Top Curr Chem (Z) (2018) 376:6
1 3
separated by T rev . Examples of the FID signals from carbonyl sulfide (OCS) [59]
and acetonitrile (CH 3 CN) [31] gases excited by one single-cycle THz pulse generated from LiNbO 3 and detected by EOS are shown in Fig. 10b, c, respectively. The
revival periods are T rev = 82 ps for OCS and T rev = 54.5 ps for CH 3 CN, both consistent with literature values of their rotational constants B. Fourier transformation of
the periodic FID signal in Fig. 10c yields the linear rotational spectrum (the absorption spectrum) of CH 3 CN consisting of equally spaced peaks separated by 2Bc as
shown in Fig. 10d. Each rotational transition between adjacent rotational states is
resolved as a sharp peak.
3.2 Molecular Alignment Induced by THz Pulses and Two‑Quantum
THz‑THz‑Optical Rotational Spectroscopy
The molecular orientational 1QCs discussed in Sect. 3.1 are the linear responses
induced by one THz field-dipole interaction. Second-order nonlinear rotational
responses resulting from two successive THz field-dipole interactions, manifested
as 2-quantum coherences (2QCs) and non-thermal populations, have also been demonstrated. The second-order field-dipole interaction Hamiltonian takes the approximate form H 2 = (− ⋅ THz (t))
2 =
2 E THz (t)
2 cos
2 , where we are neglecting other
excitation pathways including stimulated scattering. 2QCs and the excited rotational
population correspond to net alignment of molecular dipoles, described by the alignment factor ‹cos
2
θ›, with no net molecular orientation or associated macroscopic
polarization because the dipoles may be antiparallel as well as parallel. Optical
detection methods such as optical birefringence can be used to measure the alignment since it leads to anisotropy in the optical refractive indices between the direction of alignment (THz electric field polarization direction) and the direction normal
to the alignment direction. The experimentally measured birefringence is proportional to cos
2
θ.
Rotational 2QCs result from two successive THz field-dipole interactions that
generate coherent superpositions of first J and J + 1 levels and then J, J + 1 and J + 2
levels through successive transitions with the selection rule ΔJ = ± 1. The 2QCs
between levels J and J + 2 evolve in time at frequencies of f J,J+2 = 2Bc(2J + 3), and
their superposition leads to periodic, short-lived revivals of constructive interference
similar to those of the 1QCs but with a period of T rev /2 = (4Bc)
−1
. The measurement
results from OCS in Fig. 11a show that the 2QC revivals appear as expected. Fourier
transformation of the birefringence signal yields the rotational spectrum in Fig. 11b.
Note that the successive resonant THz field interactions with the dipoles are completely different from nonresonant optical excitation of 2QCs through stimulated
rotational Raman interactions with the molecular polarizabilities, with the selection
rule ΔJ = ± 2 [67].
The periodic 2QC signals are superimposed on the steady-state second-order
population response that is also induced by successive THz field interactions that
produce first the 1QCs between adjacent levels J and J + 1 and then excited-state
populations in levels J + 1. The excited rotational populations are anisotropic
because each thermally populated level J includes equal populations in all of
290
Reprinted from the journal
1 3
separated by T rev . Examples of the FID signals from carbonyl sulfide (OCS) [59]
and acetonitrile (CH 3 CN) [31] gases excited by one single-cycle THz pulse generated from LiNbO 3 and detected by EOS are shown in Fig. 10b, c, respectively. The
revival periods are T rev = 82 ps for OCS and T rev = 54.5 ps for CH 3 CN, both consistent with literature values of their rotational constants B. Fourier transformation of
the periodic FID signal in Fig. 10c yields the linear rotational spectrum (the absorption spectrum) of CH 3 CN consisting of equally spaced peaks separated by 2Bc as
shown in Fig. 10d. Each rotational transition between adjacent rotational states is
resolved as a sharp peak.
3.2 Molecular Alignment Induced by THz Pulses and Two‑Quantum
THz‑THz‑Optical Rotational Spectroscopy
The molecular orientational 1QCs discussed in Sect. 3.1 are the linear responses
induced by one THz field-dipole interaction. Second-order nonlinear rotational
responses resulting from two successive THz field-dipole interactions, manifested
as 2-quantum coherences (2QCs) and non-thermal populations, have also been demonstrated. The second-order field-dipole interaction Hamiltonian takes the approximate form H 2 = (− ⋅ THz (t))
2 =
2 E THz (t)
2 cos
2 , where we are neglecting other
excitation pathways including stimulated scattering. 2QCs and the excited rotational
population correspond to net alignment of molecular dipoles, described by the alignment factor ‹cos
2
θ›, with no net molecular orientation or associated macroscopic
polarization because the dipoles may be antiparallel as well as parallel. Optical
detection methods such as optical birefringence can be used to measure the alignment since it leads to anisotropy in the optical refractive indices between the direction of alignment (THz electric field polarization direction) and the direction normal
to the alignment direction. The experimentally measured birefringence is proportional to cos
2
θ.
Rotational 2QCs result from two successive THz field-dipole interactions that
generate coherent superpositions of first J and J + 1 levels and then J, J + 1 and J + 2
levels through successive transitions with the selection rule ΔJ = ± 1. The 2QCs
between levels J and J + 2 evolve in time at frequencies of f J,J+2 = 2Bc(2J + 3), and
their superposition leads to periodic, short-lived revivals of constructive interference
similar to those of the 1QCs but with a period of T rev /2 = (4Bc)
−1
. The measurement
results from OCS in Fig. 11a show that the 2QC revivals appear as expected. Fourier
transformation of the birefringence signal yields the rotational spectrum in Fig. 11b.
Note that the successive resonant THz field interactions with the dipoles are completely different from nonresonant optical excitation of 2QCs through stimulated
rotational Raman interactions with the molecular polarizabilities, with the selection
rule ΔJ = ± 2 [67].
The periodic 2QC signals are superimposed on the steady-state second-order
population response that is also induced by successive THz field interactions that
produce first the 1QCs between adjacent levels J and J + 1 and then excited-state
populations in levels J + 1. The excited rotational populations are anisotropic
because each thermally populated level J includes equal populations in all of
290
Reprinted from the journal