Ultracold Atomic Physics Laboratory National Cheng Kung University, Tainan, Taiwan 2007 OSU...

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Ultracold Atomic Physics LaboratoryNational Cheng Kung University, Tainan, Taiwan

2007 OSU Symposium

Ray-Yuan Chang June 22, 2007 22, 2007

Investigation of the Investigation of the

L-uncoupling and Λ-doubling L-uncoupling and Λ-doubling

in the Rydberg states of the sodium dimerin the Rydberg states of the sodium dimer

$$ : National Science Council and National Space Program Office, Taiwan

Ray-Yuan Chang, Thou-Jen Whang, Chuen-Ping Cheng, and Chin-Chun TsaiNational Cheng Kung University, Tainan, 70148 Taiwan

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2007 OSU Symposium


L-uncoupling for the Rydberg states

L

R K

Case (d)

2Na

Case (a)

J N

LNa+Na

For singlet stateFor singlet state

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2007 OSU Symposium


J

02

3

10

4

42

2

4

3

214

3

210

4

3

2

341

56

4 32

31

5

12

32

RK

Case (d)

Case (a)

1

1

1L

R K

Case (d)

Coupling case transition

Case (a)

J N

L

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2007 OSU Symposium


Ground state(X1g

+)

Intermediate state (B1u)

Fluorescence

a3u+

(23g or 33g)( 51g 、 51g )

( 35350 ～ 40300 cm-1 )

Experimental energy range 35350 ～ 40300 cm-1

Ar+ laser9-lines

Dye-Ring laser( DCM )

6022.0286 cm-1

(29328 ～ 34278 cm-1 )

( 19440 ～ 22000 cm-1 )

( U.V. 292 ～ 341 nm )

Probing energy rangeProbing energy range

Detection

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Ar+ Laser

Interface Box

Computer Lock-inAmplifier

BS

Dye-ring Laser

Verdi-10Laser

PMT+Filter

ChopperController

Heat Pipe Oven

I2 Cell PMT+Filter

L

L II

C

M

M

OODR-Experimental setup

Systematic accuracy ～～ 0.03cm0.03cm-1-1

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2007 OSU Symposium


2,

0 0

1[ ( 1) ]

2

ij

v J iji j

T Y v J J

Lower terms of Dunham Coefficients (Yij)

j\i 0 1 2 3 4 ……..

0 y00 ωe -ωexe ωeye ωeze

1 Be -αe γe δe .. 2 -De -βe .. .. .. 3 He .. .. .. .. 4 Le .. .. .. .. .. .. .. .. .. ..

Dunham Coefficients

Harmonic Oscillator

Anharmonicpart

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2007 OSU Symposium


36000

36500

37000

37500

38000

38500

39000

0 500 1000 1500 2000 2500 3000 3500

B(0,42)

B(9,38)

B(6,43)

B(10,12)

B(6,27)

B(17,38)

B(7,43)

B(8,28)

B(12,36)

B(9,56)

B(10,42)

B(17,45)

35500

36000

36500

37000

37500

38000

38500

0 2000 4000 6000 8000

B(0,42)

B(10,12)

B(6,27)

B(6,43)

B(7,43)

B(8,28)

B(9,38)

B(17,38)

B(9,56)

B(2,82)

B(9,64)

B(9,64)

B(7,25)

B(9,36)

15 g state 15 g state

Data Fitting

En

ergy

(cm

-1)

J （ J+1 ） -Λ2 J （ J+1 ） -Λ2

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2007 OSU Symposium


J+1

J=J

J-1

J +1

J =J

J -1

J

e

e

f

f

e

fe

f

e

e

e

P P

P

R

R Q

QRQ

1uB

1gX

Separation of e/f levels

Case (a)

1, 0,1J , ,P Q R

,P R

e e

f f

Q

e f

51g

51g

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2007 OSU Symposium


Corrected DescriptionCorrected Description

0

1

for e parity

for f parity

q0q Splitting Constant

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2007 OSU Symposium


0 500 1000 1500 2000 2500 3000 3500 4000-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

f-e(c

m-1)

0 5 10 15 20-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

12

v 21J J

5511gg ：： e/f level differencee/f level difference

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2007 OSU Symposium


Splitting constantsSplitting constants

5511gg ：： Least Square FittingLeast Square Fitting

σσ=0.04 cm=0.04 cm-1-1

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2007 OSU Symposium


0 500 1000 1500 2000 2500

-0.10

-0.05

0.00

0.05

0.10

R

esid

ual

s (c

m-1)

σ=0.026 cm-1

Eigenvalue (cm-1)

