2 Mechanism of Population Inversion in N 2
+
33
Fig. 2.4 Final population
transferred to the excited
state as a function of the
coupling strength. Solid line
represents the population
transferred to B 2 u
+ , and
the dashed line represents the
population transferred to the
excited state. The laser field
conditions are the same as
those in Fig. 2.3
0
0.2
0.4
0.6
0.8
1
0
0.2
0.4
0.6
0.8
1
2.3.2 Floquet Interpretation
In order to interpret the mechanism of the efficient population inversion achieved in
N 2
+
, we solve the time-dependent Schrödinger equations numerically and obtain the
time-dependent populations in the Floquet states of N 2
+
.
In the calculation, four vibrational states are included in the respective electronic
states and the dressed photon number is taken up m = 6. In Fig. 2.1a, the populations
in the seven most populated Floquet states are plotted. In the calculation, the angle
θ between the N–N molecular axis and the polarization direction of the laser field
was set to be 45
◦ .
As seen in Fig. 2.5, the B(v = 0) Floquet state has 15% population when the field
is suddenly turned on. The population in the B(v = 0) Floquet is almost constant
during the interaction with the half laser pulse after N
+
2 is generated by the ionization
process. The constant population suggests the adiabatic property of the B(v = 0)
Floquet state, which eventually becomes the vibrational ground state of the B state.
At the same time, in the state is also transferred to the A Floquet states through the
non-adiabatic Floquet coupling between the X and A states at one-photon resonance.
Finally, when the pulse vanishes, the population in the field-free X(v = 0) state is
smaller than that of the B(v = 0) state, resulting in the population inversion between
the X and B states.
In order to analyze the initial population in the B(v = 0) state, we decompose the
B(v = 0) Floquet state in the time domain. As shown in Fig. 2.6, the components
from X(v = 0) and X(v = 1), both of which are dressed by 0 photon, have significant
contribution to the B(v = 0) Floquet state at t = 0, which ensures a creation of
a certain amount of population in the B(v = 0) Floquet state when the pulse is
suddenly turned on. As time evolves, the contribution from X
2
g
+ in this Floquet
+
33
Fig. 2.4 Final population
transferred to the excited
state as a function of the
coupling strength. Solid line
represents the population
transferred to B 2 u
+ , and
the dashed line represents the
population transferred to the
excited state. The laser field
conditions are the same as
those in Fig. 2.3
0
0.2
0.4
0.6
0.8
1
0
0.2
0.4
0.6
0.8
1
2.3.2 Floquet Interpretation
In order to interpret the mechanism of the efficient population inversion achieved in
N 2
+
, we solve the time-dependent Schrödinger equations numerically and obtain the
time-dependent populations in the Floquet states of N 2
+
.
In the calculation, four vibrational states are included in the respective electronic
states and the dressed photon number is taken up m = 6. In Fig. 2.1a, the populations
in the seven most populated Floquet states are plotted. In the calculation, the angle
θ between the N–N molecular axis and the polarization direction of the laser field
was set to be 45
◦ .
As seen in Fig. 2.5, the B(v = 0) Floquet state has 15% population when the field
is suddenly turned on. The population in the B(v = 0) Floquet is almost constant
during the interaction with the half laser pulse after N
+
2 is generated by the ionization
process. The constant population suggests the adiabatic property of the B(v = 0)
Floquet state, which eventually becomes the vibrational ground state of the B state.
At the same time, in the state is also transferred to the A Floquet states through the
non-adiabatic Floquet coupling between the X and A states at one-photon resonance.
Finally, when the pulse vanishes, the population in the field-free X(v = 0) state is
smaller than that of the B(v = 0) state, resulting in the population inversion between
the X and B states.
In order to analyze the initial population in the B(v = 0) state, we decompose the
B(v = 0) Floquet state in the time domain. As shown in Fig. 2.6, the components
from X(v = 0) and X(v = 1), both of which are dressed by 0 photon, have significant
contribution to the B(v = 0) Floquet state at t = 0, which ensures a creation of
a certain amount of population in the B(v = 0) Floquet state when the pulse is
suddenly turned on. As time evolves, the contribution from X
2
g
+ in this Floquet