Transcript Slide 1

JQI seminar
July 8, 2010
Atomic calculations:
recent advances and
modern applications
Marianna Safronova
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 CI+all-order method for group II atoms
• Future prospects
Atomic
calculations for
study of
fundamental
symmetries
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]
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]
r ─r
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.
Parity violation in atoms
Nuclear
spin-independent
PNC:
Searches for new
physics
beyond the
Standard Model
e
q
e
Z0
q
Weak Charge QW
Nuclear
spin-dependent
PNC:
Study of PNC
In the nucleus
a
Nuclear anapole
moment
Standard Model
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
The most precise measurement
of PNC amplitude (in cesium)
C.S. Wood et al. Science 275, 1759 (1997)
F=4
7s
F=3
2
1
6s
F=4
F=3
Im  E PN C 
0.3% accuracy
b
1
  1.6349(80) m V cm
 
mV
  1.5576(77 ) cm 2
Stark interference scheme to measure ratio of the
PNC amplitude and the Stark-induced amplitude b
Parity violation in atoms
Nuclear
spin-independent
PNC:
Searches for new
physics
beyond the
Standard Model
Present status:
agreement with the
Standard Model
Nuclear
spin-dependent
PNC:
Study of PNC
In the nucleus
a
Nuclear anapole
moment
Spin-dependent parity violation:
Nuclear anapole moment
a
Parity-violating nuclear moment
F=4
7s
F=3
2
H
(a)
PNC

GF
2
 a α  I  v (r )
1
6s
F=4
F=3
Valence
nucleon
density
Anapole moment
Nuclear anapole moment is parity-odd, time-reversal-even
E1 moment of the electromagnetic current operator.
Constraints on nuclear weak
coupling contants
W. C. Haxton and C. E. Wieman, Ann. Rev. Nucl. Part. Sci. 51, 261 (2001)
Nuclear anapole moment:
test 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.
NEED NEW EXPERIMENTS!!!
Fr, Yb, Ra+
*M.S. Safronova, Rupsi Pal, Dansha Jiang, M.G. Kozlov,
W.R. Johnson, and U.I. Safronova, Nuclear Physics A 827 (2009) 411c
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!
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]
Permanent electric-dipole
moment ( EDM )
Time-reversal invariance must be violated for an
elementary particle or atom to possess a permanent
EDM.
S
d
t  t
d
S  S
d d
d d
d 0
S
S
S
EDM and New physics
Many theories beyond the Standard Model predict EDM within
or just beyond the present experimental capabilities.
Yale I
Yale II
(projected) (projected)
Berkeley
(2002)
David DeMille, Yale
PANIC 2005
MultiHiggs
Extended
Technicolor
Left-Right
Symmetric
Lepton FlavorChanging
Standard
Model
Alignment
Split SUSY
SO(10) GUT
Seesaw Neutrino Yukawa Couplings
Accidental
Cancellations
-25
10
-26
Exact
Universality
Approx.
Universality
Heavy
sFermions
Naïve SUSY
10
Approx.
CP
10
-27
10
-28
10
-29
10
-30
10
-31
10
de (ecm)
-32
10
-33
10
-34
~
10
-39
10
-40
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) | < 3.1 x 10-29 e cm
Phys. Rev. Lett. 102, 101601 (2009)
Atomic 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).
Atomic calculations & more precise clocks
(1)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.
Blackbody radiation shift
Level B
Clock
transition
Level A
T=0K
T = 300 K
DBBR
Transition frequency should be corrected to account for the
effect of the black body radiation at T=300K.
BBR shift and polarizability
BBR shift of atomic level can be expressed in terms of a
scalar static polarizability to a good approximation [1]:
D  BBR
4
 T (K ) 
   0 (0)(831.9V / m ) 
 (1+  )
2
 300 
1
2
Dynamic correction
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.
[1] Sergey Porsev and Andrei Derevianko, Physical Review A 74, 020502R (2006)
microWave
transitions
optical
transitions
Sr+
Cs
6s F=4
4d5/2
5s1/2
6s F=3
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.
DDT
(1 )
, DT
(1 )
D,T
(1 )
2
D terms
Lowest-order polarizability
2
 