5511gg ：： Regenerate the eigenvalueRegenerate the eigenvalue

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2007 OSU Symposium


0 500 1000 1500 2000 2500 3000-0.3

-0.2

-0.1

0.0

0 5 10 15 20-0.35

-0.30

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

f-e(c

m-1)

12

v 21J J

5511gg ：： e/f level differencee/f level difference

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2007 OSU Symposium


Splitting constantsSplitting constants

5511gg ：： Least Square FittingLeast Square Fitting

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2007 OSU Symposium


-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0 500 1000 1500 2000

Res

idu

als

(cm

-1)

σ=0.028 cm-1

Eigenvalue (cm-1)

5511gg ：： Regenerate the eigenvalueRegenerate the eigenvalue

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＊ We’ve observed the L-uncoupling in the Na2 by using the high resolution OODR spectroscopy. ＊ The energy splitting of both the 51g 、 51g states have been figured out with

σ< 0.03 cm-1

ConclustionConclustion

＊ The transient Hund’s case transition process can be mapped out by the investigation of the higher Rydberg series in (nd) 1g 、 (nd)1g states

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2007 OSU Symposium


(B1u) First order splitting constant

The Λ -doubling splitting increases as a quadratic function of rotational quantum number J and the dependence on the vibrational quantum number v is weak.

The large Λ -doubling splitting constants indicate that the effects are from the perturbations between the adjacent electronic states as well as the uncoupling of orbital angular momentum L.

26 intermediate levels of the B state are populated by nine Argon laser lines.

230 rovibrational levels are assigned to the 5spg state.

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2007 OSU Symposium


References： * P. Kusch and M. M. Hessel , J. Chem. Phys. 68, 2591 (1978). J J Camacho , Spectrochimica Acta Part A56, 769 (2000).

B1Πu X1Σg+Ar+ laser

Ar+ laser lines： 514.5*, 501.7, 496.5*, 488.0*, 476.5*, 472.7, 465.8, 457.9*, 454.5nm 。

Pumping to the Intermediate Levels

Laser line(nm) Energy(cm-1) B(v’,J’) TB(v’,J’) X(v”,J”) TX(v”,J”)

496.5 20135.057 (4,30) 20976.0696 (4,30) 840.8850

(7,43) 21430.7481 (6,44) 1295.6275

(8,28) 21415.3652 (7,29) 1280.2374

Levels in B1u state populated by one of Ar+ laser lines

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Symmetries in the cold collisions

Two atoms collide with channels doubled

Atom1, Rb 5s 2S1/2 Atoms, Rb 5s 2S1/2

Ground state collisions

Electron spin s1=1/2 s2=1/2 total S=s1+s2

Angular momentum l1=0 l2=0 total L=l1+l2

R (interatomic distance)

S=0 or 1 and L=0

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2007 OSU Symposium


Symmetries– Electronic states

Orbital angular momentum ： L

L

=0, 1, 2, …, L, called … Electronic states.ML= L, L-1, …., -L, and =|ML|

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2007 OSU Symposium


Electronic spin S= si

For 0, the internal magnetic field causes a precession of S about the field direction (internuclear axis).

Components of the precession: = S, S-1, S-2, …, -S

S

Symmetries– Electronic spin

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2007 OSU Symposium


J

02

3

10

4

42

2

4

3

214

3

210

4

3

2

341

56

4 32

31

5

12

32

RK

Case (d)

Case (a)

1

1

1L

R K

Case (d)

Coupling case transition

Case (a)

J N

L

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2007 OSU Symposium


For example (S=1) :

2S+1333

Multiplet structure

S

S

S

Symmetries– Total angular momentum

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2007 OSU Symposium


Symmetries– Hund’s coupling cases

Hund’s case(a)

S

is ： individual electron spiniS s

Total electron spin

L

： individual electron angular momentum

iL i

Total orbital angular momentum

J N

Nuclei rotation

N

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2007 OSU Symposium


Symmetries– Hund’s coupling cases

S

NJ

L

Hund’s case(a)

2S+1

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Ψ(x, y, z)

Case(a)

2 1S

Symmetries– Electronic eigenfunctions

Plane symmetry ( , , ) ( , , )x y z x y zσΨ Ψ

Non-degenerate states =0+: even symmetry as +- : odd symmetry as -

Ψ(x, y, z)

Inversion symmetry

( , , ) ( , , )i x y z x y zΨ Ψ

+: even symmetry as gerade state, g- : odd symmetry as ungerade state, u

/g u

Ψ(-x, -y, -z)

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2007 OSU Symposium


The standard deviation excess the systematic accuracy!!～～ 0.03cm0.03cm-1-1

Is there something wrong!?

Dunham Coefficients?

15 g state 15 g state10.27 cmσ 10.39 cmσ

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