46
S. Kerbstadt et al.
In the perturbative regime,
1 nonlinear light matter interactions involving the
absorption of N photons, such as multiphoton excitation or MPI, can be studied by
analyzing the higher-order nonlinear optical spectrum F
E
N
(t)
(ω) of the driving
field [25]. Temporally overlapping bichromatic fields give rise to additional spectral
contributions in the higher order spectrum at the frequencies (N − k)ω 1 + kω 2 with
k = 0, . . . , N , as illustrated in Fig. 3.1b for N = 2, 3 and 4. Mathematically, these
contributions result from multiple convolutions of the one-photon spectrum ˜
E(ω)
of the bichromatic field. The physical interpretation of these spectral bands is based
on the absorption of (N − k) photons with a frequency of ω 1 and k photons with
a frequency of ω 2 . The bichromatic ‘N versus N ’ control scenario is based on the
emergence of these spectral bands. Overlapping higher order spectra of different
orders N 1 and N 2 lead to interferences via paths with a different number of photons,
as illustrated in Fig. 3.1c. In this case, interferences in the nonlinear N 1 - and N 2 -
order spectra, i.e. F
E
N 1 (t)
+ F
E
N 2 (t)
, unlock the bichromatic ‘N 1 versus N 2 ’
control scenario which introduces the CEP as an addition control parameter.
In the following, we explore these scenarios using bichromatic polarizationshaped fields (Sect. 3.2.1) to control three-dimensional (3D) photoelectron momentum distributions (PMDs) and to study the ultrafast photoionization dynamics. Examples include coherent control by absorption of photons with different polarization
and frequency (Sect. 3.3.1), directional photoemission (Sect. 3.3.2), photoelectron
vortices (Sect. 3.3.3) and odd-numbered electron wave packets from bichromatic
MPI (Sect. 3.3.4). The analysis of the intriguing interplay of the symmetry of the
bichromatic laser field and the symmetry of the observed shaped free electron wave
packet reveals that the underlying physical mechanism for control is based on the
superposition of specific angular momentum states. Finally, we demonstrate the capability of the shaper-based bichromatic scheme to probe ultrafast dynamics. To this
end, a linear spectral phase—resulting in a variable time delay τ —is introduced in
the bichromatic pulse sequence, which allows us to map the dynamics of bound
Rydberg wave packets (Sect. 3.3.5) and spin-orbit wave packets (Sect. 3.3.6) into the
continuum PMD.
3.2 Experimental Techniques
In the experiments below, we employ polarization-tailored light fields for the spatial control of electron excitation/ionization dynamics and use a highly differential
photoelectron detection scheme for 3D measurement of the light-induced dynamics.
To this end, we combine white light polarization pulse shaping (Sect. 3.2.1) with
high-resolution photoelectron tomography (Sect. 3.2.2).
1 For weak interactions, i.e. when perturbation theory applies, the ground state is not depleted during
the light-matter interaction. The above statement holds if there are no intermediate resonances or
Stark shifts.
S. Kerbstadt et al.
In the perturbative regime,
1 nonlinear light matter interactions involving the
absorption of N photons, such as multiphoton excitation or MPI, can be studied by
analyzing the higher-order nonlinear optical spectrum F
E
N
(t)
(ω) of the driving
field [25]. Temporally overlapping bichromatic fields give rise to additional spectral
contributions in the higher order spectrum at the frequencies (N − k)ω 1 + kω 2 with
k = 0, . . . , N , as illustrated in Fig. 3.1b for N = 2, 3 and 4. Mathematically, these
contributions result from multiple convolutions of the one-photon spectrum ˜
E(ω)
of the bichromatic field. The physical interpretation of these spectral bands is based
on the absorption of (N − k) photons with a frequency of ω 1 and k photons with
a frequency of ω 2 . The bichromatic ‘N versus N ’ control scenario is based on the
emergence of these spectral bands. Overlapping higher order spectra of different
orders N 1 and N 2 lead to interferences via paths with a different number of photons,
as illustrated in Fig. 3.1c. In this case, interferences in the nonlinear N 1 - and N 2 -
order spectra, i.e. F
E
N 1 (t)
+ F
E
N 2 (t)
, unlock the bichromatic ‘N 1 versus N 2 ’
control scenario which introduces the CEP as an addition control parameter.
In the following, we explore these scenarios using bichromatic polarizationshaped fields (Sect. 3.2.1) to control three-dimensional (3D) photoelectron momentum distributions (PMDs) and to study the ultrafast photoionization dynamics. Examples include coherent control by absorption of photons with different polarization
and frequency (Sect. 3.3.1), directional photoemission (Sect. 3.3.2), photoelectron
vortices (Sect. 3.3.3) and odd-numbered electron wave packets from bichromatic
MPI (Sect. 3.3.4). The analysis of the intriguing interplay of the symmetry of the
bichromatic laser field and the symmetry of the observed shaped free electron wave
packet reveals that the underlying physical mechanism for control is based on the
superposition of specific angular momentum states. Finally, we demonstrate the capability of the shaper-based bichromatic scheme to probe ultrafast dynamics. To this
end, a linear spectral phase—resulting in a variable time delay τ —is introduced in
the bichromatic pulse sequence, which allows us to map the dynamics of bound
Rydberg wave packets (Sect. 3.3.5) and spin-orbit wave packets (Sect. 3.3.6) into the
continuum PMD.
3.2 Experimental Techniques
In the experiments below, we employ polarization-tailored light fields for the spatial control of electron excitation/ionization dynamics and use a highly differential
photoelectron detection scheme for 3D measurement of the light-induced dynamics.
To this end, we combine white light polarization pulse shaping (Sect. 3.2.1) with
high-resolution photoelectron tomography (Sect. 3.2.2).
1 For weak interactions, i.e. when perturbation theory applies, the ground state is not depleted during
the light-matter interaction. The above statement holds if there are no intermediate resonances or
Stark shifts.