3 Bichromatic Control of Free Electron Wave Packets
55
in CEP-stable few-cycle pulses [37, 38, 54, 55], bichromatic (ω:2ω) fields [38, 53,
56] and bichromatic (7ω:8ω) PLP fields [23].
In few-cycle MPI, CEP-sensitive N 1 - versus N 2 -photon interferences arise naturally in the energetic overlap region between the threshold and adjacent above
threshold ionization (ATI) channels. In this case, a multitude of quantum pathways
lead to the same photoelectron energy. Their intricate interference conceals the underlying physical mechanisms for control and makes the precise manipulation of the
final state wave function by forward design of the fundamental field difficult [23,
55, 57]. Recently, we showed that shaper-generated bichromatic fields with center
frequencies ω i tailored to the order of the MPI process allow to create almost pure
N 1 - versus N 2 -photon interferences in a selected energy window [23]. In this experiment, we employed (7ω:8ω) PLP fields to control asymmetries in the photoemission
from high-order MPI of xenon (Xe) atoms. It was demonstrated that the shaper-based
bichromatic approach preserves the CEP-sensitivity of the excitation and provides
refined optical control over the multipath interference of the target states. In particular, the efficiency of the involved ionization pathways was individually adjustable
via the bichromatic amplitude ratio and the quantum phases of the interfering target
states were controlled via the spectral phases of the two colors.
Here, we present experimental results on the control of spatial asymmetries in
the PMD from MPI of sodium (Na) and K atoms using shaper-generated (3ω:4ω)
PLP fields. The corresponding excitation scheme is displayed in Fig. 3.1c. Commensurable center wavelengths λ 1 = 880 nm (red pulse) and λ 2 =
3
4
λ 1 = 660 nm (blue
pulse) are chosen to induce interference of photoelectron wave packets from 3- and
4-photon ionization of the alkali atoms. The former gives rise to f (m = 0)-type
wave packets (odd parity), whereas the latter creates g (m = 0)-type wave packets
(even parity), as illustrated in the top insets to Fig. 3.6a, b. The total photoelectron
wave function in the relevant energy window can be written as [24]
ψ dir ∝ ψ 3,0 + i ψ 4,0 e
−iϕ
,
(3.6)
with ϕ = 4ϕ 1 − 3ϕ 2 + ϕ ce + τ ω. As shown in the top insets to Fig. 3.6c, d, the
final-state wave function is asymmetric along the y-axis i.e. in the polarization direction of the PLP fields. The asymmetry is determined by the relative quantum phase
ϕ between the interfering photoelectron wave packets. In a first proof-of-principle
experiment performed on K atoms, we utilize this asymmetry as a sensitive probe to
verify the coherence properties of the shaper-generated bichromatic (3ω:4ω) fields
by investigating the temporal, spatial and energetic overlap of the created photoelectron wave packets. To this end, the bichromatic fields are focused into the VMI
spectrometer (focus intensity I = 2 × 10
12 W/cm
2 ) and 2D photoelectron images
are measured for different values of the CEP ϕ ce , while setting ϕ i = 0 and τ = 0.
In order to analyze the photoelectron asymmetry, 2D sections through the PMD in
the polarization plane (x-y-plane) are retrieved via Abel inversion using the pBASEX algorithm [39]. All 2D sections are energy-calibrated following the procedure
described in [58]. Figure 3.6a, b display the g- and f -type single-color photoelectron spectra, obtained by MPI with only the red and the blue pulse, respectively in
55
in CEP-stable few-cycle pulses [37, 38, 54, 55], bichromatic (ω:2ω) fields [38, 53,
56] and bichromatic (7ω:8ω) PLP fields [23].
In few-cycle MPI, CEP-sensitive N 1 - versus N 2 -photon interferences arise naturally in the energetic overlap region between the threshold and adjacent above
threshold ionization (ATI) channels. In this case, a multitude of quantum pathways
lead to the same photoelectron energy. Their intricate interference conceals the underlying physical mechanisms for control and makes the precise manipulation of the
final state wave function by forward design of the fundamental field difficult [23,
55, 57]. Recently, we showed that shaper-generated bichromatic fields with center
frequencies ω i tailored to the order of the MPI process allow to create almost pure
N 1 - versus N 2 -photon interferences in a selected energy window [23]. In this experiment, we employed (7ω:8ω) PLP fields to control asymmetries in the photoemission
from high-order MPI of xenon (Xe) atoms. It was demonstrated that the shaper-based
bichromatic approach preserves the CEP-sensitivity of the excitation and provides
refined optical control over the multipath interference of the target states. In particular, the efficiency of the involved ionization pathways was individually adjustable
via the bichromatic amplitude ratio and the quantum phases of the interfering target
states were controlled via the spectral phases of the two colors.
Here, we present experimental results on the control of spatial asymmetries in
the PMD from MPI of sodium (Na) and K atoms using shaper-generated (3ω:4ω)
PLP fields. The corresponding excitation scheme is displayed in Fig. 3.1c. Commensurable center wavelengths λ 1 = 880 nm (red pulse) and λ 2 =
3
4
λ 1 = 660 nm (blue
pulse) are chosen to induce interference of photoelectron wave packets from 3- and
4-photon ionization of the alkali atoms. The former gives rise to f (m = 0)-type
wave packets (odd parity), whereas the latter creates g (m = 0)-type wave packets
(even parity), as illustrated in the top insets to Fig. 3.6a, b. The total photoelectron
wave function in the relevant energy window can be written as [24]
ψ dir ∝ ψ 3,0 + i ψ 4,0 e
−iϕ
,
(3.6)
with ϕ = 4ϕ 1 − 3ϕ 2 + ϕ ce + τ ω. As shown in the top insets to Fig. 3.6c, d, the
final-state wave function is asymmetric along the y-axis i.e. in the polarization direction of the PLP fields. The asymmetry is determined by the relative quantum phase
ϕ between the interfering photoelectron wave packets. In a first proof-of-principle
experiment performed on K atoms, we utilize this asymmetry as a sensitive probe to
verify the coherence properties of the shaper-generated bichromatic (3ω:4ω) fields
by investigating the temporal, spatial and energetic overlap of the created photoelectron wave packets. To this end, the bichromatic fields are focused into the VMI
spectrometer (focus intensity I = 2 × 10
12 W/cm
2 ) and 2D photoelectron images
are measured for different values of the CEP ϕ ce , while setting ϕ i = 0 and τ = 0.
In order to analyze the photoelectron asymmetry, 2D sections through the PMD in
the polarization plane (x-y-plane) are retrieved via Abel inversion using the pBASEX algorithm [39]. All 2D sections are energy-calibrated following the procedure
described in [58]. Figure 3.6a, b display the g- and f -type single-color photoelectron spectra, obtained by MPI with only the red and the blue pulse, respectively in