The 1 states of NaCs: spectroscopy,
lifetimes, permanent and transition
dipole moments.
R. FERBER, O. DOCENKO, I. KLINCARE, O. NIKOLAYEVA, M. TAMANIS, J. ZAHAROVA
University of Latvia, Department of Physics, 19 Rainis blvd., LV-1586, Riga, Latvia;
A. PASHOV
Sofia University, Department of Physics, 5 J Bourchier blvd, 1164 Sofia, Bulgaria;
H. KNÖCKEL, E. TIEMANN
Leibniz Universität Hannover, Inst.f. Quantenoptik,
Welfengarten 1, 30167 Hannover, Germany;
Leibniz Universität Hannover
A. V. STOLYAROV, E. A. PAZYUK, A. ZAITSEVSKII
Moscow State University, Department of Chemistry, Moscow, 119899, Russia.
Outline:
• Motivation and background
• Spectroscopy and PECs
– G(3)1 state
– B(1)1 state
• Permanent dipole moments
• Lifetimes and transitions moments
• Conclusions
Motivation
Heteronuclear alkali diatomic molecules with large permanent electric
dipole moment are promising for:
– PA and ultracold molecule formation
– ultracold X1+ (v = 0) in absorption-emission cycle from a3+ via
B(1)1~c(2)3+ [Kerman PRL 2004], A1+~b3 [Stwalley EPJD 2004]
– fast and robust quantum-computing schemes
– tests of fundamental theories (by limits of the electron dipole moment)
Ultracold NaCs molecule:
– inelastic cold collisions in a Na-Cs trap […Bigelow, PRA 1999]
– translationally cold a3+ NaCs obtained by PA […Bigelow, PRA 2004; JPB
2006]
Background (NaCs molecule)
• high accuracy FTS ground state data [Docenko et al. EPJD 2004,
JPB 2006]
• almost no experimental data on excited states […W. Demtröder
CPL1984 D(2)1, v<3]
• extensive theoretical study [Korek Can.J.Ph.2000, JCP 2007;
Ayamar, Dulieu MP 2007]
• no data on lifetimes and permanent electric dipole moments — to
exploit our experience on NaK and NaRb.
Spectroscopy and PECs
24
This work, JCP, 2006
3
(3) 
3 +
(4) 
1 +
(5) 
Na(3p)+Cs(6s)
22
1 +
(4) 
1
(3) 
20
W. Demtröder,
CPL, 1984
Na(3s)+Cs(5d)
1
D(2) 
18
3
d(2) 
3 +
e(3) 
3 +
c(2) 
1
B(1) 
14
Na(3s)+Cs(6p)
1 +
Energy, 10 cm
-1
16
1 +
C(3) 
A(2) 
3
b(1) 
3
This work, JCP, 2007
12
10
8
6
3 +
a(1) 
Na(3s)+Cs(6s)
4
2
1 +
X(1) 
0
2
4
6
8
R, Å
10
12
14
Spectroscopy and PECs
LU Riga
FTS Bruker IFS-125
(emissiom and absorption,
25000 – 4700 cm-1,
resolution up to 0.006 cm-1 )
Heat-pipe
Oven for the heat-pipe
Spectroscopy and PECs
v"= 53
1
v"= 16
1 +
G  (21, 75) <- X  (0, 75)
Na2
1 +
B u -> X  g
1
One LIF line
NaCs
1
1 +
G  -> X 
1
17000
1 +
v"= 38 G  (25, 67) <- X  (2, 68)
v"= 57
17500
18000
18500
-1
wavenumbers, cm
19000
19500
No buffer gas, no relaxation lines
Add buffer gas, e.g. argon,
and you get....
17055
17060
17065
17070
Spectroscopy and PECs
v"= 53
1
v"= 16
1 +
G  (21, 75) <- X  (0, 75)
Na2
1 +
B u -> X  g
1
Instead of one LIF line
NaCs
1
1 +
G  -> X 
J'= 82 81 80 79 78 77 76 75 74 73 72 71 70 69
50
Q branch
45
LIF Q line
40
1
17000
1 +
v"= 38 G  (25, 67) <- X  (2, 68)
v"= 57
17500
18000
18500
-1
wavenumbers, cm
19000
19500
manifold of lines from different rotational
levels
0
Plenty of data at one shot!
P branch
85 84 83 82 81 80 79 78 77 76 75 74 73 72 71
R branch
78 77 76 75 74 73 72 71 70 69 68
A relatively simple method (one
laser experiment) for studying
excited states!
17055
17060
17065
wavenumber, cm
17070
-1
The G(3)1 state of NaCs
1.2
G(3)1 →X1Σ+ LIF
