ultracold atomic physics laboratory national cheng kung university, tainan, taiwan 2007 osu...
TRANSCRIPT
1
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
2
Ultracold Atomic Physics LaboratoryNational Cheng Kung University, Tainan, Taiwan
2007 OSU Symposium
Ray-Yuan Chang June 22, 2007 22, 2007
L-uncoupling for the Rydberg states
L
R K
Case (d)
2Na
Case (a)
J N
LNa+Na
For singlet stateFor singlet state
3
Ultracold Atomic Physics LaboratoryNational Cheng Kung University, Tainan, Taiwan
2007 OSU Symposium
Ray-Yuan Chang June 22, 2007 22, 2007
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
4
Ultracold Atomic Physics LaboratoryNational Cheng Kung University, Tainan, Taiwan
2007 OSU Symposium
Ray-Yuan Chang June 22, 2007 22, 2007
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
5
Ultracold Atomic Physics LaboratoryNational Cheng Kung University, Tainan, Taiwan
2007 OSU Symposium
Ray-Yuan Chang June 22, 2007 22, 2007
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
6
Ultracold Atomic Physics LaboratoryNational Cheng Kung University, Tainan, Taiwan
2007 OSU Symposium
Ray-Yuan Chang June 22, 2007 22, 2007
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
7
Ultracold Atomic Physics LaboratoryNational Cheng Kung University, Tainan, Taiwan
2007 OSU Symposium
Ray-Yuan Chang June 22, 2007 22, 2007
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
8
Ultracold Atomic Physics LaboratoryNational Cheng Kung University, Tainan, Taiwan
2007 OSU Symposium
Ray-Yuan Chang June 22, 2007 22, 2007
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
9
Ultracold Atomic Physics LaboratoryNational Cheng Kung University, Tainan, Taiwan
2007 OSU Symposium
Ray-Yuan Chang June 22, 2007 22, 2007
Corrected DescriptionCorrected Description
0
1
for e parity
for f parity
q0q Splitting Constant
10
Ultracold Atomic Physics LaboratoryNational Cheng Kung University, Tainan, Taiwan
2007 OSU Symposium
Ray-Yuan Chang June 22, 2007 22, 2007
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
11
Ultracold Atomic Physics LaboratoryNational Cheng Kung University, Tainan, Taiwan
2007 OSU Symposium
Ray-Yuan Chang June 22, 2007 22, 2007
Splitting constantsSplitting constants
5511gg :: Least Square FittingLeast Square Fitting
σσ=0.04 cm=0.04 cm-1-1
12
Ultracold Atomic Physics LaboratoryNational Cheng Kung University, Tainan, Taiwan
2007 OSU Symposium
Ray-Yuan Chang June 22, 2007 22, 2007
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
13
Ultracold Atomic Physics LaboratoryNational Cheng Kung University, Tainan, Taiwan
2007 OSU Symposium
Ray-Yuan Chang June 22, 2007 22, 2007
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
14
Ultracold Atomic Physics LaboratoryNational Cheng Kung University, Tainan, Taiwan
2007 OSU Symposium
Ray-Yuan Chang June 22, 2007 22, 2007
Splitting constantsSplitting constants
5511gg :: Least Square FittingLeast Square Fitting
15
Ultracold Atomic Physics LaboratoryNational Cheng Kung University, Tainan, Taiwan
2007 OSU Symposium
Ray-Yuan Chang June 22, 2007 22, 2007
-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
16
Ultracold Atomic Physics LaboratoryNational Cheng Kung University, Tainan, Taiwan
2007 OSU Symposium
Ray-Yuan Chang June 22, 2007 22, 2007
* 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
17
Ultracold Atomic Physics LaboratoryNational Cheng Kung University, Tainan, Taiwan
2007 OSU Symposium
Ray-Yuan Chang June 22, 2007 22, 2007
(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.
18
Ultracold Atomic Physics LaboratoryNational Cheng Kung University, Tainan, Taiwan
2007 OSU Symposium
Ray-Yuan Chang June 22, 2007 22, 2007
19
Ultracold Atomic Physics LaboratoryNational Cheng Kung University, Tainan, Taiwan
2007 OSU Symposium
Ray-Yuan Chang June 22, 2007 22, 2007
20
Ultracold Atomic Physics LaboratoryNational Cheng Kung University, Tainan, Taiwan
2007 OSU Symposium
Ray-Yuan Chang June 22, 2007 22, 2007
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
21
Ultracold Atomic Physics LaboratoryNational Cheng Kung University, Tainan, Taiwan
2007 OSU Symposium
Ray-Yuan Chang June 22, 2007 22, 2007
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
22
Ultracold Atomic Physics LaboratoryNational Cheng Kung University, Tainan, Taiwan
2007 OSU Symposium
Ray-Yuan Chang June 22, 2007 22, 2007
Symmetries– Electronic states
Orbital angular momentum : L
L
=0, 1, 2, …, L, called … Electronic states.ML= L, L-1, …., -L, and =|ML|
23
Ultracold Atomic Physics LaboratoryNational Cheng Kung University, Tainan, Taiwan
2007 OSU Symposium
Ray-Yuan Chang June 22, 2007 22, 2007
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
24
Ultracold Atomic Physics LaboratoryNational Cheng Kung University, Tainan, Taiwan
2007 OSU Symposium
Ray-Yuan Chang June 22, 2007 22, 2007
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
25
Ultracold Atomic Physics LaboratoryNational Cheng Kung University, Tainan, Taiwan
2007 OSU Symposium
Ray-Yuan Chang June 22, 2007 22, 2007
For example (S=1) :
2S+1333
Multiplet structure
S
S
S
Symmetries– Total angular momentum
26
Ultracold Atomic Physics LaboratoryNational Cheng Kung University, Tainan, Taiwan
2007 OSU Symposium
Ray-Yuan Chang June 22, 2007 22, 2007
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
27
Ultracold Atomic Physics LaboratoryNational Cheng Kung University, Tainan, Taiwan
2007 OSU Symposium
Ray-Yuan Chang June 22, 2007 22, 2007
Symmetries– Hund’s coupling cases
S
NJ
L
Hund’s case(a)
2S+1
28
Ultracold Atomic Physics LaboratoryNational Cheng Kung University, Tainan, Taiwan
2007 OSU Symposium
Ray-Yuan Chang June 22, 2007 22, 2007
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)
29
Ultracold Atomic Physics LaboratoryNational Cheng Kung University, Tainan, Taiwan
2007 OSU Symposium
Ray-Yuan Chang June 22, 2007 22, 2007
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