Analysis of strongly perturbed1 1P – 2 3S+ – b 3P states of the KRb molecule

J. T. Kim1, Y. Lee2, and B. Kim3

1Department of Photonic Engineering, Chosun University.2Department of Chemistry, Mokpo National University.3Department of Chemistry, KAIST.

D. WangDepartment of Physics, The Chinese University of Hong Kong.

W. C. Stwalley, P. L. Gould, and E. E. EylerPhysics Department, University of Connecticut.

Supported by the National Science Foundation, the Air Force Office of Scientific Research, the National Research

Foundation of Korea, and KOSEF through NRL in Korea.

• Initial state for ultracold molecule (UM) spectra isa 3S+, mainly in v=20 and v=21, at low J.

• Initial state for molecular beam (MB) spectra is X 1S+, v=0 and v=1, at low J.

Motivation I: Assignment ofperturbed spectra

2 4 6 8 10 12 14 16 180

5

10

15

Ener

gy (X

103 c

m-1

)

R (Å)

X 1S+(v =0, J )a 3S+(v, J)

b 3P

2 3S+1 1P

K(4S1/2)+Rb(5PJ)

K(4S1/2)+Rb(5S1/2)

• Selection rules allow only W=1 for triplet states in the MB spectra, but W=0,1,2 for UM spectra.

• No rotational resolution due to pulsed laser linewidth, ~ 0.1 cm−1.

• To date, molecules with T < 1 mK can be produced only by combining ultracold atoms using photoassociation (PA) or magnetoassociation (MA).

• Both normally produce levels of very high v.

• Transfer to low v requires either:

1. Unusual PA mechanisms (e.g., FOPA).

2. Resonant coupling of small-R and large R levels due to electronic perturbations.

3. STIRAP-type Raman transfer. Optimal path often not obvious. The MB-UM method identifies it automatically.

Motivation II: how to producev=0 molecules?

Experimental scheme for UM (Storrs)

1) PA to form ultracold KRb*.

2) Spontaneous decay into the triplet ground state, a 3Σ+.

3) REMPI detection via intermediate states e(v, J ) .

2 4 6 8 10 12 14 16 180

5

10

15

Ener

gy (X

103 c

m-1

)

R (Å)

Ionization Continuum

PASpont. Emission

REMPI

X 1S+(v =0, J )a 3S+(v, J)

b 3P

2 3S+1 1P

e(v , J )e (v , J )K(4S1/2)+Rb(5PJ)

K(4S1/2)+Rb(5S1/2)

Experimental scheme for MB (Korea)

2 4 6 8 10 12 14 16 180

5

10

15

Ener

gy (X

103 c

m-1

)

R (Å)

Ionization Continuum

MB RE2PI

X 1S+(v =0, J )a 3S+(v, J)

b 3P

2 3S+1 1P

e (v , J )K(4S1/2)+Rb(5PJ)

K(4S1/2)+Rb(5S1/2)

1) Supersonic beam forms X 1S+ with v=0, 1.

2) REMPI detection via intermediate states e(v, J ).

2 4 6 8 10 12 14 16 180

5

10

15

Ener

gy (X

103 c

m-1

)

R (Å)

Ionization Continuum

PASE

UM RE2PIMB RE2PI

SR1

X 1S+(v =0, J )a 3S+(v, J)

b 3P

2 3S+1 1P

SR2

e(v , J )e (v , J )K(4S1/2)+Rb(5PJ)

K(4S1/2)+Rb(5S1/2)

Combined UM and MB spectra

• Intermediate states e(v, J ) can coincide.

• Comparison facilitates assignments.

• Multiplicative spectrum UMMB identifies Raman pathway SR1+SR2.

Excitation windows

4 6 8 10 1212

13

14

15

16

17

4 6 8 10 12

UM

WMB

2 11 1

3 1+

2 3+

b 3

A 1+

Ene

rgy

(103 cm

-1)

R (Å)

WUM

Intermediatelevel

MB

Complete spectra from the MB and UM experiments

15000 15200 15400 15600 15800 16000

0.0

0.5

1.0

0.0

0.5

1.0

b 3

2 3

15 10 5

Inte

nsity

(ar

b. u

nits

)

Energy (cm-1)

v'=01 1

MB Spectra

UM Spectra

Franck-Condon factors

15000 15500 160000.000

0.005

0.010

0.015

2 3+ (v') a 3+ (v" = 21)1 1 (v') a 3+ (v" = 21)

FC

F

Energy (cm-1)

14000 14500 15000 15500 160000.0

0.1

0.2

0.3

1 1 (v') X 1+ (v" = 0)

FC

F

Energy (cm-1)

2 3+ (v') X 1+ (v" = 0)

15000 15500 160000.0000.0020.0040.0060.008

b 3 (v') a 3+ (v" = 21)

FC

F

Energy (cm-1)

• Calculated from the potential energy curves of Rousseau, Allouche, and Aubert-Frécon, J. Mol. Spectrosc. 203, 235 (2000).