Ee  E  Δ  qJ'(J' 1 )
f
ef
Experiment
linear fit
22.5
1
0.8
-5
q factor, 10 cm
-1
(3)  state dissociation limit
22.0
v'
Energy, 10 cm
-1
35
30
25
3
0.4
21.5
q( ' )  q0  q1 '
20
21.0
15
0.0
10
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
20.5
Vibrational quantum number, v'
+
Ar ; Nd:YAG Hanover
+
Ar Rīgā
5
20.0
0
0
10000
J'(J'+1)-1
20000
30000
About 820 rovibronic term values of the (3)1 state have been obtained with
accuracy 0.01 cm−1 covering v' = 0 to 37 in a wide range of J' = 3 to 190 and
characterizing ca. 95% of the (3)1 state potential well depth.
The G(3)1 state of NaCs
De=1928.88 ± 0.20 cm-1 – Na(3p1/2)+Cs(3s1/2)
Te=19981.47 ± 0.10 cm-1
Na(3p)+Cs(6s)
22.0
Re=4.894 Å
3
E, 10 cm
-1
21.5
21.0
UIPA
20.5
Uab initio (Korek et al., 2000)
Udif
20.0
4
5
6
7
8
9
10
11
R, Å
•A direct IPA fit allowed constructing a pointwise potential (33 grid points, R = 3 to
11 Å), which reproduces the observed experimental term values with standard
deviation of 0.0074 cm−1;
•No pronounced perturbations, except of weak perturbations at v' = 29 and 30.
The B(1)1 state of NaCs
0.3
(Δ) 105 energy levels
Laser
0.2
1
3 
B ~c 
16.6
1 +
X
a
16.4
25
3
Energy, 10 cm
-1
0.05
v'
3 +
0.00
11000
12000 13000 14000
-1
wavenumber, cm
0.05
15000
16000
20
16.2
15
16.0
Laser
10
1
1 +
B  -- X 
0.04
15.8
0.03
5
0.02
15.6
0.01
v' = 025; J' = 5 168
(•) 741 energy levels 15.4
0.00
11000
12000 13000 14000
-1
wavenumber, cm
15000
16000
0
0
5000
10000
J'(J'+1)-1
15000
20000
The B(1)1 state of NaCs
-6
q, 10 cm
q - factor
-1
-6
q, 10 cm
-1
40.0
4.0
20.0
2.0
0.0
20
0.0
60
70
80
90
100
40
60
80
100
120
140
-20.0
-2.0
-40.0
-4.0
-60.0
The difference between observed and calculated (from IPA) term energies
E0.015
-Ecalc, cm
expt
-1
0.8
Eexpt-Ecalc, cm
-1
0.6
0.010
0.4
0.005
0.2
0.000
60
70
80
90
100
J'
-0.005
0.0
20
40
60
80
100
-0.010
-0.015
v' = 0
140
J'
-0.2
f
e
120
f
e
-0.4
-0.6
v' = 4
The B(1)1 state of NaCs
UIPA
17
Uab initio (Korek et al., 2000)
Uab initio (Korek et al., 2007)
-1
v'=25
3
Energy, 10 cm
Na(3s) + Cs(6p3/2)
16
Na(3s) + Cs(6p1/2)
A final direct IPA fit
was realized using
the data field of
weakly perturbed 543
(from 741) energy
levels, which covers
about 87% of the
potential well depth.
15
4
6
8
10
Internuclear distance, Å
12
The obtained PEC reproduces:
v' = 0 to 7 with a standard deviation 0.011 cm-1 (omitted 198 levels from 631 by
anomalous q (90) and Δ>0.03 cm-1 (108)).
v' = 8 to 25 with a deviation less than 1 cm-1 (with some exceptions).
Permanent electric dipole moments
24
3
(3) 
3 +
(4) 
1 +
(5) 
Na(3p)+Cs(6s)
22
1 +
(4) 
1
(3) 
20
Na(3s)+Cs(5d)
1
D(2) 
This work, JCP, 2006
18
3
d(2) 
3 +
e(3) 
3 +
c(2) 
1
B(1) 
14
Na(3s)+Cs(6p)
1 +
Energy, 10 cm
-1
16
1 +
C(3) 
A(2) 
3
3
b(1) 
12
10
8
6
3 +
a(1) 
Na(3s)+Cs(6s)
4
2
1 +
X(1) 
0
2
4
6
8
R, Å
10
12
14
ground
X1 state
excited
1 state
Experiment: method
Jef   RF
forbidden
+
e J
f
+
+
e J+1
e J (odd)
e J-1
v' = 8, J' = 25
v' = 6, J' = 19
dc or RF electric field has been used
to mix e and f components in the
exited 1 state, thus leading to the
appearance of “forbidden” lines in the
LIF spectra. To resolve spectral lines
double monochromator has been
used.
E = 0 V/cm
578.42 nm 578.58 nm
Laser
572.75 nm
Na+Cs
E = 250 V/cm
 Jef
EM 
 
