3 Bichromatic Control of Free Electron Wave Packets
67
an intra-series and an inter-series beating. Using spectroscopic data from [85], the
intra-series beating is assigned to states 8 f -9 f and the inter-series oscillation occurs
between states 11 p-11 f and 16 p-11 f , respectively. In contrast, the mode labeled
by (2), corresponding to the T 260 fs oscillation, is exclusively found in the gzero spectrum. This implies that the slow angular dynamics are mainly caused by
contributions from the d-type photoelectron wave packets. Mode (2) is thus identified
as an inter-series beating of states 12 p and 11 f [85]. To conclude, the pronounced
angular dynamics observed in the photoelectron spectrum arise from interference
of wave functions with the same parity, i.e. s-, d- and g-type photoelectron wave
packets, and are an example for phase control over the differential photoionization
cross section [19].
In [49], the angular-selective analysis described above was verified by two independent methods. First, a fitting model (green and blue solid lines in Fig. 3.12c)
was employed to decompose the measured photoelectron wave packet dynamics
into superpositions of s-, d- and g-type wave packets achieving excellent agreement with the experimental results. Second, a supplementary measurement was performed using COCP pump-probe pulse sequences to selectively address the Rydberg
n f -series which is probed exclusively into the g-type continuum. These additional
results were in very good accordance with both the differential data analysis and the
fitting model.
3.3.6 Spin-Orbit Wave Packet Dynamics
A different class of electron dynamics with distinct physical properties arises due to
the coupling of the electron spin and orbital angular momentum. Spin-orbit (SO)
interaction gives rise to the fine structure splitting of atomic energy levels into
multipletts. In the case of alkali atoms, the n states split into doublets n j with
j = ± 1/2, i.e., into two states separated by the fine structure energy ε. Coherent
excitation of several fine structure states by an ultrashort laser pulse creates a spinorbit wave packet (SOWP). In contrast to Rydberg wave packets (cf. Sect. 3.3.5)
which, in general, oscillate in the radial direction, SO interaction induces an angular
motion of the bound electron leading to a realignment of the electron orbital. This
angular dynamics can be interpreted as the precession of the spin and orbital angular
momentum about the total angular momentum with a precession period given by
T = h//ε [86].
SOWPs were among the first electron wave packets studied in real time. For
example, SOWPs have been observed in Rydberg atoms on the picosecond timescale
[87–89] and in alkali atoms [86, 90] and noble gases [91–93] on the femtosecond
timescale. Observation of the sub-femtosecond motion of SOWPs in krypton ions was
reported in [94]. In addition, coherent control of SOWPs using shaped femtosecond
laser pulses was demonstrated [93, 95–97] and the photoionization of atoms by
polarization-shaped laser pulses was investigated as a means to produce highly spinpolarized electrons [89, 90, 98, 99].
67
an intra-series and an inter-series beating. Using spectroscopic data from [85], the
intra-series beating is assigned to states 8 f -9 f and the inter-series oscillation occurs
between states 11 p-11 f and 16 p-11 f , respectively. In contrast, the mode labeled
by (2), corresponding to the T 260 fs oscillation, is exclusively found in the gzero spectrum. This implies that the slow angular dynamics are mainly caused by
contributions from the d-type photoelectron wave packets. Mode (2) is thus identified
as an inter-series beating of states 12 p and 11 f [85]. To conclude, the pronounced
angular dynamics observed in the photoelectron spectrum arise from interference
of wave functions with the same parity, i.e. s-, d- and g-type photoelectron wave
packets, and are an example for phase control over the differential photoionization
cross section [19].
In [49], the angular-selective analysis described above was verified by two independent methods. First, a fitting model (green and blue solid lines in Fig. 3.12c)
was employed to decompose the measured photoelectron wave packet dynamics
into superpositions of s-, d- and g-type wave packets achieving excellent agreement with the experimental results. Second, a supplementary measurement was performed using COCP pump-probe pulse sequences to selectively address the Rydberg
n f -series which is probed exclusively into the g-type continuum. These additional
results were in very good accordance with both the differential data analysis and the
fitting model.
3.3.6 Spin-Orbit Wave Packet Dynamics
A different class of electron dynamics with distinct physical properties arises due to
the coupling of the electron spin and orbital angular momentum. Spin-orbit (SO)
interaction gives rise to the fine structure splitting of atomic energy levels into
multipletts. In the case of alkali atoms, the n states split into doublets n j with
j = ± 1/2, i.e., into two states separated by the fine structure energy ε. Coherent
excitation of several fine structure states by an ultrashort laser pulse creates a spinorbit wave packet (SOWP). In contrast to Rydberg wave packets (cf. Sect. 3.3.5)
which, in general, oscillate in the radial direction, SO interaction induces an angular
motion of the bound electron leading to a realignment of the electron orbital. This
angular dynamics can be interpreted as the precession of the spin and orbital angular
momentum about the total angular momentum with a precession period given by
T = h//ε [86].
SOWPs were among the first electron wave packets studied in real time. For
example, SOWPs have been observed in Rydberg atoms on the picosecond timescale
[87–89] and in alkali atoms [86, 90] and noble gases [91–93] on the femtosecond
timescale. Observation of the sub-femtosecond motion of SOWPs in krypton ions was
reported in [94]. In addition, coherent control of SOWPs using shaped femtosecond
laser pulses was demonstrated [93, 95–97] and the photoionization of atoms by
polarization-shaped laser pulses was investigated as a means to produce highly spinpolarized electrons [89, 90, 98, 99].