54
S. Kerbstadt et al.
outermost ( p 3 ) contributions from single-color ionization exhibit rotated | f, m = 0symmetry. In accordance with the associated laser polarizations, the wave packet
in the p 0 -channel is aligned vertically along the x-axis while the wave packet in
the p 3 -channel is aligned horizontally along the y-axis. The wave packets in the
two inner channels ( p 1 and p 2 ), created by intra-pulse frequency mixing, are also
aligned perpendicular to each other – best discernible in the simulations. These
rather unusual wave packets are mainly composed of the two ’counter-rotating’
states | f, ±3 with only minor contributions of the states | f, ±1 [22]. The resulting
superposition creates an almost pure standing wave pattern with quasi c 6 rotational
symmetry in azimuthal (φ) direction (cf. Sect. 3.3.4).
In conclusion, the results presented in this section exemplify the power of
polarization-shaped bichromatic fields with incommensurable center frequencies to
sculpture the 3D PMD from atomic MPI by creation of unusual angular momentum
superposition states. In the prototypical OLP case discussed here, we demonstrated
the design of a rotated ‘ f within f ’ wave packet and a pair of wave packets with quasi
c 6 rotational symmetry. Both examples represent free electron wave packets which
can not be created by single-color MPI. In a second experiment based on bichromatic
CRCP pulses, we demonstrated the selective creation of individual angular momentum eigenstates [22]. It should be noted, that the interference of frequency mixing
pathways of the same order is insensitive to the CEP ϕ ce . However, control of the 3D
PMD via the relative optical phase ϕ = ϕ 2 − ϕ 1 between the two colors is possible
if the different ionization channels overlap energetically, i.e., if the bandwidth of the
N -th order frequency mixing contribution is larger than the channel separation. In
general, the underlying physical mechanism is based on the interplay of ionization
pathway selection via quantum mechanical selection rules for optical transitions and
intra-pulse frequency mixing of spectral bands with different ellipticity.
3.3.2 Control of Directional Photoemission
Coherent control of atomic and molecular MPI in the perturbative regime is generally
based on the interference of different multiphoton excitation pathways. Different
control scenarios may be distinguished by the parity of the involved target states.
If the interfering target states are of the same parity, control of both the integral
(yield) and differential (angular distribution) photoionization cross section [19] is
possible, but the final-state wave function is always spatially (left-right) symmetric.
An example of this type of control is presented in Sect. 3.3.3, where we discuss the
creation of even-numbered photoelectron vortices by MPI with single-color CRCP
pulse sequence [21, 50]. In contrast, spatial asymmetries in the photoelectron angular
distribution are induced by the interference of continuum states with opposite parity.
These states are addressed by MPI with different numbers of photons [19, 37, 38,
53], e.g., via N 1 - versus N 2 -photon ionization with N 2 = N 1 + 1. Recent examples
for this kind of spatial control exerted on the final state wave function comprise the
phase-sensitive directional emission of photoelectrons along the laser polarization
S. Kerbstadt et al.
outermost ( p 3 ) contributions from single-color ionization exhibit rotated | f, m = 0symmetry. In accordance with the associated laser polarizations, the wave packet
in the p 0 -channel is aligned vertically along the x-axis while the wave packet in
the p 3 -channel is aligned horizontally along the y-axis. The wave packets in the
two inner channels ( p 1 and p 2 ), created by intra-pulse frequency mixing, are also
aligned perpendicular to each other – best discernible in the simulations. These
rather unusual wave packets are mainly composed of the two ’counter-rotating’
states | f, ±3 with only minor contributions of the states | f, ±1 [22]. The resulting
superposition creates an almost pure standing wave pattern with quasi c 6 rotational
symmetry in azimuthal (φ) direction (cf. Sect. 3.3.4).
In conclusion, the results presented in this section exemplify the power of
polarization-shaped bichromatic fields with incommensurable center frequencies to
sculpture the 3D PMD from atomic MPI by creation of unusual angular momentum
superposition states. In the prototypical OLP case discussed here, we demonstrated
the design of a rotated ‘ f within f ’ wave packet and a pair of wave packets with quasi
c 6 rotational symmetry. Both examples represent free electron wave packets which
can not be created by single-color MPI. In a second experiment based on bichromatic
CRCP pulses, we demonstrated the selective creation of individual angular momentum eigenstates [22]. It should be noted, that the interference of frequency mixing
pathways of the same order is insensitive to the CEP ϕ ce . However, control of the 3D
PMD via the relative optical phase ϕ = ϕ 2 − ϕ 1 between the two colors is possible
if the different ionization channels overlap energetically, i.e., if the bandwidth of the
N -th order frequency mixing contribution is larger than the channel separation. In
general, the underlying physical mechanism is based on the interplay of ionization
pathway selection via quantum mechanical selection rules for optical transitions and
intra-pulse frequency mixing of spectral bands with different ellipticity.
3.3.2 Control of Directional Photoemission
Coherent control of atomic and molecular MPI in the perturbative regime is generally
based on the interference of different multiphoton excitation pathways. Different
control scenarios may be distinguished by the parity of the involved target states.
If the interfering target states are of the same parity, control of both the integral
(yield) and differential (angular distribution) photoionization cross section [19] is
possible, but the final-state wave function is always spatially (left-right) symmetric.
An example of this type of control is presented in Sect. 3.3.3, where we discuss the
creation of even-numbered photoelectron vortices by MPI with single-color CRCP
pulse sequence [21, 50]. In contrast, spatial asymmetries in the photoelectron angular
distribution are induced by the interference of continuum states with opposite parity.
These states are addressed by MPI with different numbers of photons [19, 37, 38,
53], e.g., via N 1 - versus N 2 -photon ionization with N 2 = N 1 + 1. Recent examples
for this kind of spatial control exerted on the final state wave function comprise the
phase-sensitive directional emission of photoelectrons along the laser polarization