DeMille

Group

Dave DeMille, E. Altuntas, J. Ammon, S.B. Cahn, R. Paolino*Physics Department, Yale University

*Physics Department, US Coast Guard Academy

Narrow opposite-parity level crossings in a diatomic free radical

Funding: NSF

• Motivation: nuclear spin-dependent parity violation

• PV measurement strategy: Zeeman-tuned rotational degeneracies

• Measurements: Stark-induced transitions near a rotational level crossing

• Outlook

VN+AN

Ve+Ae

Z0

N

e

NSD-PV from direct Z0 exchange:

numerically suppressed

Electroweak coupling to nuclear spin: “NSD-PV”

3( )

( )( ) ( )

W

Z an

H

I p r

VN+AN

Ve+Ae

Z0

N

e

Mechanisms for atomic/molecular parity violation

e

PV weak interactionsinside nucleus induce

nuclear “anapole moment” that couples to electron

magnetically

g

N Z0, W±

e

Inuclear spin I

+Weak-interaction

Hamiltonian HW mixeshyperfine states with

opposite parity

+

Enhanced parity mixing via systematic level degeneracies in diatomic free radicals

+ nuclear spin(I=1/2)

0+

1-

0-

1+

2-

1-

B

Typically several crossingsfor B = 0.3 - 1 T

Effective energy separationD ~ 1 kHz ~ 10-11 eV near crossing 1011 enhancement vs. atoms!

1/2+

3/2-

1/2-

Rotation JP + e- spin 1/2

Example: 2S with single nuclear spin I=1/2 (e.g. 138BaF)

Z O

M B

I E

S

eeman-tuned

ptically prepared and detected

olecular

eams for the

nvestigation of

lectroweak effects using

tark interference

The ZOMBIES NSD-PV experiment at Yale

Molecule PV experimental schematic

E0

B

|->

|+>

(1) (2) (3) (4)

(1)

(2) (3) (4)

Superconducting solenoid

Lase

r E0La

ser

Stark interference method:apply oscillating E-field to mix nearly-degenerate levels

E+

E-

E

Center of Magnet:Homogeneity dB/B < 10-7

( )BD

Zeem

an-s

hifte

d E

nerg

y E

Position z Time t = z/v

Strategy to detect PV in near-degenerate levels

0 ( )

( )W

W

iH d tH

iH d t

æ ö+ ÷ç ÷ç= ÷ç ÷- +ç ÷è øD

E

E

|+>

|->

0

0

,

( ) sin( )

d

t t

w

w

D

=é ùë û? E

E E

Small Weak Term Odd in E0

Large Stark TermEven in E0

22

2 0 0( ) 4sin 22

Wd H dT

S Tyw w

é ùæ öæ öD ê ú÷÷çç ÷÷= + = +çç ê ú÷÷çç ÷ ÷ç ç Dê úè øè øê úë û

E E

D.D., S.B. Cahn, D. Murphree, D.A. Rahmlow, and M.G. KozlovPhys. Rev. Lett. 100, 023003 (2008)

( )BD

w

0sin( )twE

Signal, Asymmetry, Sensitivity

( )2

2 0 00 0

0 0

--Measure signal 4 sin 22

with opposite-sign -fields ,

Wd H dT

S Nw w

é ùæ öæ öD ê ú÷÷çç ÷÷ +çç ê ú÷÷çç ÷ ÷ç ç Dê úè øè øê úë û+

»

-

E EE

E E E

0 0

0 0 0

--Form asymmetry to extract in terms of known quantities:

( ) ( )

( ) ( )

W

WH

S S H

S S dw+ - -

= »+ + - D

E

E EA

E

E

0

1 1 1

2 2

Statistical Uncertainty

WHTN

best sensitivity from

large interaction time

with constant

T

Experimental study of Stark-induced transitions at level crossings in 138BaF

4600 4625 46506400

6450

6500

6550

Ene

rgy

(MH

z)