 2
2

Jef
578.49 nm
R Q P
572.69 nm
572.81 nm
R Q P
2
  dEM 
 

  J ( J  1) 

2
Experiment: typical results
dc electric field
forbidden / allowed signal
0.7
RF electric field
RF-ODR signal
1
for NaCs G (3) , v'=17, J'=47 level
y

1
2.0
for NaCs G (3) , v'=17, J'=47 level
exc
0.6
obs
E
z
0.4
rel. intensity
intensity ratio (IP,R/IQ)
1.8
x
0.5
0.3
d
J
 ef
0.2
0.1
1.6

J
ef
1.4
1.2
1.0
0.0
0
1000
2000
3000
4000
electric field E, V/cm
5000
160 180 200 220
240 260 280 300 320 340 360
frequency, MHz
Experiment and ab initio for (3)1 state
permanent electric dipole moment
9.0
8.5
8.0
  qJ (J  1)
J
ef
|d| (Debye)
8
7
39
4766
7.0
25
6.5
50
67
6.0
5.5
46
experiment
MPPT calculation (J'=50)
4.5
q( ' )  q0  q1 '
19
4.0
53
25
0
6
-6
-1
q factor (10 cm )
45
19 25
45
5.0
9
22
24
7.5
q - factor
10
53
8
4
47 66
3
cubic fit
2
75
25
q( ' )  q0  q1 'q2 ( ' ) 2  q3 ( ' )3
1
67
50
46
0
0
4
8
12
16
20
12
16
20
24
vibrational quantum number, v'
theory
39
5
4
24
vibrational quantum number, v'
28
32
36
28
32
Experiment and MPPT ab initio for (3)1 state
permanent electric dipole moment
1
B (1) 
2
0
20
24
1
D (2) 
d, D
-2
-4
46
-6
45
24
19 25
53
39
4766
50
25
67
1
G (3) 
-8
-10
-2
0
2
4
6
8
10 12 14 16 18 20 22 24 26 28 30 32 34
vibrational quantum number, v
Lifetimes and transitions moments
24
Na(3s)+Cs(7s)
1 +
(5) 
Na(3p)+Cs(6s)
Energy (103 cm-1)
This work, Phys.Rev.A,
2007
1 +
E
1
(3) 
20
Na(3s)+Cs(5d)
1
(1) 
1 +
C
1
3
(1) 
16
D
Na(3s)+Cs(6p)
1
B
3 
c
3
b
1 +
A
12
3 
a
5
Na(3s)+Cs(6s)
1 +
X
4
E1+
18.9
18.8
3
18.7
(1)3
18.6
2
18.5
D1
18.4
1
18.3
(1)1
3.5 4.0 4.5 5.0 5.5
0
2
4
6
8
10
12
14
Internuclear distance, (Å)
16
18
Experiment: method
experiment
monoexponential decay fit
excitation laser pulse
LIF decay