0
v
1
3( 2 j v

 1)
n
2
D term
n D v
En  Ev
Blackbody radiation shifts in
optical frequency standards:
(1) monovalent systems
(2) divalent systems
(3) other, more complicated systems
C a (4 s1/ 2  3 d 5 / 2 )
+
S r (5 s1/ 2  4 d 5 / 2 )
+
B a (6 s1/ 2  5 d 5 / 2 )
Mg, Ca, Zn, Cd, Sr, Al+, In+, Yb, Hg
( ns2 1S0 – nsnp 3P)
+
R a (7 s1/ 2  6 d 5 / 2 )
+
Hg+ (5d 106s – 5d 96s2)
Yb+ (4f 146s – 4f 136s2)
Example: BBR shift in sr+
Present
0(5s1/2)
91.3(9)
Need precise lifetime measurements
0(4d5/2)
62.0(5)
nf tail contribution issue
has been resolved
Present
D(5s1/2 → 4d5/2) 0.250(9)
Ref.[1]
0.33(12)
Ref. [2]
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+:
Ca+:
Dansha Jiang, Bindiya Arora, M. S. Safronova, and Charles W. Clark,
J. Phys. B 42 154020 (2010).
Bindiya Arora, M.S. Safronova, and Charles W. Clark,
Phys. Rev. A 76, 064501 (2007)
Summary of the fractional uncertainties d/0 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.
Present
M. S. Safronova et al., IEEE - TUFFC 57, 94 (2010).
510-17
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)
magic wavelength
Atom in state B
sees potential UB
Atom in state A
sees potential UA
Magic wavelength magic is the wavelength for
which the optical potential U experienced
by an atom is independent on its state
U   ( )
Locating magic wavelength
α 
S State
P State
wavelength
 m a g ic
Polarizability of an alkali atom in a state
   c   vc   v
Core term
 v   
Valence term
(dominant)
Compensation term
Electric-dipole
reduced matrix
element
Example:
Scalar dipole polarizability
1
3( 2 j v

 1)
n
 En  Ev 
v
2
n D v
 En  Ev 
2

2
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
H Ψv = E Ψv
Calculate “derived” properties
useful for particular problems
Results for alkali-metal atoms:
E1 transition matrix elements in
Na
3 p 1 /2 -3 s
A ll-o rd e r
3 .5 3 1
K
4 p 1 /2 -4 s
Rb
5 p 1 /2 -5 s
Cs
6 p 1 /2 -6 s
4 .0 9 8
4 .2 2 1
4 .4 7 8
4 .2 5 6
4 .2 7 7 (8 )
E xp e rim e n t
3 .5 2 4 6 (2 3 ) 4 .1 0 2 (5 ) 4 .2 3 1 (3 )
4 .4 8 9 (6 )
D iffe re n ce
0 .1 8 %
0 .2 4 %
0 .1 %
0 .2 4 %
Fr
7 p 1 /2 -7 s
0 .5 %
Experiment Na,K,Rb: U. Volz and H. Schmoranzer, Phys. Scr. T65, 48 (1996),
Theory
Cs:
R.J. Rafac et al., Phys. Rev. A 60, 3648 (1999),
Fr:
J.E. Simsarian et al., Phys. Rev. A 57, 2448 (1998)
M.S. Safronova, W.R. Johnson, and A. Derevianko,
Phys. Rev. A 60, 4476 (1999)
Example: “Best set” Rb matrix elements
Magic wavelengths for the
5p3/2 - 5s transition of Rb.
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.
Magic wavelength for Cs
 v   0   2 MJ = ±3/2
 v   0   2 MJ = ±1/2
10000
6S1/2
6P3/2
8000
 (a .u .)
magic
6000
932 nm
Other*
938 nm
0+ 2
4000
2000
magic around 935nm
0- 2
0
925
930
935
940
 (n m )
945
950
955
* Kimble et al. PRL 90(13), 133602(2003)
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.
Surface plot for the 5s and 5p3/2 |m| = 1/2 state
polarizabilities as a function of laser wavelengths 1
and 2 for equal intensities of both lasers.
Magic wavelengths for the the 5s and 5p3/2 | m| = 1/2 states for
1 =800-810nm and 2=2 1 for various intensities of both lasers.
The intensity ratio (e1/e2)2 ranges from 1 to 2.
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
•…
MONovalent systems:
Very brief summary of what we
calculated with all-order method
Properties
Systems
• Energies
• Transition matrix elements (E1, E2, E3, M1)
Li, Na, Mg II, Al III,
• Static and dynamic polarizabilities & applications Si IV, P V, S VI, K,
Dipole (scalar and tensor)
Ca II, In, In-like ions,
Quadrupole, Octupole
Ga, Ga-like ions, Rb,
Light shifts
Cs, Ba II, Tl, Fr, Th IV,
Black-body radiation shifts
U V, other Fr-like ions,
Magic wavelengths
Ra II
• 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
http://www.physics.udel.edu/~msafrono
how to evaluate
uncertainty of
theoretical
calculations?
Theory: evaluation of the
uncertainty
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:
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)
3D5/2 quadrupole moment in Ca+
Lowest order
2.451
3D5/2 quadrupole moment in Ca+
Lowest order
2.451
Third order
1.610
3D5/2 quadrupole moment in Ca+
Lowest order
2.451
Third order
1.610
All order (SD)
1.785
3D5/2 quadrupole moment in Ca+
Lowest order
2.451
Third order
1.610
All order (SD)
1.785
All order (SDpT)
1.837
3D5/2 quadrupole moment in Ca+
Lowest order
2.451
Third order
1.610
All order (SD)
1.785
All order (SDpT)
1.837
Coupled-cluster SD (CCSD)
1.822
3D5/2 quadrupole moment in Ca+
Lowest order
2.451
Third order
1.610
All order (SD)
1.785
All order (SDpT)
1.837
Coupled-cluster SD (CCSD)
1.822
Estimate
omitted
corrections
Final results: 3d5/2 quadrupole moment
Lowest order
2.454
Third order
1.849 (13)
1.610
All order (SD), scaled
All-order (CCSD), scaled
All order (SDpT)
All order (SDpT), scaled
1.849
1.851
1.837
1.836
Final results: 3d5/2 quadrupole moment
Lowest order
2.454
Third order
1.849 (13)
1.610
All order (SD), scaled
All-order (CCSD), scaled
All order (SDpT)
All order (SDpT), scaled
1.849
1.851
1.837
1.836
Experiment
1.83(1)
Experiment: C. F. Roos, M. Chwalla, K. Kim, M. Riebe, and R. Blatt, Nature 443, 316 (2006).
Development of high-precision
methods
Present status of theory and
need for further development
All-order
Correlation potential
CI+MBPT
Motivation:
study of group II – type systems
•
•
•
•
Mg
Ca
Sr
Ba
Ra
Atomic clocks
Study of parity violation (Yb)
Zn
Search for EDM (Ra)
Cd
Degenerate quantum gases,
Hg
alkali-group II mixtures
Yb
• Quantum information
• Variation of fundamental constants
Divalent ions: Al+, In+, etc.
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
GOAL of the present project:
calculate properties of group II
atoms with precision comparable
to alkali-metal atoms
Configuration interaction
method
 
