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Fig. 2.5 a Time-dependent electric field of the laser pulse employed in the simulation. b Timedependent populations in the Floquet states of N 2
+ at the field intensity of 2 × 10 14 Wcm −2 . The
label “α(n)” stands for “the α(v = n) Floquet state”. The angle θ between the molecular axis of N 2
+
and the laser polarization direction is set to be θ = 45 ◦ . Only the seven most populated states are
shown here. 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
state gradually decreases to 0 and the contribution from B
2
u
+ , dressed by 1 photon,
gradually increases from around 0.9 to 1.0, and finally this Floquet state becomes
the vibrational ground state of B
2
u
+ .
2.3.3 Population Inversion Assisted by A 2 u State
Because the coupling between B
2
u
+ and X
2
g
+ is orthogonal to that between A
2
u
and X
2
g
+ , by varying the value of alignment angle θ , the relative contribution of
these transitions can be adjusted. When θ increases from 0
◦ to 90
◦ , the direction of
the N-N molecular axis of N 2
+ changes from parallel to perpendicular with respect
to the polarization direction of the laser field.