96
T. Szidarovszky et al.
fixed quantization axis. Since a linearly polarized dressing field (and the weak probe
pulse with identical polarization) can not mix states with different m quantum numbers, one can restrict the simulation to the m = 0 manifold when T = 0 K. In the
finite temperature calculations, one needs to determine the light-dressed states and
corresponding transitions for the different m manifolds, and include them in the
spectrum with appropriate weights given by (4.41).
Figure 4.6 shows the light-dressed spectra of Na 2 at different temperatures when
Na 2 is dressed by a light field whose wavelength and intensity are 662 nm and 5×10
7
Wcm
−2 , respectively. The upper panel of Fig. 4.6 demonstrates that the absorption
peaks exhibit splittings and that the height of the split peaks decrease significantly
when the temperature increases. This is because the low-lying rotational states are
populated at finite temperatures. Nonetheless, the height of the spectrum envelope is
much less sensitive to the temperature than the individual peak heights. The effects of
a temperature increase appear more significantly in the stimulated emission spectrum
than in the absorption spectrum, as shown in the lower panel of Fig. 4.6.
Figure 4.7 shows the dependence of the light-dressed spectra on the dressing light
intensity at T = 0.5 K. In a similar manner as in Fig. 4.6, the intensities of the spectral
peaks in Fig. 4.7 are more influenced by the increase of temperature than the entire
spectral envelope.
4.4.5 Effects of the Dressing-Field Turn-On Time on the
Light-Dressed States
Up to this point it was assumed that the dressing field is turned on adiabatically. As
explained in Sect. 4.2.2, the result is that an initial field-free eigenstate is transformed
into a single light-dressed state during the dressing process. If the dressing field is
not turned on adiabatically, the generated light-dressed wave function becomes a
superposition of light-dressed states, with the coefficients depending on the turn-on
time [35, 38, 43, 44].
Figure 4.8 demonstrates the population of the different field-free eigenstates in
the wave function for dressing-fields of different turn-on time () and intensity.
The functional form of the dressing light was assumed to be E 1 (t) = 0 for t < 0,
E 1 (t) = E max sin(ω 1 t)sin
2
(π t/ /) for 0 < t < t. The populations shown in Fig. 4.8 were computed for t = /2 by solving the
TDSE directly.
Based on the |X 0 0 ↔ |X 0 1 transition of Na 2 , the characteristic timescale
of molecular rotations is around 100 ps. Panels (b) and (c) of Fig. 4.8 demonstrate
that when the turn-on time is shorter than this characteristic timescale, the degree of
rotational excitation is reduced. In fact, in the excited electronic state the rotational
excitation is limited to that required by the optical selection rules (J = ±1). Panels
(b) and (c) of Fig. 4.8 also demonstrate that as the turn-on time of the dressing light
T. Szidarovszky et al.
fixed quantization axis. Since a linearly polarized dressing field (and the weak probe
pulse with identical polarization) can not mix states with different m quantum numbers, one can restrict the simulation to the m = 0 manifold when T = 0 K. In the
finite temperature calculations, one needs to determine the light-dressed states and
corresponding transitions for the different m manifolds, and include them in the
spectrum with appropriate weights given by (4.41).
Figure 4.6 shows the light-dressed spectra of Na 2 at different temperatures when
Na 2 is dressed by a light field whose wavelength and intensity are 662 nm and 5×10
7
Wcm
−2 , respectively. The upper panel of Fig. 4.6 demonstrates that the absorption
peaks exhibit splittings and that the height of the split peaks decrease significantly
when the temperature increases. This is because the low-lying rotational states are
populated at finite temperatures. Nonetheless, the height of the spectrum envelope is
much less sensitive to the temperature than the individual peak heights. The effects of
a temperature increase appear more significantly in the stimulated emission spectrum
than in the absorption spectrum, as shown in the lower panel of Fig. 4.6.
Figure 4.7 shows the dependence of the light-dressed spectra on the dressing light
intensity at T = 0.5 K. In a similar manner as in Fig. 4.6, the intensities of the spectral
peaks in Fig. 4.7 are more influenced by the increase of temperature than the entire
spectral envelope.
4.4.5 Effects of the Dressing-Field Turn-On Time on the
Light-Dressed States
Up to this point it was assumed that the dressing field is turned on adiabatically. As
explained in Sect. 4.2.2, the result is that an initial field-free eigenstate is transformed
into a single light-dressed state during the dressing process. If the dressing field is
not turned on adiabatically, the generated light-dressed wave function becomes a
superposition of light-dressed states, with the coefficients depending on the turn-on
time [35, 38, 43, 44].
Figure 4.8 demonstrates the population of the different field-free eigenstates in
the wave function for dressing-fields of different turn-on time () and intensity.
The functional form of the dressing light was assumed to be E 1 (t) = 0 for t < 0,
E 1 (t) = E max sin(ω 1 t)sin
2
(π t/ /) for 0 < t < t. The populations shown in Fig. 4.8 were computed for t = /2 by solving the
TDSE directly.
Based on the |X 0 0 ↔ |X 0 1 transition of Na 2 , the characteristic timescale
of molecular rotations is around 100 ps. Panels (b) and (c) of Fig. 4.8 demonstrate
that when the turn-on time is shorter than this characteristic timescale, the degree of
rotational excitation is reduced. In fact, in the excited electronic state the rotational
excitation is limited to that required by the optical selection rules (J = ±1). Panels
(b) and (c) of Fig. 4.8 also demonstrate that as the turn-on time of the dressing light