Atomic Parity Violation in
Ytterbium
K. Tsigutkin, D. Dounas-Frazer, A. Family,
and D. Budker
http://budker.berkeley.edu
PV Amplitude: Current results
150
Theoretical prediction
Mean value
68% confidence band
z/b (mV/cm)
100
50
0
-50
0
2
4
6
8
10
12
14
16
18
20
Run number
z/b=39(4)stat.(5)syst. mV/cm  |z|=8.7±1.4×10-10 ea0
Accuracy is affected by HV amplifier noise, fluctuations of stray fields, and
laser drifts → to be improved
Sources of parity violation in atoms
Z0-exchange between e and nucleus
 P-violating, T-conserving product of
axial and vector currents
G
hˆ  
2
C1n
e
Z0
 C
1N
e    5e N   N  C2 N e   e N    5 N 
N
is by a factor of 10 larger than C , C
leading to a dominance of the time-like
nuclear spin-independent interaction (Ae,VN)
1p
2N
A contribution to APV due to Z0 exchange between electrons is
suppressed by a factor ~1000 for heavy atoms.
Nuclear Spin-Independent (NSI)
electron-nucleon interaction
NSI Hamiltonian in non-relativistic limit assuming equal proton and neutron densities
(r) in the nucleus:
G
ˆ
hW  
2 2
QW  5  ( r )
The nuclear weak charge QW to lowest order in the
electroweak interaction is
QW   N  Z (1  4 sin W )   N
2
sin W
2
 MW 
 1 

M
Z 

The nuclear weak charge is protected from strong-interaction effects by
conservation of the nuclear vector current. Thus, APV measurements allows
for extracting weak couplings of the quarks and for searching for a new
physics beyond SM
• NSI interaction gives the largest PNC effect compared to other mechanisms
• PV interaction is a pseudo-scalar  mixes only electron states of same
angular momentum
2
NSI interaction and particle physics
implications
APV utilizes low-energy system and
gives an access to the weak mixing
angle, Sin2(W), at low-momentum
transfer.
• J.L. Rosner, PRD 1999
• V.A. Dzuba, V.V. Flambaum, and O.P. Sushkov,
PRA 1997
• J. Erler and P. Langacker, Ph.Lett. B 1999
Isotope ratios and neutron distribution
The atomic theory errors can be excluded by taking ratios of APV measurements
along an isotopic chain. While the atomic structure cancels in the isotope ratios, there
is an enhanced sensitivity to the neutron distribution n(r).
APV   atomic (QW  QW )
nuc
nuc
QW
f(r) is the variation of the electron
wave functions inside the nucleus
normalized to f(0)=1.
  N (qn  1)  Z (1  4 sin W )( q p  1)
2
qn    n ( r ) f ( r )d r , q p    p ( r ) f ( r )d r
3
3
R
APV ( N ')
APV ( N )

QW ( N ')
QW ( N )
1  qn 
qn  qn  qn
R is sensitive to the difference in the neutron distributions.
~Z3 scaling of APV effects
Considering the electron wave functions in nonrelativistic limit and pointlike nucleus the NSI Hamiltonian becomes:
hˆW 
G
4 2me
σ  p 
3
(r)   (r) σ  p
3
Since it is a local and a scalar operator
it mixes only s and p1/2 states.
2
p1/ 2 hˆW s  Z QW
• Z due to scaling of the probability of the valence
electron to be at the nucleus
• Z from the operator p, which near the nucleus
(unscreened by electrons)  Z.
• |QW|N~Z.
Strong enhancement of the APV effects in heavy atoms

