3 Bichromatic Control of Free Electron Wave Packets
69
The starting point of the experiment, τ = 0, was discussed in Sect. 3.3.1 in the
context of intra-pulse frequency mixing by temporally overlapping colors. In this
case, the photoelectron wave packet in the ε 1 -channel is aligned in the laser polarization plane (x-y-plane) and exhibits approximate c 6 rotational symmetry (see p 1 -inset
to Fig. 3.5). As discussed in [51], this symmetry reflects the initial dumbbell-shaped
electron distribution of the excited SOWP, aligned along the y-axis in accordance
with the horizontal pump pulse polarization. Next we varied the time delay between
the two colors to investigate the time evolution of the SOWP. The results are shown
in Fig. 3.13b, c, where we focus on the ε 1 -contribution sensitive to the dynamics.
At about half the SOWP oscillation period, τ ≈ T /2, we observe a counterintuitive
rotation of the PMD by 90
◦ about the x-axis. The reconstructed photoelectron density shown in Fig. 3.13b is aligned coplanar to the laser propagation direction in the
x-z-plane. In addition, the nodal structure of the photoelectron angular distribution is
altered, no longer showing the approximate c 6 symmetry. To interpret the experimental results, we modeled the 3D photoelectron wave packet from MPI of K atoms by
bichromatic OLP pulse sequences, taking the electron spin into account. To this end,
we numerically solved the time-dependent Schrödinger equation in the coupled basis
for the interaction of the neutral atom with the linearly polarized pump and calculated
the 3D PMD created by the orthogonally polarized probe using second order timedependent perturbation theory [51]. The simulated photoelectron density, shown in
the bottom left inset to Fig. 3.13b, is in excellent agreement with the measured PMD
allowing us to analyze the underlying neutral dynamics. The derived SOWP in the
4 p fine structure states is illustrated in the right inset. Apparently, after the excitation,
the system state has evolved under SO interaction from the initial dumbbell-shaped
electron distribution aligned along the y-axis into a torus-shaped distribution aligned
in the x-z-plane. This orbital realignment is indicated by the measured photoelectron
angular distribution. After a full period, τ = T , the reconstructed photoelectron density recovers the initial shape measured for τ = 0 (cf. Fig. 3.5c). Again we observe
the photoelectron wave packet with quasi c 6 rotational symmetry. In accordance
with this observation, the simulations yield a dumbbell-shaped neutral electron distribution aligned in pump polarization direction, confirming the completion of a full
SOWP cycle.
These results highlight the capabilities of the experimental technique, combining polarization-shaped bichromatic pump-probe sequences with highly differential
photoelectron detection, for the background-free observation of spatiotemporal quantum dynamics. A promising future perspective is the use of tailored pump pulses to
coherently control and image the time evolution of electron dynamics in atoms and
molecules.
3.4 Conclusion and Outlook
In this chapter, we reviewed recent developments in the coherent control of photoelectron momentum distributions (PMDs) using Bichromatic Carrier-Envelope
69
The starting point of the experiment, τ = 0, was discussed in Sect. 3.3.1 in the
context of intra-pulse frequency mixing by temporally overlapping colors. In this
case, the photoelectron wave packet in the ε 1 -channel is aligned in the laser polarization plane (x-y-plane) and exhibits approximate c 6 rotational symmetry (see p 1 -inset
to Fig. 3.5). As discussed in [51], this symmetry reflects the initial dumbbell-shaped
electron distribution of the excited SOWP, aligned along the y-axis in accordance
with the horizontal pump pulse polarization. Next we varied the time delay between
the two colors to investigate the time evolution of the SOWP. The results are shown
in Fig. 3.13b, c, where we focus on the ε 1 -contribution sensitive to the dynamics.
At about half the SOWP oscillation period, τ ≈ T /2, we observe a counterintuitive
rotation of the PMD by 90
◦ about the x-axis. The reconstructed photoelectron density shown in Fig. 3.13b is aligned coplanar to the laser propagation direction in the
x-z-plane. In addition, the nodal structure of the photoelectron angular distribution is
altered, no longer showing the approximate c 6 symmetry. To interpret the experimental results, we modeled the 3D photoelectron wave packet from MPI of K atoms by
bichromatic OLP pulse sequences, taking the electron spin into account. To this end,
we numerically solved the time-dependent Schrödinger equation in the coupled basis
for the interaction of the neutral atom with the linearly polarized pump and calculated
the 3D PMD created by the orthogonally polarized probe using second order timedependent perturbation theory [51]. The simulated photoelectron density, shown in
the bottom left inset to Fig. 3.13b, is in excellent agreement with the measured PMD
allowing us to analyze the underlying neutral dynamics. The derived SOWP in the
4 p fine structure states is illustrated in the right inset. Apparently, after the excitation,
the system state has evolved under SO interaction from the initial dumbbell-shaped
electron distribution aligned along the y-axis into a torus-shaped distribution aligned
in the x-z-plane. This orbital realignment is indicated by the measured photoelectron
angular distribution. After a full period, τ = T , the reconstructed photoelectron density recovers the initial shape measured for τ = 0 (cf. Fig. 3.5c). Again we observe
the photoelectron wave packet with quasi c 6 rotational symmetry. In accordance
with this observation, the simulations yield a dumbbell-shaped neutral electron distribution aligned in pump polarization direction, confirming the completion of a full
SOWP cycle.
These results highlight the capabilities of the experimental technique, combining polarization-shaped bichromatic pump-probe sequences with highly differential
photoelectron detection, for the background-free observation of spatiotemporal quantum dynamics. A promising future perspective is the use of tailored pump pulses to
coherently control and image the time evolution of electron dynamics in atoms and
molecules.
3.4 Conclusion and Outlook
In this chapter, we reviewed recent developments in the coherent control of photoelectron momentum distributions (PMDs) using Bichromatic Carrier-Envelope