4 Light-Dressed Spectroscopy of Molecules
79
4.2 Theoretical Approach
Our approach to compute light-dressed spectra of molecules is based on three welldefined steps. First, we compute all field-free molecular rovibronic states relevant
to the light-induced processes. Second, using the field-free eigenstates as molecular
basis functions, we determine the light-dressed states induced by a medium-intensity
light field within the framework of Floquet theory [14, 33, 34]. Third, we compute
the transitions between the light-dressed states, induced by a weak probe pulse.
In order to facilitate the required computations, we make the following assumptions: (1) Initially the molecule is in a field-free eigenstate in the gas phase. (2)
The molecule is exposed to a medium-intensity dressing light, which is turned on
adiabatically, i.e., its envelope varies much slower than the rovibronic timescales
characterizing the molecule. (3) The probe pulse, introduced to record the static
rovibronic spectrum of the light-dressed molecule, is weak and can be treated in a
perturbative manner.
4.2.1 Determination of Light-Dressed States
4.2.1.1 General Considerations
In this section we review some aspects of the Floquet approach [14, 33, 34] which
we use to compute the light-dressed states generated by a medium-intensity pump
pulse. For a dressed Hamiltonian periodic in time t, such as
ˆ
H d (t) = ˆ
H mol + ˆ
W 1 (t),
(4.1)
ˆ
H d (t + T ) = ˆ
H d (t),
(4.2)
where ˆ
H mol is the field-free molecular Hamiltonian, T = 2π/ω 1 is the time period of
the periodicity, and ˆ
W 1 (t) is the interaction between the molecule and the dressing
field, the time-dependent Schrödinger equation (TDSE)
i∂ t |ψ(t) = ˆ
H d (t)|ψ(t)
(4.3)
has the general solution
|ψ(t) =
k
c k e
−
i
ε k t
| k (t),
(4.4)
where ε k are the so-called quasienergies, and | k (t) are the Floquet states (also
called light-dressed states in our work). The Floquet states satisfy
79
4.2 Theoretical Approach
Our approach to compute light-dressed spectra of molecules is based on three welldefined steps. First, we compute all field-free molecular rovibronic states relevant
to the light-induced processes. Second, using the field-free eigenstates as molecular
basis functions, we determine the light-dressed states induced by a medium-intensity
light field within the framework of Floquet theory [14, 33, 34]. Third, we compute
the transitions between the light-dressed states, induced by a weak probe pulse.
In order to facilitate the required computations, we make the following assumptions: (1) Initially the molecule is in a field-free eigenstate in the gas phase. (2)
The molecule is exposed to a medium-intensity dressing light, which is turned on
adiabatically, i.e., its envelope varies much slower than the rovibronic timescales
characterizing the molecule. (3) The probe pulse, introduced to record the static
rovibronic spectrum of the light-dressed molecule, is weak and can be treated in a
perturbative manner.
4.2.1 Determination of Light-Dressed States
4.2.1.1 General Considerations
In this section we review some aspects of the Floquet approach [14, 33, 34] which
we use to compute the light-dressed states generated by a medium-intensity pump
pulse. For a dressed Hamiltonian periodic in time t, such as
ˆ
H d (t) = ˆ
H mol + ˆ
W 1 (t),
(4.1)
ˆ
H d (t + T ) = ˆ
H d (t),
(4.2)
where ˆ
H mol is the field-free molecular Hamiltonian, T = 2π/ω 1 is the time period of
the periodicity, and ˆ
W 1 (t) is the interaction between the molecule and the dressing
field, the time-dependent Schrödinger equation (TDSE)
i∂ t |ψ(t) = ˆ
H d (t)|ψ(t)
(4.3)
has the general solution
|ψ(t) =
k
c k e
−
i
ε k t
| k (t),
(4.4)
where ε k are the so-called quasienergies, and | k (t) are the Floquet states (also
called light-dressed states in our work). The Floquet states satisfy