Magneto-optical trapping of radioactive

francium atoms:

toward search for electron electric dipole moment

Ken-ichi Harada

1Cyclotron and Radioisotope Center (CYRIC), Tohoku University, Japan

Electron Electric Dipole Moment (eEDM)

Many theoretical models predict larger values for eEDM.

The eEDM is a sensitive tool for exploring new physics

beyond the Standard Model.

Non-zero EDM = Violation of time reversal symmetry

CP-violation

CPT invariance

The Standard Model predicts the value of the eEDM to be ~ 10-38

ecm.

The best limit on eEDM has been obtained in the ThO experiment:

1.1×10-29

ecm

de

(e cm)

Present

ACME collaboration, Nature 562, 355 (2018)

𝐻 = −𝜇𝒔

|𝒔|∙ 𝑩 − 𝑑

𝒔

|𝒔|∙ 𝑬 𝐻 = −𝜇

𝒔

𝒔∙ 𝑩 + 𝑑

𝒔

|𝒔|∙ 𝑬

Parity (P)

Time reversal (T)

S

Interaction Hamiltonian

μ: Magnetic moment

B: Magnetic field

d: Electric dipole moment

E: Electric field

S: Spin

23Zd

dR

e

atom =

Francium EDM search

Fr

ed

Ԧ𝑑𝐹𝑟 = 900 × Ԧ𝑑𝑒

Rb Cs

Tl

Fr

Electron EDM ~ magnified in the paramagnetic atoms

Francium:

• Heaviest alkali element

• EDM enhancement: largest ~ 900

• Atomic structure: simple

• Radioactive atom: decay time ~ 3 min (210

Fr)

Atomic number

suitable for laser cooling and trapping

D. Mukherjee et al.

J. Phys. Chem. A 113, 12549 (2009).

B. M. Roberts, et al.,

Phys. Rev. A 88, 042507 (2013).

Enhancement

factor

EDM measurement

ΔU = −𝑑𝑎𝑡𝑜𝑚 ⋅ 𝐄 = −𝑅𝑑𝑒𝐅

𝐹⋅ 𝐄

Interaction energy of an atom in electric field

|+>

|−>

ΔU

ΔU

ΔU

ΔU

E // B E // -BE=0

（parallel） （anti-parallel）

ℎ𝜈↑↑ = −2𝜇 ⋅ 𝐵 − 2𝑑𝑎𝑡𝑜𝑚 ⋅ 𝐸

ℎ𝜈↑↓ = −2𝜇 ⋅ 𝐵 + 2𝑑𝑎𝑡𝑜𝑚 ⋅ 𝐸

⇒ ℎΔ𝜈 = 4𝑑𝑎𝑡𝑜𝑚 ⋅ 𝐸

Atomic electric dipole moment : datom

（parallel）

（anti-parallel）

The atomic EDM is estimated

by the frequency difference between two.

μ: Magnetic moment

B: Magnetic field

de: electron electric dipole moment

E: Electric field

F: Total angular momentum

ーB E

+

ー

ー

+ EB

EDM search with laser cooled atoms

EDM sensitivity

one measurement

R : enhancement factor

E : external electric field

t : interaction time

N : number of atoms

n = T / t : number of measurements

T: total experimental time

𝐵𝑚 =𝑣 × 𝐸

𝑐2

t

Laser cooling

Cold atom experiment (t ～ 1 s)

Systematic errors in EDM experiments

• Motional magnetic fields,

• Magnetic field inhomogeneity

Velocity vElectric field E

Magnetic field B0

Atomic beam experiment (t ～ 1 ms)

Electric field

Atomic beam

Cold atoms

Accurate measurement is possible.

• Suppression of the motion-induced

magnetic filed

• Atomic ensembles in a small region

The interaction time is about 1 s with laser cooled atoms, which is about 103

times

longer than that of the atomic or molecular beam experiments.

eEDM search experiments

|de| < 1.1×10-29

e cm using ThO.

The ACME Collaboration,

Nature 562, 355 (2018).

The eEDM experiments are ongoing in the world, using paramagnetic atoms, molecules and solid state.

Goal:

de≲ 10

-29e cm

2018

From AVF Cyclotron

Fusion reaction:

18O +

197Au → 210

Fr + 5n

Entire apparatus for MOT

Optical fibers of 150 m

Laser room (non radiation-controlled area)

We have constructed a beamline

for magneto-optical trapping (MOT) of Fr. @ CYRIC

Wall

106

ions/s @ 0.2 μA of 18

O

(Tohoku Univ.)

Rb atomsOxygen beam

Poster presentation

by Ozawa

Neutralizer and MOT cell

Work function of Y: 3.2 eV

・ Possible to accumulate Fr ions.