• Not shown is b 3P X 1S+, for which the FCFs are negligibly small.

• The 1 1P X transition has a larger electronic transition moment than 2 3S+ X, in addition to its larger FCFs.

Central portion, with assignments

15450 15500 15550 15600

b 31

b 30,1, 2

2 31

2 31,0-

1 11

1 11

Energy(cm-1)

UM

MB

Due to singlet-triplet mixing, the 1 1P1 and 2 3S+

1 levels are evident in both spectra.

The b 3P1 level is weak, but nevertheless visible, in the MB spectrum.

Avoided crossing near 6.5 Å

5.0 5.5 6.0 6.5 7.0 7.513000

14000

15000

16000

4(0+) 3 1+

2(0)1(2)

3(0+)4(0+) 3 1+

b 31 1

2 3+2(1)

4(1)

3(0) 3(0+)

1(2)

3(1)

2(0)

Ene

rgy(

cm-1

)

R (Å)

3(0)

3(1)

Avoided crossings between levels of equal W cause anomalous spin-orbit splittings for large R, much smaller for the 2 3S+ state than for b 3P.

High-frequency portion, showing reversedfine structure for the 2 3S+ state

15650 15700 15750 15800 15850

b 31

2 30-, 1b 3

0,1, 2

2 31

+

1 11

Energy(cm-1)

UM

MB

1 11

Predicted and measured W splitting

13000 14000 15000 16000 17000-5

0

5

10

15

Ene

rgy

Diff

eren

ces

(cm

-1)

Energy (cm-1)

Ab initio

Experiment

Prior experiments:1. N. Okada, S. Kasahara, T. Ebi, M. Baba, and H. Kato,

J. Chem. Phys. 105, 3458 (1996).

2. S. Kasahara, C. Fujiwara, N. Okada, H. Kato, and M. Baba, J. Chem. Phys. 111, 8857 (1999).

Vibrational intervals DG from UM spectra

• Agreement of overall trends with theory shows that the potential energy curves have the correct shape.

• Some perturbations and scatter are evident, due to admixture between states

• Agreement with prior experiments for 1 1P is excellent, with just one level in disagreement.

0 50 100 150 2000

20

40

60

80

0 20 40 60

0

20

40

60

0 50 100 150

0

10

20

30

40

50

Gv'

+1/

2 (

cm-1

)

v'

Experiment Theory (Rousseau et al.)

(b)

(c)

Experiment (This work) Prior Experiments Theory (Rousseau et al.)

Gv'

+1/

2 (

cm-1

)

v'

(a)

1 1

2 3

b 3

Experiment Theory (Rousseau et al.)

Gv'

+1/

2 (

cm-1

)

v'

MBUM product spectra: interpretation

15400 15450 15500 15550

b 30

1 11

2 3+

1

2 3+

0 b 31

b 32

b 31

1 11

Energy (cm-1)

UM

2 3+

1

MB

MBUM

Ultracold Molecule intensity:

Molecular Beam intensity:

Stimulated Raman rate:

For Raman transfer from a 3S+ (v=21) X 1S+ (v=0), need an upper state in common between both spectra

a 3S+ (v=21)

X 1S+ (v =0, J =0)

2

2

MB UM

, , , ,

, , , 0, 0 ,

so .

a e

e X

I a v J d e v J

e v J d X v J

I I I

2

MB , 0, 0 , , .e XI X v J d e v J

2

UM , , , , .a eI X v J d e v J

SR1SR2

e (v ,J )

Largest amplitude is via v =7 of the 1 1P1 state.

MBUM product spectra: results

15400 15450 15500 15550

b 30

1 11

2 3+

1

2 3+

0 b 31

b 32

b 31

1 11

Energy (cm-1)

UM

2 3+

1

MB

MBUM

20

30

40

50

60

20

30

40

50

60

15200 15600 16000

b 3(=1)G

v+1/2 (cm

-1 )

Tv(cm-1)

15

1 1

Gv+

1/2 (cm

-1 )

v'=0 5

10

v=7

2 3+(=1)

This level is also noticeably perturbed on the DG plot (expanded below.

Summary

• Numerous new assignments to the perturbed 1 1P – 2 3S+ – b 3P states of 39K85Rb are made by comparing UM and MB spectra.

• Good agreement with previous experiments (where available) and with potential curves from Rousseau, et al.

• The MBUM product spectrum automatically selects optimal pathways for STIRAP transfer of ultracold molecules to X 1S+, v=0.

• To be published in PCCP special issue (spectra) and JPC Letters (Raman pathway via MBUM product.)