Polarizabilities, Atomic Clocks, and Magic Wavelengths

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DAMOP 2008 focus session Atomic polarization and
dispersion
Polarizabilities, Atomic Clocks, and Magic
Wavelengths
May 29, 2008
Marianna Safronova Bindiya arora
Charles W. clark NIST, Gaithersburg
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Outline

• Motivation
• Method
• Applications
• Frequency-dependent polarizabilities of alkali
  atoms
• and magic frequencies
• Atomic clocks blackbody radiation shifts
• Future studies

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Motivation 1Optically trapped atoms
Atom in state B sees potential UB
Atom in state A sees potential UA
State-insensitive cooling and trapping for
quantum information processing
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Motivation 2
Atomic clocks Next Generation
Microwave Transitions
Optical Transitions
http//tf.nist.gov/cesium/fountain.htm, NIST Yb
atomic clock
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Motivation 3
Parity violation studies with heavy atoms
search for Electron electric-dipole moment
http//CPEPweb.org, http//public.web.cern.ch/,
Cs experiment, University of Colorado
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Motivation

• Development of the high-precision methodologies
• Benchmark tests of theory and experiment
• Cross-checks of various experiments
• Data for astrophysics
• Long-range interactions
• Determination of nuclear magnetic and anapole
  moments
• Variation of fundamental constants with time

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Atomic polarizabilities
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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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How to accurately calculate various matrix
elements ?
Very precise calculation of atomic properties
We also need to evaluate uncertainties of
theoretical values!
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How to accurately calculate various matrix
elements ?
Very precise calculation of atomic properties
WANTED!
We also need to evaluate uncertainties of
theoretical values!
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All-order atomic wave function (SD)
core valence electron any excited orbital
Core
Lowest order
Single-particle excitations
Double-particle excitations
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All-order atomic wave function (SD)
core valence electron any excited orbital
Core
Lowest order
Single-particle excitations
Double-particle excitations
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Actual implementation codes that write formulas
The derivation gets really complicated if you add
triples!
Solution develop analytical codes that do all
the work for you!
Input ASCII input of terms of the type
Output final simplified formula in LATEX to be
used in the all-order equation
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Problem with all-order extensions TOO MANY TERMS
The complexity of the equations increases. Same
issue with third-order MBPT for two-particle
systems (hundreds of terms) . What to do with
large number of terms?
Solution automated code generation !
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Automated code generation
Codes that write formulas
Codes that write codes
Input list of formulas to be
programmed Output final code (need to be put
into a main shell)
Features simple input, essentially just type in
a formula!
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Results for alkali-metal atoms
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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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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Polarizabilities Applications

• Optimizing the Rydberg gate
• Identification of wavelengths at which two
  different alkali atoms have the same oscillation
  frequency for simultaneous optical trapping of
  two different alkali species.
• Detection of inconsistencies in Cs lifetime and
  Stark shift experiments
• Benchmark determination of some K and Rb
  properties
• Calculation of magic frequencies for
  state-insensitive cooling and trapping
• Atomic clocks problem of the BBR shift

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Polarizabilities Applications

• Optimizing the Rydberg gate
• Identification of wavelengths at which two
  different alkali atoms have the same oscillation
  frequency for simultaneous optical trapping of
  two different alkali species.
• Detection of inconsistencies in Cs lifetime and
  Stark shift experiments
• Benchmark determination of some K and Rb
  properties
• Calculation of magic frequencies for
  state-insensitive cooling and trapping
• Atomic clocks problem of the BBR shift

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ApplicationsFrequency-dependent polarizabilities
of alkali atoms from ultraviolet through infrared
spectral regions
Goal First-principles calculations of the
frequency-dependent polarizabilities of ground
and excited states of alkali-metal
atoms Determination of magic wavelengths
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Magic wavelengths

• Excited states determination of magic
  frequencies in alkali-metal atoms for
  state-insensitive cooling and trapping, i.e.
• When does the ground state and excited np state
  has the same ac Stark shift?

Bindiya Arora, M.S. Safronova, and Charles W.
Clark, Phys. Rev. A 76, 052509 (2007) Na, K, Rb,
and Cs
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What is 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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What do we need?
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What do we need?
Lots and lots of matrix elements!
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What do we need?
Lots and lots of matrix elements!
Cs
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What do we need?
Lots and lots of matrix elements!
All-order database over 700 matrix elements
for alkali-metal atoms and other monovalent
systems
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Theory (This work)
Experiment
w0
(3P1/2)
Na
359.9(4)
359.2(6)
(3P3/2)
361.6(4)
360.4(7)
(3P3/2)
-88.4(10)
-88.3 (4)
(4P1/2)
K
606.7(6)
606(6)
(4P3/2)
616(6)
614 (10)
(4P3/2)
-109(2)
-107 (2)
(5P1/2)
Rb
807(14)
810.6(6)
869(14)
(5P3/2)
857 (10)
-166(3)
(5P3/2)
-163(3)
Zhu et al. PRA 70 03733(2004)
Excellent agreement with experiments !
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Frequency-dependent polarizabilities of Na atom
in the ground and 3p3/2 states. The arrows show
the magic wavelengths
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Magic wavelengths for the 3p1/2 - 3s and 3p3/2 -
3s transition of Na.
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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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ac Stark shifts for the transition from 6p3/2F'5
M'sublevels to 6s FM sublevels in Cs.The
electric field intensity is taken to be 1 MW/cm2.
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Applicationsatomic clocks
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atomic clocksblack-body radiation ( BBR ) shift
Motivation BBR shift gives the larges
uncertainties for some of the optical atomic
clock schemes, such as with Ca
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Blackbody radiation shift in optical frequency
standard with 43Ca ion
Bindiya Arora, M.S. Safronova, and Charles W.
Clark, Phys. Rev. A 76, 064501 (2007)
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Motivation
For Ca, the contribution from Blackbody
radiation gives the largest uncertainty to the
frequency standard at T 300K
DBBR 0.39(0.27) Hz 1
1 C. Champenois et. al. Phys. Lett. A 331, 298
(2004)
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Frequency standard
Level B
Clock transition
Level A
T 0 K
Transition frequency should be corrected to
account for the effect of the black body
radiation at T300K.
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Frequency standard
Level B
Clock transition
DBBR
Level A
T 300 K
Transition frequency should be corrected to
account for the effect of the black body
radiation at T300K.
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Why Ca ion?
The clock transition involved is 4s1/2F4 MF0 ?
3d5/2 F6 MF0
4p3/2
Easily produced by non-bulky solid state or diode
lasers
854 nm
4p1/2
3d5/2
866 nm
Lifetime1.2 s
393 nm
3d3/2
397 nm
E2
729 nm
732 nm
4s1/2
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BBR shift of a level