eff=19.96 ns
2000
eff
i

1

rad
i
 nCs i v
1500
1000
5.5
v'=3, J'=45
500
rad
 =29.15 ns
5.0
0
100
200
Channel number
0
60
Time (ns)
=4.6 x 10
-14
cm
2
120
7 -1
0
1/eff (10 s )
Counts (arb.units)
1
v'=3; J'=45
2500
4.5
4.0
3.5
0
1
2
nCsv (10
20
3
-2 -1
cm s )
4
Experiment and ab initio calculations
1
34
48
40
30
J'=50
J'=100
J'=45
28
J'=16
36
35
34
26
36
rad, ns
44
rad, ns
(ns)
rad
1
D(2) 
38
37
32
Radiative lifetime, 
(3) 
J'=106
33
24
32
3
32
0
1
2
v'
28
J'=45
24
v'
(3)1 J'=50
J'=25
J'=47
20
J'=67
16
0
4
8
12
16
20
24
Vibrational quantum number v'
MPPT (——) – A. Zaitsevskii
CPP (——) – Ayamar, Dulieu
28
Transition dipole moments for the NaCs molecule
The radiative lifetimes of the NaCs (1-3)1
(J' = 1) states predicted by Eq.(*) using
MPPT and CPP transition dipole moments
dijab (R) and corresponding ΔUijab(R)
functions. The vibrational upper state
wavefunctions were calculated by the
relevant "difference-based" PECs Uidif(R).
Ab initio transition dipole moments (a.u.)
D B
3.0
B
2.5
X
2.0
D
A
1.5
1
(3) 
1.0
X
0.5


8 2

v i' ( J ' )  U ij3 d ij2  v i' ( J ' ) ()
3 0
 j

1
0.0
 rad
-0.5
-1.0
D
X
rad
-1.5
3
4
5

44
6
7
8
9
10
Internuclear distance (Å)
=890 ns
CPP (dash lines)
MPPT (solid circles)
40
1
D(2) 
36
, (ns)
MPPT (solid symbols) – A. Zaitsevskii
CPP (dash lines) – Ayamar, Dulieu
Cs 5D
32
rad

Cs(6P)
=29.8 ns
1
B(1) 
28
24
1
(3) 
20
rad

Na(3P)
=16.4 ns
16
0
4
8
12
16
20
24
28
Vibrational quantum number v'
32
Conclusions
• FTS study applied and empirical PECs obtained for NaCs (1,3)1 states
• Permanent electric dipole moments measured in (2,3)1 states,
calculated in (1-3)1 states of NaCs
• Large PEDMs of ca. 7.5 D obtained in (3)1 state in perfect agreement
with theory; similar to NaK and NaRb correlating to (32p)Na
• -doublings measured in (1,3)1 states by FTS and RF-ODR and
supported by theory
• Lifetime values measured for (2,3)1 states and compared with MPPT
and CPP theory
Future plans (NaCs molecule)
• to study A1+ ~b3 complex and simulate a3+  A1+~b3  X1+
(v = 0) cycle
• to study B1~c3+ complex and simulate a3+  B1~c3+  X1+
(v = 0) cycle