2 Mechanism of Population Inversion in N 2
+
37
0
5
10
15
20
25
30
0
5
10
15
20
25
30
0
0.01
0.02
0.03
0
0.01
0.02
0.03
0
5
10
15
20
25
30
0
0.01
0.02
0.03
(b)
(a)
(c)
Fig. 2.8 Final population distribution in the rotational levels of N 2
+ obtained after the interaction
with an intense 800 nm laser pulse with the field intensities of a 2 × 10 14 Wcm −2 , b 4 × 10 14
Wcm −2 and c 6 × 10 14 Wcm −2 . The label “α(v = n)” stands for the nth vibrational state of the α
state. The initial populations in the X 2 g
+ , A 2 u , and B 2 u
+ states are
V max
v=0 |c X,v (t = 0)| 2 =
1, |c A,v (t = 0)| 2 = 0 and |c B,v (t = 0)| 2 = 0, respectively
ζ =
K max
K =0
g K (2K + 1)e
−
B α,K K (K +1)
k B T
.
(2.38)
The K max in (2.37) is set to be 40.
Because N 2
+ is estimated to be prepared in the electronic ground X
2
g
+ state with
90% probability according to molecular Ammosov-Delone-Krainov (MO-ADK) theory [44] and because the Franck-Condon factor for the ionization from the vibrational
+
37
0
5
10
15
20
25
30
0
5
10
15
20
25
30
0
0.01
0.02
0.03
0
0.01
0.02
0.03
0
5
10
15
20
25
30
0
0.01
0.02
0.03
(b)
(a)
(c)
Fig. 2.8 Final population distribution in the rotational levels of N 2
+ obtained after the interaction
with an intense 800 nm laser pulse with the field intensities of a 2 × 10 14 Wcm −2 , b 4 × 10 14
Wcm −2 and c 6 × 10 14 Wcm −2 . The label “α(v = n)” stands for the nth vibrational state of the α
state. The initial populations in the X 2 g
+ , A 2 u , and B 2 u
+ states are
V max
v=0 |c X,v (t = 0)| 2 =
1, |c A,v (t = 0)| 2 = 0 and |c B,v (t = 0)| 2 = 0, respectively
ζ =
K max
K =0
g K (2K + 1)e
−
B α,K K (K +1)
k B T
.
(2.38)
The K max in (2.37) is set to be 40.
Because N 2
+ is estimated to be prepared in the electronic ground X
2
g
+ state with
90% probability according to molecular Ammosov-Delone-Krainov (MO-ADK) theory [44] and because the Franck-Condon factor for the ionization from the vibrational