44
S. Kerbstadt et al.
bichromatic polarization shaping of carrier-envelope phase (CEP) stable white light
supercontinua [18].
An important physical mechanism for coherent control of optically driven dynamics is based on the interference of multiple quantum pathways connecting a given
initial state and a preselected final target state [7] or target wave packet. In general, the
target wave packet is a coherent superposition of a set of states optically coupled to
the initial state. Control over the target wave packet is achieved when the driving field
connects identical states via different pathways or induces relative quantum phases
within the set of interfering optically coupled states. Depending on the polarization
of the driving field and the number of photons involved, different coherent control
schemes can be distinguished based on the available optical control parameters and
the symmetry properties of the final state [19]. Atomic and molecular multiphoton
excitation or multiphoton ionization (MPI) are ideally suited to implement coherent
control scenarios based on multipath interference. For example, coherent control of
the momentum distributions of free electron wave packets via interfering pathways
with the same number of photons (N ) has been studied on atomic MPI. Single-color
pulse sequences have been initially employed to manipulate the interference fringes
in the photoelectron energy spectrum [20], and more recently, to create photoelectron
vortices in the laser polarization plane [21].
A new twist in coherent control of atomic MPI has been introduced by the use
of bichromatic polarization-tailored fields. Bichromatic fields have been used to
disentangle the controlled generation of radial and angular momentum electron wave
packets [22] and to localize interfering angular momentum wave packets in specific
kinetic energy windows [23]. Depending on the polarization, in the single-color ‘N -
versus N ’-photon ionization scheme depicted in Fig. 3.1a both the differential and
the integral photoionization cross section can be controlled by the optical phases
of the laser pulses. In contrast, the bichromatic ‘N versus N ’ scenario shown in
Fig. 3.1b permits the generation of energetically disentangled uncommon angular
momentum superposition states without changing the photoionization cross section
by optical phases. New possibilities for coherent control of photoionization arise
when quantum paths with a different number of photons for ionization (N 1 and N 2 )
interfere in the continuum, as illustrated in Fig. 3.1c [23, 24]. In the scenario ‘N 1
versus N 2 ’ an odd-numbered difference N 2 − N 1 results in photoelectron momentum
distributions (PMDs) which are, depending on the driving field polarization states,
either asymmetric or have an odd-numbered rotational symmetry. As we will show
below, these symmetry properties are sensitive to the CEP and therefore require a
CEP-stable light source.
In this chapter, we focus on the coherent control of atomic MPI using polarizationshaped bichromatic femtosecond laser pulse sequences. In the time domain, these
fields are described by
E(t) = e q 1 E 1 (t)e
i(ϕ 1 +ϕ ce ) e
iω 1 t
+ e q 2 E 2 (t − τ )e
i(ϕ 2 +ϕ ce ) e
iω 2 t
,
(3.1)
where the envelope functions E i (t) with i = 1, 2 characterize the shape of each individual pulse. Experimentally, the bichromatic fields are generated in the frequency
S. Kerbstadt et al.
bichromatic polarization shaping of carrier-envelope phase (CEP) stable white light
supercontinua [18].
An important physical mechanism for coherent control of optically driven dynamics is based on the interference of multiple quantum pathways connecting a given
initial state and a preselected final target state [7] or target wave packet. In general, the
target wave packet is a coherent superposition of a set of states optically coupled to
the initial state. Control over the target wave packet is achieved when the driving field
connects identical states via different pathways or induces relative quantum phases
within the set of interfering optically coupled states. Depending on the polarization
of the driving field and the number of photons involved, different coherent control
schemes can be distinguished based on the available optical control parameters and
the symmetry properties of the final state [19]. Atomic and molecular multiphoton
excitation or multiphoton ionization (MPI) are ideally suited to implement coherent
control scenarios based on multipath interference. For example, coherent control of
the momentum distributions of free electron wave packets via interfering pathways
with the same number of photons (N ) has been studied on atomic MPI. Single-color
pulse sequences have been initially employed to manipulate the interference fringes
in the photoelectron energy spectrum [20], and more recently, to create photoelectron
vortices in the laser polarization plane [21].
A new twist in coherent control of atomic MPI has been introduced by the use
of bichromatic polarization-tailored fields. Bichromatic fields have been used to
disentangle the controlled generation of radial and angular momentum electron wave
packets [22] and to localize interfering angular momentum wave packets in specific
kinetic energy windows [23]. Depending on the polarization, in the single-color ‘N -
versus N ’-photon ionization scheme depicted in Fig. 3.1a both the differential and
the integral photoionization cross section can be controlled by the optical phases
of the laser pulses. In contrast, the bichromatic ‘N versus N ’ scenario shown in
Fig. 3.1b permits the generation of energetically disentangled uncommon angular
momentum superposition states without changing the photoionization cross section
by optical phases. New possibilities for coherent control of photoionization arise
when quantum paths with a different number of photons for ionization (N 1 and N 2 )
interfere in the continuum, as illustrated in Fig. 3.1c [23, 24]. In the scenario ‘N 1
versus N 2 ’ an odd-numbered difference N 2 − N 1 results in photoelectron momentum
distributions (PMDs) which are, depending on the driving field polarization states,
either asymmetric or have an odd-numbered rotational symmetry. As we will show
below, these symmetry properties are sensitive to the CEP and therefore require a
CEP-stable light source.
In this chapter, we focus on the coherent control of atomic MPI using polarizationshaped bichromatic femtosecond laser pulse sequences. In the time domain, these
fields are described by
E(t) = e q 1 E 1 (t)e
i(ϕ 1 +ϕ ce ) e
iω 1 t
+ e q 2 E 2 (t − τ )e
i(ϕ 2 +ϕ ce ) e
iω 2 t
,
(3.1)
where the envelope functions E i (t) with i = 1, 2 characterize the shape of each individual pulse. Experimentally, the bichromatic fields are generated in the frequency