3 Bichromatic Control of Free Electron Wave Packets
61
and odd-numbered photoelectron vortices by ionization of atoms [71] and molecular
ions [66, 72] with circularly polarized bichromatic laser fields [18] were investigated.
In the following, we present an experimental scheme to create and manipulate
3D free electron wave packets with arbitrary rotational symmetry by combining
bichromatic white light shaping [18] with high-resolution photoelectron tomography
[40] as shown in Fig. 3.4. We exert full spatial control over photoelectron wave
packets by designing specific energy and angular momentum superposition states.
For this purpose, we use shaper-generated CEP-stable bichromatic (3ω:4ω) COCP
and CRCP femtosecond laser pulses to create 7-fold rotationally symmetric and
asymmetric PMDs by MPI of Na atoms (the pulse parameters are given in Sect. 3.3.2).
In the CRCP case, with a red LCP pulse and a blue RCP pulse, the final-state wave
function is the superposition of two counter-rotating torus-shaped wave packets:
ψ cr ∝ ψ 3,−3 + i ψ 4,4 e
−i
,
(3.11)
with = 4ϕ 1 − 3ϕ 2 + ϕ ce . The superposition state in (3.11) describes a spherical
standing wave with S wp = N 2 + N 1 = 7 lobes in the laser polarization plane (x-yplane), i.e., with c 7 rotational symmetry, as shown in Fig. 3.9a. Examples for other
frequency ratios are depicted in Fig. 3.10. As described by (3.2) and (3.3), the shapergenerated cycloidal fields depend on both the CEP and the relative phases between
the fields of the two colors. The optical phases enter with different weights into the
relative quantum phase ϕ between the interfering wave functions. Switching from
CRCP to COCP allows us to localize the photoelectrons in one half of the polarization
plane. The resulting photoelectron wave packet is described by the wave function
Fig. 3.9 Odd-numbered photoelectron wave packets from MPI of Na atoms with (3ω:4ω) CRCP
and COCP fields, reconstructed using high-resolution photoelectron tomography. a Photoelectron
wave packet with CEP-sensitive c 7 rotational symmetry from MPI of Na atoms with a (3ω:4ω)
CRCP field. b Switching to a COCP field allows to localize the photoelectron in one half of the
polarization plane. The photoelectron wave packet is crescent-shaped and asymmetric. c Introducing
a time delay between both colors of the (3ω:4ω) CRCP field creates a 7-armed photoelectron vortex,
retaining the c 7 symmetry despite the circular symmetry of the ionizing laser field
61
and odd-numbered photoelectron vortices by ionization of atoms [71] and molecular
ions [66, 72] with circularly polarized bichromatic laser fields [18] were investigated.
In the following, we present an experimental scheme to create and manipulate
3D free electron wave packets with arbitrary rotational symmetry by combining
bichromatic white light shaping [18] with high-resolution photoelectron tomography
[40] as shown in Fig. 3.4. We exert full spatial control over photoelectron wave
packets by designing specific energy and angular momentum superposition states.
For this purpose, we use shaper-generated CEP-stable bichromatic (3ω:4ω) COCP
and CRCP femtosecond laser pulses to create 7-fold rotationally symmetric and
asymmetric PMDs by MPI of Na atoms (the pulse parameters are given in Sect. 3.3.2).
In the CRCP case, with a red LCP pulse and a blue RCP pulse, the final-state wave
function is the superposition of two counter-rotating torus-shaped wave packets:
ψ cr ∝ ψ 3,−3 + i ψ 4,4 e
−i
,
(3.11)
with = 4ϕ 1 − 3ϕ 2 + ϕ ce . The superposition state in (3.11) describes a spherical
standing wave with S wp = N 2 + N 1 = 7 lobes in the laser polarization plane (x-yplane), i.e., with c 7 rotational symmetry, as shown in Fig. 3.9a. Examples for other
frequency ratios are depicted in Fig. 3.10. As described by (3.2) and (3.3), the shapergenerated cycloidal fields depend on both the CEP and the relative phases between
the fields of the two colors. The optical phases enter with different weights into the
relative quantum phase ϕ between the interfering wave functions. Switching from
CRCP to COCP allows us to localize the photoelectrons in one half of the polarization
plane. The resulting photoelectron wave packet is described by the wave function
Fig. 3.9 Odd-numbered photoelectron wave packets from MPI of Na atoms with (3ω:4ω) CRCP
and COCP fields, reconstructed using high-resolution photoelectron tomography. a Photoelectron
wave packet with CEP-sensitive c 7 rotational symmetry from MPI of Na atoms with a (3ω:4ω)
CRCP field. b Switching to a COCP field allows to localize the photoelectron in one half of the
polarization plane. The photoelectron wave packet is crescent-shaped and asymmetric. c Introducing
a time delay between both colors of the (3ω:4ω) CRCP field creates a 7-armed photoelectron vortex,
retaining the c 7 symmetry despite the circular symmetry of the ionizing laser field