1 3
Top Curr Chem (Z) (2018) 376:6
is very good agreement between the experimental data and calculation. The strong
features at ν t = 22 THz are mainly due to field-induced interband tunneling of carriers and interband two-photon absorption, which are in the strongly nonperturbative
regime due to the extremely large transition dipole between the valence and conduction bands [33]. The weak features at ν t = 10 THz originate from the two-phonon
resonances in InSb, which are isolated from the 2D spectra and analyzed in the time
domain in detail in the following.
The 2D time-domain signals as functions of coherence time and real time resulting from inverse Fourier transformation of selected isolated spectral peaks in
Fig. 19c–e are shown in Fig. 20. There is good agreement between the experimental
data and calculations. The signal in Fig. 20b is assigned as a rephasing signal as
the phase front of the signal is perpendicular to the phase front of pulse A (orange
dashed line), i.e., the nonlinear signal is phase-reversed with respect to the coherences generated by pulse A. Due to the lack of even-order signals in the data and
the nonresonant nature of the two-phonon coherence generation, the seventh-order
(χ
(7)
) pathway shown by diagram (i) in Fig. 21 was proposed [33] as the lowestorder pathway to describe the light-matter interactions. According to the diagrams,
pulse A induces a two-phonon coherence via impulsive excitation with two interactions, and pulse B projects the two-phonon coherence back to the ground state also
impulsively with two interactions. Finally, pulse C generates a rephased two-phonon
coherence of seventh order also via impulsive excitation, but with three interactions.
This excitation process is shown separately in diagram (i). The two-phonon coherence radiates the nonlinear signal shown in Fig. 20b.
The origins of the nonlinear signals in Fig. 20a, c were assigned to an eleventhorder (χ
(11)
) NR pathway, which was proposed as the lowest-order pathway that can
lead to these signals. It is described by the ladder diagram (iii) in Fig. 21 and analyzed as follows. Each pulse has to interact at least once to lead to the nonlinear signal. Due to the observation that the phase front of the signal is independent of that
of pulse A, pulse A should interact an even number of times. A third-order process
hence is not sufficient to explain the signal origin. As shown in Fig. 4 of Ref. [33],
the nonlinear signal at T w = 827 fs is found to be a direct continuation in amplitude and phase of that at T w = 35 fs. Besides, its phase is independent of the pulse
sequences. Hence, the nonlinear two-phonon coherence signal follows the phase of
pulse B only, while pulses A and C create long-lived electronic excitations in InSb
whose bandgap is about 41 THz, twice the frequency of the THz pulses. The ladder
diagram (iii) shown in Fig. 21 can be read as follows. Pulse A excites an electronic
population via four interactions, pulse B impulsively induces a two-phonon coherence via three interactions, pulse C promotes this two-phonon coherence from the
first electronic excited state to the second one, and finally the two-phonon coherence
at the second electronic excited state radiates the nonlinear signal.
In this experiment, the exceptionally high-order nonlinear interactions were proposed on the basis of the huge transition dipole moments associated with the electronic and vibronic transitions in the InSb sample. In pure vibrational systems where
nonlinearity is not as dramatic, 2D spectra resulting from all THz interactions have
so far not been available. Hybrid 2D THz-Raman methods can provide better sensitivity because of simultaneous interactions via dipole and polarizability. Several
301
Reprinted from the journal
Top Curr Chem (Z) (2018) 376:6
is very good agreement between the experimental data and calculation. The strong
features at ν t = 22 THz are mainly due to field-induced interband tunneling of carriers and interband two-photon absorption, which are in the strongly nonperturbative
regime due to the extremely large transition dipole between the valence and conduction bands [33]. The weak features at ν t = 10 THz originate from the two-phonon
resonances in InSb, which are isolated from the 2D spectra and analyzed in the time
domain in detail in the following.
The 2D time-domain signals as functions of coherence time and real time resulting from inverse Fourier transformation of selected isolated spectral peaks in
Fig. 19c–e are shown in Fig. 20. There is good agreement between the experimental
data and calculations. The signal in Fig. 20b is assigned as a rephasing signal as
the phase front of the signal is perpendicular to the phase front of pulse A (orange
dashed line), i.e., the nonlinear signal is phase-reversed with respect to the coherences generated by pulse A. Due to the lack of even-order signals in the data and
the nonresonant nature of the two-phonon coherence generation, the seventh-order
(χ
(7)
) pathway shown by diagram (i) in Fig. 21 was proposed [33] as the lowestorder pathway to describe the light-matter interactions. According to the diagrams,
pulse A induces a two-phonon coherence via impulsive excitation with two interactions, and pulse B projects the two-phonon coherence back to the ground state also
impulsively with two interactions. Finally, pulse C generates a rephased two-phonon
coherence of seventh order also via impulsive excitation, but with three interactions.
This excitation process is shown separately in diagram (i). The two-phonon coherence radiates the nonlinear signal shown in Fig. 20b.
The origins of the nonlinear signals in Fig. 20a, c were assigned to an eleventhorder (χ
(11)
) NR pathway, which was proposed as the lowest-order pathway that can
lead to these signals. It is described by the ladder diagram (iii) in Fig. 21 and analyzed as follows. Each pulse has to interact at least once to lead to the nonlinear signal. Due to the observation that the phase front of the signal is independent of that
of pulse A, pulse A should interact an even number of times. A third-order process
hence is not sufficient to explain the signal origin. As shown in Fig. 4 of Ref. [33],
the nonlinear signal at T w = 827 fs is found to be a direct continuation in amplitude and phase of that at T w = 35 fs. Besides, its phase is independent of the pulse
sequences. Hence, the nonlinear two-phonon coherence signal follows the phase of
pulse B only, while pulses A and C create long-lived electronic excitations in InSb
whose bandgap is about 41 THz, twice the frequency of the THz pulses. The ladder
diagram (iii) shown in Fig. 21 can be read as follows. Pulse A excites an electronic
population via four interactions, pulse B impulsively induces a two-phonon coherence via three interactions, pulse C promotes this two-phonon coherence from the
first electronic excited state to the second one, and finally the two-phonon coherence
at the second electronic excited state radiates the nonlinear signal.
In this experiment, the exceptionally high-order nonlinear interactions were proposed on the basis of the huge transition dipole moments associated with the electronic and vibronic transitions in the InSb sample. In pure vibrational systems where
nonlinearity is not as dramatic, 2D spectra resulting from all THz interactions have
so far not been available. Hybrid 2D THz-Raman methods can provide better sensitivity because of simultaneous interactions via dipole and polarizability. Several
301
Reprinted from the journal