H
c
i
i
Single-electron valence
basis states
i
eff
 E  0
1
r1  r2
Example: two particle system:
H
eff
 h1 ( r1 )  h1 ( r2 )  h 2 ( r1 , r2 )
one  body
part
tw o  body
part
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.
Configuration interaction
method + all-order
Heff is modified using all-order calculation
h1  h1   1
h2  h2   2
H
eff
 E  0
 1 ,  2 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.
CI + ALL-ORDER RESULTS
Two-electron binding energies, differences with experiment
Atom
Mg
Ca
Zn
Sr
Cd
Ba
Hg
Ra
CI
CI + MBPT
1.9%
0.11%
4.1%
0.7%
8.0%
0.7%
5.2%
1.0%
9.6%
1.4%
6.4%
1.9%
11.8% 2.5%
7.3%
2.3%
CI + All-order
0.03%
0.3%
0.4 %
0.4%
0.2%
0.6%
0.5%
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).
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
CI
CI+MBPT
CI+All-order
5s2 1S0
59.2
45.82
46.55
5s5p 3P0
91.2
76.75
76.54
Cd
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)
*From expt. matrix elements, S. G. Porsev and A. Derevianko, PRA 74, 020502R (2006).
Cd, Zn, Sr, and Hg magic wavelengths,
preliminary results (nm)
Sr
Present
813.45
Cd
Zn
Present
423(4)
414(5)
Hg
Present
365(5)
Expt. [1]
813.42735(40)
Theory [2]
360
[1] A. D. Ludlow et al., Science 319, 1805 (2008)
[2] H. Hachisu et al., Phys. Rev. Lett. 100, 053001 (2008)
Conclusion
Parity Violation
Atomic
Clocks
P1/2
Future:
New Systems
New Methods,
New Problems
D5/2
Qubit
S1/2
Quantum information