Signature of the weak interaction in
atoms
hNSI mixes s1/2 and p1/2 states of valence electron 
APV of dipole-forbidden transition.
If APC is also induced, the amplitudes interfere.
R  APC  APV
2
 APC  2 APC APV  o( APV )
2
2
Interference
E-field
Stark-effect
E1 PC-amplitude  E
E1-PV interference term
is odd in E
Reversing E-field changes transition rate
Transition rate  APVAStark
Atomic structure of Yb
Proposed by D. DeMille,
PRL 1995
By observing the 6s2 1S0 – 6s6p 3P1
556 nm decay the pumping rate of
the 6s2 1S0 – 6s5d 3D1 408 nm
transition is determined.
The population of 6s6p 3P0 metastable
level is probed by pumping the 6s6p 3P0 6s7s 3S1 649 nm transition.
Yb isotopes and abundances
Seven stable isotopes, two have non-zero spin
C.J. Bowers et al, PRA 1999
Rotational invariant and geometry of
the Yb experiment
 
εB

  
ε EB
 
AStark  i b ( 1)
q
q
E  ε

Reversals:
B – even
E – odd
 p/2 – odd
j , m,1, m  m j , m
-q
A PV  i  ( 1) ε -q j , m,1, m  m j , m ; q  m  m
q
q
|b| = 2.24(25)10-8 e a0/(V/cm) – Stark transition polarizability (Measured by
J.Stalnaker at al, PRA 2006)
|z| = 1.08(24)10-9 (QW/104) e a0 – Nuclear spin-independent PV amplitude
(Calculations by Porsev et al, JETP Lett 1995; B. Das, PRA 1997 )
PV effect on line shapes:
even isotopes
E  (E,0,0)
ε  (0,sinθ , cos θ)
R b E
0
R
1
2

2
b 2 E2
sin θ  2E b sin θ cos θ
2
cos θ  E b sin θ cos θ
2
2
174Yb
PV-Stark
interference
terms
Rate modulation
under the E-field
reversal yields:
RE   RE 
2

RE   RE 
bE
Experimental setup
Light
collection
efficiency:
Interaction
region: ~0.2%
(556 nm)
Detection
region: ~25%
Yb density in the beam ~1010 cm-3
E-field up to 15 kV/cm, spatial homogeneity 99%
Reversible B-field up to 100 G, homogeneity 99%
Optical system and control
electronics
Light powers:
Ar+: 12W
Ti:Sapp (816 nm): 1W
Doubler (408 nm): 50 mW
PBC:
Asymmetric design, 22 cm
Finesse 17000
Power 10 W
Locking:
Pound-Drever-Hall
technique
Fast (70 Hz) E-modulation scheme
to avoid low-frequency noise and drift issues
R0  b E sin   2 E b cos  sin 
2
Transition rates
R1 
1
2
2
b 2 E 2 cos 2   E b cos  sin 
2
E-field modulation E  Edc  E0 cos t
m = +1
m=0
m = -1
3D
1
R+1
R0
R-1
1S
0
1st
PV-asymmetry:
K
Α 1
2 nd
A 1
1st
1st

A 1
2 nd
A 1
2
A0
2 nd
A0

16 
b E0
Fast E-modulation scheme: Profiles
174Yb
Effective integration time: 10 s p-p
E0=5 kV/cm
Edc=40 V/cm
=p/4
Shot noise limited SNR in respect to
PV signal ~2 (for 1 s integration time)
 0.1% accuracy in 70 hours
• Lineshape scan: ~20 s
DC bias 43 V/cm
• E-field reversal: 14 ms (70 Hz)
• B-field reversal: 20 minutes
• Polarization angle: 10 minutes
• E-field magnitude
• B-field magnitude
• Angle magnitude
PV Amplitude: Current results
150
Theoretical prediction
Mean value
68% confidence band
z/b (mV/cm)
100
50
0
-50
0
2
4
6
8
10
12
14
16
18
20
Run number
z/b=39(4)stat.(5)syst. mV/cm  |z|=8.7±1.4×10-10 ea0
Accuracy is affected by HV amplifier noise, fluctuations of stray fields, and
laser drifts → to be improved
Fast E-modulation scheme:
Systematics
Assume stray electric and magnetic fields (non-reversing dc)
and small ellipticity of laser light:

b  bx , by , bz 

e  ex , e y , ez 
  0, e iP sin  , cos  
PV asymmetry and systematics give four unknowns:
K 
16
16bx e y
b E0
Bz E0

