4 Light-Dressed Spectroscopy of Molecules
91
mixing of field-free states through the light-matter coupling with the dressing field.
Such type of peak splittings are similar to the well-known Autler–Townes effect [24],
which is a useful tool in spectroscopy, see, for example [25–27]. The upper panel
of Fig. 4.3 not only demonstrates splitting of the peak, in which the sum of individual peak intensities remain unchanged, but exhibits an overall increase in the peak
intensities when the strength of the dressing field is increased. In spectroscopy the
changes in transition peak intensities resulting from couplings between eigenstates
of a zeroth-order Hamiltonian is called intensity borrowing [39].
The lower panel of Fig. 4.3 shows the progression of three peaks, which appear
as new peaks rather than arising from the splitting of a field-free peak. These transitions occur between the initial state (light-dressed state correlating to the field-free
ground state) composed primarily of |X 0 0 with smaller contributions from |X 0 2
and |A 1 1 and the light-dressed states composed primarily of the |X 4 0, |X 4 2,
and |X 4 4 states. Such transitions are forbidden in the limit of zero dressing-light
intensity; however, they become visible as the light-matter coupling with the dressing field mixes the |X 4 J states (J even) with |A v 1-type states, to which |X 0 0
has non-zero transition probability. The appearance of transition peaks as a result of
such a mixing can be understood as an intensity-borrowing effect.
As to the stimulated emission peaks shown in the lower panel of Fig. 4.2, they represent transitions from the initial state to the light-dressed states composed primarily
of the vibrationally highly excited |X v 0- and |X v 2-type states, with |A v
J -type
states (J odd) also giving a small contribution.
4.4.2.1 Predicting Field-Free Properties Using Extrapolation
Although light-dressed spectroscopy might yield transition peaks forbidden in the
field-free case, the transition wavenumbers between light-dressed states are in general different from the transition wavenumbers between field-free states. If one is
interested in obtaining field-free transition wavenumbers, one can record the lightdressed spectrum at several dressing-field intensities and extrapolate to the zero
intensity limit. Such a procedure is of course most valuable when the transition is
forbidden in the field-free case.
As an example, we examine the stimulated emission peak at around 13,770 cm
−1
(see Fig. 4.4). The emission peak around 13,770 cm
−1 represents a transition in which
the initial state is composed primarily of the |X 0 0 ground state and has small contributions from the |X 0 2 and |A 1 1 states, and in which the final state is composed
primarily of |X 9 2, with |X 9 0 and |A 13 1 giving a small contribution, as well. In
the limit of zero dressing-light intensity, the initial and final states correlate to |X 0 0
and |X 9 2, respectively. Transitions between these two field-free states is forbidden;
nonetheless, their accurate transition wavenumber can be obtained by extrapolating
the light-dressed transition wavenumber to the limit of zero dressing light intensity. As expected and seen in Fig. 4.4, linear extrapolation might be pursued if data
points at low dressing-light intensities are used. On the other hand, by increasing the
dressing-light intensity above a certain level, the relation between intensity and tran-
91
mixing of field-free states through the light-matter coupling with the dressing field.
Such type of peak splittings are similar to the well-known Autler–Townes effect [24],
which is a useful tool in spectroscopy, see, for example [25–27]. The upper panel
of Fig. 4.3 not only demonstrates splitting of the peak, in which the sum of individual peak intensities remain unchanged, but exhibits an overall increase in the peak
intensities when the strength of the dressing field is increased. In spectroscopy the
changes in transition peak intensities resulting from couplings between eigenstates
of a zeroth-order Hamiltonian is called intensity borrowing [39].
The lower panel of Fig. 4.3 shows the progression of three peaks, which appear
as new peaks rather than arising from the splitting of a field-free peak. These transitions occur between the initial state (light-dressed state correlating to the field-free
ground state) composed primarily of |X 0 0 with smaller contributions from |X 0 2
and |A 1 1 and the light-dressed states composed primarily of the |X 4 0, |X 4 2,
and |X 4 4 states. Such transitions are forbidden in the limit of zero dressing-light
intensity; however, they become visible as the light-matter coupling with the dressing field mixes the |X 4 J states (J even) with |A v 1-type states, to which |X 0 0
has non-zero transition probability. The appearance of transition peaks as a result of
such a mixing can be understood as an intensity-borrowing effect.
As to the stimulated emission peaks shown in the lower panel of Fig. 4.2, they represent transitions from the initial state to the light-dressed states composed primarily
of the vibrationally highly excited |X v 0- and |X v 2-type states, with |A v
J -type
states (J odd) also giving a small contribution.
4.4.2.1 Predicting Field-Free Properties Using Extrapolation
Although light-dressed spectroscopy might yield transition peaks forbidden in the
field-free case, the transition wavenumbers between light-dressed states are in general different from the transition wavenumbers between field-free states. If one is
interested in obtaining field-free transition wavenumbers, one can record the lightdressed spectrum at several dressing-field intensities and extrapolate to the zero
intensity limit. Such a procedure is of course most valuable when the transition is
forbidden in the field-free case.
As an example, we examine the stimulated emission peak at around 13,770 cm
−1
(see Fig. 4.4). The emission peak around 13,770 cm
−1 represents a transition in which
the initial state is composed primarily of the |X 0 0 ground state and has small contributions from the |X 0 2 and |A 1 1 states, and in which the final state is composed
primarily of |X 9 2, with |X 9 0 and |A 13 1 giving a small contribution, as well. In
the limit of zero dressing-light intensity, the initial and final states correlate to |X 0 0
and |X 9 2, respectively. Transitions between these two field-free states is forbidden;
nonetheless, their accurate transition wavenumber can be obtained by extrapolating
the light-dressed transition wavenumber to the limit of zero dressing light intensity. As expected and seen in Fig. 4.4, linear extrapolation might be pursued if data
points at low dressing-light intensities are used. On the other hand, by increasing the
dressing-light intensity above a certain level, the relation between intensity and tran-