optimizing the fast Rydberg quantum gate, M.S.
Safronova, C. J. Williams, and C. W. Clark,
Phys. Rev. A 67, 040303 (2003)
. Frequency-dependent polarizabilities of alkali
atoms from ultraviolet through infrared spectral
regions, M.S. Safronova, Bindiya Arora, and
Charles W. Clark, Phys. Rev. A 73, 022505
(2006) 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). Theory and
applications of atomic and ionic polarizabilities
(review paper), J. Mitroy, M.S. Safronova, and
Charles W. Clark, submitted to J. Phys. B
(2010) State-insensitive bichromatic optical
trapping, Bindiya Arora, M.S. Safronova, and C.
W. Clark, submitted to Phys. Rev. A (2010)
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magic wavelength
Atom in state B sees potential UB
Atom in state A sees potential UA
Magic wavelength lmagic is the wavelength for
which the optical potential U experienced by an
atom is independent on its state
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Locating magic wavelength
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Polarizability of an alkali atom in a state v
Valence term (dominant)
Core term
Compensation term
Electric-dipole reduced matrix element
Example Scalar dipole polarizability
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Relativistic all-order method

• Sum over infinite sets of many-body
  perturbation theory (MBPT) terms.

Calculate the atomic wave functions and energies
Scheme
Calculate various matrix elements
Calculate derived properties useful for
particular problems
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Results for alkali-metal atomsE1 transition
matrix elements in
Experiment Na,K,Rb U. Volz and H. Schmoranzer,
Phys. Scr. T65, 48 (1996), Cs R.J. Rafac et
al., Phys. Rev. A 60, 3648 (1999), Fr J.E.
Simsarian et al., Phys. Rev. A 57, 2448 (1998)
Theory M.S. Safronova, W.R.
Johnson, and A. Derevianko,
Phys. Rev. A 60, 4476 (1999)
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Example Best set Rb matrix elements
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Magic wavelengths for the 5p3/2 - 5s transition
of Rb.
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ac Stark shifts for the transition from 5p3/2F'3
M'sublevels to 5s FM sublevels in Rb.The
electric field intensity is taken to be 1 MW/cm2.
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Magic wavelength for Cs
lmagic
Other
a0 a2
lmagic around 935nm
a0- a2
Kimble et al. PRL 90(13), 133602(2003)
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bichromatic optical trapping
atom
Trap laser
Control laser

• A combination of trapping and control lasers
  is used to minimize the variance of the potential
  experienced by the atom in ground and excited
  states.

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Surface plot for the 5s and 5p3/2 m 1/2 state
polarizabilities as a function of laser
wavelengths l1 and l2 for equal intensities of
both lasers.
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Magic wavelengths for the the 5s and 5p3/2 m
1/2 states for l1 800-810nm and l22 l1 for
various intensities of both lasers. The intensity
ratio (e1/e2)2 ranges from 1 to 2.
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Other applications

• Variation of fundamental constants
• Long-range interaction coefficients
• Data for astrophysics
• Actinide ion studies for chemistry models
• Benchmark tests of theory and experiment
• Cross-checks of various experiments
• Determination of nuclear magnetic moment in Fr
• Calculation of isotope shifts

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MONovalent systems Very brief summary of what
wecalculated with all-order method

• Properties
• Energies
• Transition matrix elements (E1, E2, E3, M1)
• Static and dynamic polarizabilities
  applications
• Dipole (scalar and tensor)
• Quadrupole, Octupole
• Light shifts
• Black-body radiation shifts
• Magic 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
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how to evaluateuncertainty of theoretical
calculations?
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Theory evaluation of the uncertainty
HOW TO ESTIMATE WHAT YOU DO NOT KNOW?

• I. Ab initio calculations in different
  approximations
• Evaluation of the size of the correlation
  corrections
• Importance of the high-order contributions
• Distribution of the correlation correction
• II. Semi-empirical scaling estimate missing
  terms

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Example quadrupole moment of 3d5/2 state 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)
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3D5/2 quadrupole moment in Ca
Lowest order 2.451
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3D5/2 quadrupole moment in Ca
Third order 1.610
Lowest order 2.451
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3D5/2 quadrupole moment in Ca
All order (SD) 1.785
Third order 1.610
Lowest order 2.451
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3D5/2 quadrupole moment in Ca
All order (SDpT) 1.837
All order (SD) 1.785
Third order 1.610
Lowest order 2.451
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3D5/2 quadrupole moment in Ca
Coupled-cluster SD (CCSD) 1.822
All order (SDpT) 1.837
All order (SD) 1.785
Third order 1.610
Lowest order 2.451
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3D5/2 quadrupole moment in Ca
Coupled-cluster SD (CCSD) 1.822
All order (SDpT) 1.837
All order (SD) 1.785
Third order 1.610
Lowest order 2.451
Estimate omitted corrections
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Final results 3d5/2 quadrupole moment
All order (SD), scaled
1.849 All-order (CCSD), scaled 1.851 All order
(SDpT) 1.837 All order (SDpT), scaled
1.836
Third order 1.610
Lowest order 2.454
1.849 (13)
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Final results 3d5/2 quadrupole moment
All order (SD), scaled
1.849 All-order (CCSD), scaled 1.851 All order
(SDpT) 1.837 All order (SDpT), scaled
1.836
Third order 1.610
Lowest order 2.454
1.849 (13)
Experiment1.83(1)
Experiment C. F. Roos, M. Chwalla, K. Kim, M.
Riebe, and R. Blatt, Nature 443, 316 (2006).
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Development of high-precision methods Present
status of theory and need for further development
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All-order Correlation potential
CIMBPT
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Mg Ca SrBaRaZnCdHgYb
Motivation study of group II type systems

• Atomic clocks
• Study of parity violation (Yb)
• Search for EDM (Ra)
• Degenerate quantum gases,
• alkali-group II mixtures
• Quantum information
• Variation of fundamental constants

Divalent ions Al, In, etc.
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Summary of theory methods for atomic structure

• Configuration interaction (CI)
• Many-body perturbation theory
• Relativistic all-order method (coupled-cluster)
• Correlation - potential method
• Configuration interaction second-order MBPT
• Configuration interaction all-order method

under development
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GOAL of the present project calculate
properties of group II atoms with precision
comparable to alkali-metal atoms
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Configuration interaction method
Single-electron valence basis states
Example two particle system
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Configuration interaction all-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 acquire
benefits from both approaches.
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Configuration interaction method all-order
Heff is modified using all-order calculation
are obtained using all-order method used for
alkali-metal atoms with appropriate modification
In the all-order method, dominant correlation
corrections are summed to all orders of
perturbation theory.
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CI ALL-ORDER RESULTS
Two-electron binding energies, differences with
experiment
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
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 CIMBPT CI All-order
4s2 1S0 46.2 39.45 39.28
4s4p 3P0 77.9 69.18 67.97

Cd CI CIMBPT CIAll-order
5s2 1S0 59.2 45.82 46.55
5s5p 3P0 91.2 76.75 76.54
Sr CI MBPT CIall-order Recomm.
5s2 1S0 195.6 198.0 197.2(2)
5s5p 3P0 483.6 459.4 458.3(3.6)
From expt. matrix elements, S. G. Porsev and A.
Derevianko, PRA 74, 020502R (2006).
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Cd, Zn, Sr, and Hg magic wavelengths,
preliminary results (nm)
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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Conclusion
Parity Violation
Atomic Clocks
Future New Systems New Methods, New Problems
Quantum information