16bx ez
 higher order
Bz E0
Reversals of B-field and polarization (±p/4) yield four equations
 Solve for PV asymmetry, stray fields, and noise
Problems
• Photo-induced PBC mirror deterioration in vacuum
• Technical noise (above shot-noise)
• Stray electric fields (~ V/cm)
• Laser stability
Power-buildup cavity design and
characterization
F 
2p
T1  T 2  L1  L 2
 F 
 T1T 2 

 Pin
 2p 
Ptrans
2
C. J. Hood, H. J. Kimble, J. Ye. PRA 64, 2001
0.20
Ringdown
spectroscopy
PBC transmission [V]
=2.16 s F=9253
0.15
0.10
=1.74 s F=7454
0.05
=1.33 s F=5698
0.00
-10
-5
0
Time [s]
5
10
Power-buildup cavity design and
characterization: mirrors
REO set1
l=408 nm
REO set2
l=408 nm
ATF
l=408 nm
Boulder expt.
l=540 nm
Transmission
320 ppm
45; 23 ppm
150 ppm
40; 13
S+A losses
120 ppm
213; 83 ppm
30 ppm
<1 ppm
Mirror set used during the latest APV measurements:
Finesse of 17000 with ATF mirrors
Photodegradation: a factor of 3 increase of S+A losses in 2 runs
(~8 hours of exposure with ~10 W of circulating power)
Summary
Completed Work
 Lifetime Measurements
 General Spectroscopy (hyperfine shifts, isotope
shifts)
 dc Stark Shift Measurements
 Stark-Induced Amplitude (β): 2 independent
measurements
 M1 Measurement (Stark-M1 interference)
 ac Stark shifts measured
 Verification of PV enhancement
And then…
 PV in a string of even isotopes; neutron distributions
 PV in odd isotopes: NSD PV, Anapole Moments …
Sources of NSD interaction
G 
ˆ
hNSD 
 0 γI  (r )
2 I
Weak neutral current
Anapole moment

K
I 1
K  ( 1)
 A  2  Q ;
 A  1.15 10 3 A2 / 3  g ; A  N  Z ;
w
I 1 / 2  l
( I  1 / 2)
Hyperfine correction to
the weak neutral current
2 
1/ 2  K
I 1
C2
A-Anapole moment
2-Neutral currents
QW-Radiative
corrections
Anapole moment
In the nonrelativistic approximation PNC interaction of the valence nucleon
with the nuclear core has the form:
G g (σp)
ˆ
hA 
n( r )
n(r) is core density and g is
2 2 mp
dimensionless effective weak coupling
constant for valence nucleon.
• As a result, the spin  acquires projection on
the momentum p and forms spin helix
• Spin helix leads to the toroidal current. This
current is proportional to the magnetic moment
of the nucleon and to the cross section of the
core.
Khriplovich & Flambaum
 A  1.15 103 A2 / 3  g
neutron: n=-1.2; gn=-1
proton: p=3.8; gp=5
Anapole moment is bigger for nuclei with
unpaired proton
Nuclear physics implication: weak
meson coupling constants
There are 7 independent weak couplings for p-, -, and -mesons
known as DDH constants. Proton and neutron couplings, g, can be
expressed in terms of 2 combinations of these constants:
4
0
g p  8.0  10  70fp  19.5h 
4
0
g n  8.0  10  47fp  18.9h 
fp  fp  0.12h   0.18h 
1
1
h  h   0.7h 
0
0
0
At present the values of the
coupling constants are far from
being reliably established. The
projected measurement of the
anapole moment in 173Yb should
provide an important constraint.
h0
1
PV effect on line shapes:
odd isotopes
E  (E,0,0)
ε  (0,sinθ , cos θ)
2
R
center

β FF E
6
2
R
side

β FF E
2
2
(4sin θ  cos θ)  E β FF  sin θ cos θ
2
2
2
cos θ  E β FF  sin θ cos θ
2
   I J
 NSD
zNSD10-12 ea0 for
odd Yb isotopes
z=10-9 ea0
z` must be
measured with
0.1% accuracy