Magnetic Field (Gauss)

mF=-1

mF=0

mF=+1

|ms, mI, mN>

Apply unipolar E-field pulseOpposite-parity level crossing spectroscopy

( )BD2 2

0

( )E

E t /

t

e

E-field from step potential on cylindrical boundary

E+

E-

+V-V

Simple Stark-induced transition at a level crossing

0 ( )

( )

E

E

d tH

d t

2

2

0

22 22 20

for weak excitation ( 1) Gaussian lineshape:

E/

d

S

E ,

c t d e

20 0

on resonance w/arbitrary excitation strength: Rabi flopping

0 sinE ES ; d

|+>

|->( )BD

2 2

0 ( )E E t /t e

Linewidth

1 /

Typical level-crossing data: lineshape & position

B-field at crossing from position of peak

Interaction time tfrom width of peakMatches calculatedFWHM dD ~ 6 kHz

D (kHz)

2 2

2( )S e

Rabi flopping: period vs. E0 determines d

Dipole matrix element d = 3574(7) Hz/(V/cm) [suppressed by spin flip]

Pea

k no

rmal

ized

sig

nal

Peak applied electric field E0 [V/cm]

Apply single E-field pulse

Complex lineshapes from off-resonant Stark shifts

Center of Magnet

( , )B tD

2 2

0 ( )E E t /t e

Spatially-varying detuning due to off-resonant Stark shifts

E+

E-

Data: lineshapes from off-resonant Stark shifts

Fit at several different E0 values determinescrossing position vs. B, and Stark shift strength

Data and fit including spatially-varying Stark shift

Calculated level crossings in 138BaF

4600 4625 46506400

6450

6500

6550

Ene

rgy

(MH

z)

Magnetic Field (Gauss)

mF=-1

mF=0

mF=+1

|ms, mI, mN>

16

Extracted data from 138BaF crossings:crossing positions & dipole matrix elements

Type Initial Calc.X Obs. X Calc. d Obs. d Unc.obs. (Gauss) (Gauss) (Hz/V/cm) (Hz/V/cm) (Hz/V/cm)

Generally excellent agreement with all predictions from standardspin/rotation/hyperfine + Zeeman Hamiltonian treatment;

some details still to be completed in fit

PRELIMINARY

-10 -8 -6 -4 -2 0 2 4 6 8 100

0.1

0.2

0.3

0.4

Positive E0

Negative E0

Detuning D (kHz)

Nor

mal

ized

Sig

nal S

Initial, very preliminary NSD-PV data in 138BaFShaped E-field

2

2

0 0

4sin2

2 W

TS

d H d

w w

æ öD ÷ç ÷= ç ÷ç ÷çè øé ùæ öê ú÷ç ÷´ +çê ú÷ç ÷ç Dê úè øê úë û

E E0

( )sin( )t

tw=E

E

aTake NSD-PV

data HERE

Conclusions & Outlook: Parity Violation with Diatomic Free Radicals

• Opposite-parity level-crossing spectroscopy: linewidth (as small as 4 kHz), lineshapes, positions, matrix elements, etc. all in agreement with theory

• Molecular systems very promising for study of NSD-PV: excellent S/N & systematics, leverage from developed techniques

• Multiple nuclei available for anapole moment determination(we will use 137Ba in 137BaF first; 19F in 138BaF now for testing)

• Measurements of fundamental Z0 couplings possible in long term?

• Likely extensions with new molecular data, improved molecular beams, laser cooling, etc: an “anapole factory”…?

• n.b. same level crossings suggested for simulation of conical intersections in trapped ultracold molecules [Hutson, Krems, etc.]

Emine Altuntas Jeff Ammon John Barry Colin Bruzewicz

Sid Cahn, PhD Eustace Edwards Danny McCarron,PhD Eric Norrgard

Brendon O’Leary Toshihiko Shimasaki Matt Steinecker Adam West, Ph.D

Prof. Rich PaolinoUS Coast Guard Academy

DeMille

Group