Stark Effect Motivation

Search for permanent electric dipole moments of atoms (Fr) Parity nonconservation (Cs forbiden transition)

Tests of Standard Model

Stark EffectInteraction between electric field and atoms

Spectroscopic data of polarizabilityParticularly for alkali atoms

needed

MotivationAlkali atoms: simple atomic structure Precise theoretical calculation possible

Systematic studyRelativistic effectCore contribution

Precise polarizability data : needed For tests of calculation

MotivationStark effect: strong electric field

Difficult to produce strong field

Less study for Stark effectEven for alkali atoms

Toho university:Systematic study of Stark effect for alkali atoms

Li, K, Rb, CsBy high-resolution spectroscopy

TheoryStark Effect

EpHrr

⋅−= ∑−=j

jreprr P: electric dipole

momentE: electric field

( )mFJ ,,γ

αs : scalar polarizabilityαt : tensor polarizability

( ) 221 EW ts γαα +−=Δ

2EW ∝Δ

←2nd-order perturbation

Energy Shift

∑ −=Δ j jiji

EE

HW

2φφ

Wave function

TheoryStark shift < HFS

( ) ( )[ ] ( ) ( ) ( )[ ]( )( ) ( ) ( )121222321141313,,

2

−−++++−−+−

=JJFFFF

JJFFXXFFmmFJ Fγ

( ) ( ) ( )111 +−+++= IIJJFFX

J=1/2 αt =0

J: electronic angular momentF: total angular moment of atomI: nuclear spinmF : magnetic quantum number

J≧1 αt , αs

shift

Shift+split

(J,F)(J,F’)

(J,F’,|mF |)(J,F)

Experimental Setup

Atomic Beam SourceBaffle Baffle

Laser BeamPhotomultiplier

Electrode2～3mm

AtomicBeam

Lens

Mirror

SphericalMirror

Filter

Wavemeter

Lens

MirrorBeamSplitter

BeamSplitter

Semiconductor Laser

Photodiode

Fabry-PerotInterferometer

Φ6mm 1.5m

Strong Field

High Resolution

Separated Electrode System

2.0㎜Atomic beam

Laser

・Two Electrodes: Separated

Less electric dischargeStronger field

・Hard to measure distance

Compact Electrode System

distance between electrodes: stable

Stable & uniform field

Independent of flangeEasy to set

Atomic beam

Laser

Internal Focus System

Interaction region～

Transitions Measured for Rb

D1 D2

5s

5p 2P1/2

2P3/2

2S1/2

5s 2S1/2

→5p 2P1/2 (794.8nm)

D1

5s 2S1/2

→5p 2P3/2 (780.0nm)

D2

Rel

ativ

e In

tens

ity [a

rb.u

nits

]

Relative Frequency [GHz]0.0 2.0 4.0 6.0 8.0

5s

5p

2P1/2

2S1/2

3

2

3

2

F

3 4

5 6

85Rb I＝5/2

794.8 nm

5s

5p

2P1/2

2S1/2

2

1

2

1

F

1 2

7 8

87Rb I＝3/2

794.8 nm

1

34 6

5

782

15MHｚ

HFS Spectrum of Rb D1 Transition

0 0.3 0.6 0.9 1.2 1.5 1.8

0kV/cm

81.5kV/cm

Relative Frequency [GHz]

Rel

ativ

e In

tens

ity [a

rb.u

nits

]

5s

5p

2P1/2

2S1/2

794.8nm

F

3

2

3

2

3 4

5 6

8 5 R b I ＝ 5 / 2

3 4

Stark Spectrum of Rb D1 transition

0

1 0 0

2 0 0

3 0 0

4 0 0

5 0 0

0 1 0 0 0 2 0 0 0 3 0 0 0 4 0 0 0 5 0 0 0 6 0 0 0 7 0 0 0

E2 〔（kV/cm）2〕

-Sta

rk S

hift

〔M

Hz〕

( ) ( )[ ] 22/122/1221 ESPW ss αα −−=Δ

Dependence of Stark shift on electric field D1 transition

HFS Spectrum of Rb D2 Transition R

elat

ive

Inte

nsity

[arb

.uni

ts]

Relative Frequency [GHz]2.01.0 3.0 4.00.0 5.0

5p 2P3/2

85Rb I=5/2

5s 2S1/2

780.0nm

2

2

1

3

F

3

1

2

5

6

18MHz

4

3

5p 2P3/2

87Rb I=3/2

5s 2S1/2

780.0nm

F

2

3

23

1

4

6.0

89

4 1210

711

85Rb

87Rb

87Rb

85Rb

321654

987 10 11 12

0.0kV/cm

32.3kV/cm

64.5kV/cm

80.6kV/cm

Relative Frequency [GHz]

Rel

ativ

e In

tens

ity [a

rb.u

nits

]

5s

5p

2P3/2

2S1/2

2

1

2

1

F

780.0nm

3

0

mF

32

10

10

3

1

2

3

0.2 0.4 1.21.00.80.6 1.40

Stark Spectrum of Rb D2 Transition

E2 〔（kV/cm）2〕

-Sta

rk S

hift

〔M

Hz〕

0

100

200

300

400

500

600

0 1000 2000 3000 4000 5000 6000 7000

８７Rb５ｓ 2S1/2

(F=2)→

５p 2P3/2

(F=3,|mF

|)

|mF

|=0

|mF

|=1

|mF

|=2

|mF

|=3

80.6kV/cm△

◇

Dependence of Stark Shift on Electric Field D2 Transition

( ) ( ) ( )[ ] 22/122/322/3221 ESPPW sts αγαα −+−=Δ

110.6±0.9

146±32

-54.0±3.1

-40±6

Scalar & Tensor Polarizability Rb D1, D2 Transition

α0 (2P3/2 ) – α0 (2S1/2 ) αt (2P3/2 )

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛

2

cmkVkHz

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛

2

cmkVkHz

a: Richard Marrus, Douglas Mccolm and Joseph Yellen : Phys. Rev. 147, 55 (1966).b: Arthur Salop, Edword Pollack and Benjamin Bederson: Phys. Rev. 124, 1431 (1961).

aa, b

This Work

Reference

αｓ

(2P1/2 ) – αｓ (

2S1/2 )

137.0±0.6

121±18a

D 1 D 2

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛

2

cmkVkHz

Summary

1. High-resolution UV Laser SpectroscopyHFSSpecific mass shiftElectron densityElectronic configuration

2. Stark EffectElectrode systemRb D1 and D2Stark shift and splittingScalar and tensor polarizability

Stark Effect� MotivationMotivationMotivationTheory�Theory�Experimental SetupSeparated Electrode SystemCompact Electrode SystemInternal Focus SystemTransitions Measured for RbHFS Spectrum of Rb D1 Transition �Stark Spectrum of Rb D1 transitionDependence of Stark shift on electric field � D1 transition�HFS Spectrum of Rb D2 Transition Stark Spectrum of Rb D2 Transition�Dependence of Stark Shift on Electric Field � D2 TransitionScalar & Tensor Polarizability �Rb D1, D2 TransitionSummary