(Large number of Fr atoms)

・ Possible to confine the Fr atoms in the

glass cell.

(Avoid the loss of neutral Fr atoms)

Advantages of the system

Operation of the neutralizer

・ Fr ions are accumulated on the Y target for

several tens of seconds.

・ Y target is turned in the direction of the glass

cell.

・ Y target is heated up to 1000 K.

・ Neutralized Fr atoms are released into the glass

cell.

・ Y target is returned to the initial position, and

the process is repeated again and again.

Feature of the glass cell

•Material: Quartz with AR coating

• OTS (octadecyltrichlorosilane) coating for

preventing stick of atoms on the wall.

Ionization potential of Fr: 4.0 eV,

(Rb: 4.2 eV)

To neutralize ions, an yttrium (Y) metal is used.

Neutralized atoms are dominantly released from

Y surface.

Lasers for Fr-MOT

210Fr

Repumping

718 nm

(ECLD)

Trapping

718 nm

(MBR110)

There is no Fr reference cell for stabilizing the

frequency of laser sources precisely,

No stable isotopes of Fr.

Toptica DL100 Pro

Repumping laser (718 nm)

30 mW output

Trapping laser (718 nm)

3.5 W output

VerdiMBR110

Coherent

Verdi (532 nm) MBR110

Magneto-optical trapping (MOT) is one of the techniques for cooling and trapping of atoms.

Natural linewidth of

Fr atom: 6 MHz

718 nm,

3.5 W

• Frequency modulation spectroscopy of

Iodine molecules

• Frequency offset locking by measuring the

beat frequency between two laser sources.

718 nm,

30 mW

EOM: Electro-optic modulator

ECDL

3.36 GHz

Frequency stabilization for trapping

Experimental setup for frequency

modulation spectroscopy of iodine

molecules

Trapping wavelength: 718.216 nm

（F = 13/2 → F’ = 15/2）

Lock point

0.0 0.5

Frequency [GHz]

Frequency modulation spectrum

(with 12 MHz EOM)

Sig

nal in

tensity [arb. units] P(78) 1-9 band

Presumed Fr

trapping frequency

0.5

Frequency

Repumping lightTrapping light

46 GHz

Frequency stabilization for repumping

A frequency-offset locking technique can lock the frequency difference between the

two laser sources to a constant value.

The beat frequency between the trapping and repumping lights is about 46 GHz.

• Detect a 46-GHz frequency directly using a photodiode.

• Generate first-order sideband frequency at 46 GHz with an EOM.

However, it is difficult to ...

Frequency

Repumping lightTrapping light

46 GHz

We generated a 46 GHz component as a 10th-order sideband by injecting the radio

frequency (RF) of 4.6 GHz into the EOM.

Less than 1 GHzsidebands

4.6 GHz

0th-order

(Carrier)

10th-order

The signal less than 1 GHz can be easily observed as a beat signal using a standard-fast-

silicon photo detector.

Frequency stabilization for repumping

Trapping light

without EOM modulation

with EOM modulation

Repumping light

The repumping frequency is...

• 46 GHz from the trapping frequency.

• almost corresponds to the 10th-order

sideband component.

Frequency / GHz

Transm

issio

n in

tensity /

a.u.

Photline NIR-MPX800

Fabry-Perot cavity output

The beat signal between +10th-

order sideband and the

repumping light was detected.

Beat frequency / MHz

Intensity / a.u.Trapping power 1.5 mW

Repumping power 0.4 mW

Error signal

𝜈10 / MHz

Vo

ltage

/ V

Locking point

Delayed self-

homodyne

detection

K. Harada et al., Appl. Opt. 55, 1164-1169 (2016).

ECDL

Stabilization

cirucuit

MOT of neutralized atoms

• Improvement of vacuum degree

• Increase of the number of Fr ions to improve S/N.

• Improvement of the design of the glass cell

up

down

Fr ions

Fr atoms

Coils

Trapping power: 30 mW / axis

Repumping power: 8 mW

Magnetic field gradient: 80 G/cm

Vacuum degree 107 Pa

Degradation of

vacuum degree

2 mm

Summary

We have achieved the construction of the francium beamline

and trapped Fr atoms.

Future plans

• Design of new glass cell for improving the trapping efficiency.

• Improvement of vacuum degree.

• Improvement of the number of Fr ion beam.

Development of new apparatus for magneto-optical trapping of Fr atoms.

We will achieve a large number of trapped atoms and

install the system to the beamline for EDM measurement.

Electron EDM is a good candidate to search for the physics beyond the

standard model.

Laser cooled Fr atoms are one of the best candidate for electron EDM

measurement.