• The temperature-dependent electric field created
  by the blackbody radiation is described by (in
  a.u.)

• Frequency shift caused by this electric field is

Dynamic polarizability
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BBR shift and polarizability

• BBR shift can be expressed in terms of a scalar
  static polarizability

Dynamic correction
Dynamic correction 10-3 Hz. At the present level
of accuracy the dynamic correction can be
neglected.
Vector tensor polarizability average out due to
the isotropic nature of field.
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BBR shift for a transition

• Effect on the frequency of clock transition
• is calculated as the difference between the
• BBR shifts of individual states.

3d5/2
729 nm
4s1/2
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Need BBR shifts
Need ground and excited state scalar static
polarizability
NOTE Tensor polarizability calculated in this
work is also of experimental interest.
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Contributions to the 4s1/2 scalar polarizability
( )
43Ca (w 0)
Stail
6p1/2
6p3/2
0.01
0.01
0.06
5p3/2
5p1/2
0.01
0.01
4p1/2
4p3/2
24.4
48.4
Total 76.1 1.1
4s
3.3
Core
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Contributions to the 3d5/2 scalar polarizability
( )
43Ca
nf7/2
7-12f7/2
nf5/2
6f7/2
1.7
np3/2 tail
0.2
0.5
0.3
0.01
5f7/2
5p3/2
0.01
0.8
4f7/2
4p3/2
2.4
22.8
3d5/2
Total 32.0 1.1
3.3
Core
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Comparison of our results for scalar static
polarizabilities for the 4s1/2 and 3d5/2 states
of 43Ca ion with other available results

Present Ref. 1 Ref. 2 Ref. 3
a0(4s1/2) 76.1(1.1) 76 73 70.89(15)
a0(3d5/2) 32.0(1.1) 31 23
1 C. Champenois et. al. Phys. Lett. A 331, 298
(2004) 2 Masatoshi Kajit et. al. Phys. Rev. A
72, 043404, (2005) 3 C.E. Theodosiou et. al.
Phys. Rev. A 52, 3677 (1995)
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Black body radiation shift

• Comparison of black body radiation shift (Hz)
  for the 4s1/2- 3d5/2 transition of 43Ca ion at
  T300K (E831.9 V/m).

Present Champenois1 Kajita 2
D(4s1/2 ? 3d5/2) 0.38(1) 0.39(27) 0.4
An order of magnitude improvement is achieved
with comparison to previous calculations
1 C. Champenois et. al. Phys. Lett. A 331, 298
(2004) 2 Masatoshi Kajit et. al. Phys. Rev. A
72, 043404, (2005)
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Black body radiation shift

• Comparison of black body radiation shift (Hz)
  for the 4s1/2- 3d5/2 transition of 43Ca ion at
  T300K (E831.9 V/m).

Present Champenois1 Kajita 2
D(4s1/2 ? 3d5/2) 0.38(1) 0.39(27) 0.4
Sufficient accuracy to establish The uncertainty
limits for the Ca scheme
1 C. Champenois et. al. Phys. Lett. A 331, 298
(2004) 2 Masatoshi Kajit et. al. Phys. Rev. A
72, 043404, (2005)
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relativistic All-order method
Singly-ionized ions
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Future studies more complicated system
development of the CI all-order approach

M.S. Safronova, M. Kozlov, and W.R. Johnson, in
preparation
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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 method can account for core-core and
core-valence correlation can not
accurately describe valence-valence correlation.
Therefore, two methods are combined to acquire
benefits from both approaches.
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CI ALL-ORDER PRELIMINARY RESULTS
Ionization potentials, differences with experiment
CI CI MBPT CI All-order Mg
1.9 0.12 0.03 Ca 4.1
0.6 0.3 Sr 5.2 0.9 0.3 Ba 6.4
1.7 0.5
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Conclusion

• Benchmark calculation of various
  polarizabilities and tests of theory and
  experiment
• Determination of magic wavelengths for
  state- insensitive optical cooling and trapping
• Accurate calculations of the BBR shifts
• Future studies Development of generally
  applicable
• CI all-order method for more complicated
  systems

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Conclusion
Parity Violation
Atomic Clocks
Future New Systems New Methods, New Problems
Quantum information
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Graduate students Bindiya Arora Rupsi
pal Jenny Tchoukova Dansha Jiang
P3.8 Jenny Tchoukova and M.S. Safronova Theoretic
al study of the K, Rb, and Fr lifetimes Q5.9
Dansha Jiang, Rupsi Pal, and M.S.
Safronova Third-order relativistic many-body
calculation of transition probabilities for the
beryllium and magnesium isoelectronic
sequences U4.8 Binidiya Arora, M.S. Safronova,
and Charles W. Clark State-insensitive two-color
optical trapping