Phase-resolved two-dimensional terahertz spectroscopy including off-resonant interactions beyond the χ(3) limit

Abstract

We present the first two-dimensional (2D) terahertz (THz) experiment with three phase-locked THz pulses and a fully phase-resolved detection of the nonlinearly emitted field by electrooptic sampling. In a prototype experiment we study the ultrafast dynamics of nonlinear two-phonon and two-photon interband coherences in the narrow-gap semiconductor InSb. Due to the extraordinarily large optical interband dipole of InSb the experiments were performed in the strongly nonperturbative regime of light-matter interaction allowing for impulsive off-resonant excitation of both two-phonon coherences and two-photon interband coherences, the ultrafast dynamics of which is experimentally observed as a function of the waiting time in the three-pulse 2D experiment. Our novel three-pulse 2D THz spectroscopy paves the way for the detailed investigation of nonlinear quantum coherences in solids and holds potential for an extension to other systems.

Perspective: THz-driven nuclear dynamics from solids to molecules

“…For example, a transition dipole of 120 D, corresponding to the displacement of a single charge over 25 Å, has been reported for a GaAs/AlGaAs quantum well with a size of 110 Å 56,57 . The particle-in-a-box argument still holds for other types of electronic transitions in a more qualitative sense, e.g., the transition dipole of the interband transition in graphene is as large as ∼3800 D ( e  ×   800 Å), 54 that of the ionization of shallow impurities in a doped Ge:Ga semiconductor 320 D ( e  ×   67 Å), 68 and that of the interband transition in InSb 190 D ( e  ×   40 Å) 55 …”

“…For example, as a measure of the amount of excitation that can be achieved, it is common to relate the resulting Rabi frequency μΕ / h to the length of the THz pulse 54–57,68,77 . Taking the interband transition dipole of InSb as an example (190 D) 55 and assuming an electrical field strength of 10 kV/cm from a ZnTe crystal, 79,80 one obtains a Rabi frequency of 1 THz, i.e., one can saturate the transition with a typical single-cycle THz pulse. For a two level system, which electronic transitions often are to a reasonably good approximation, saturation also implies a nonlinear THz response: in the extreme case of π/2 or π-pulses beyond the perturbative limit 55 .…”

“…Taking the interband transition dipole of InSb as an example (190 D) 55 and assuming an electrical field strength of 10 kV/cm from a ZnTe crystal, 79,80 one obtains a Rabi frequency of 1 THz, i.e., one can saturate the transition with a typical single-cycle THz pulse. For a two level system, which electronic transitions often are to a reasonably good approximation, saturation also implies a nonlinear THz response: in the extreme case of π/2 or π-pulses beyond the perturbative limit 55 . To achieve the same for a vibrational transition (0.5 D), a THz pulse with 4 MV/cm would be required, which is not out of reach, as discussed above, 87 but technologically significantly more demanding.…”

“…Given the huge transitions dipoles to low-lying electronic states in solids, which make it relatively easy to reach the interaction energies just discussed with readily available THz pulses with field strengths in the order of 10–100 kV/cm, it can be understood why by far the most nonlinear THz experiments have been performed on such transitions, e.g., in semiconductors, 55–58,60,68,106–108 superconductors, 109–112 or graphene 54,113–118 . For example, a Special Issue on nonlinear THz studies has been published recently (Ref.…”

Strong Local-Field Enhancement of the Nonlinear Soft-Mode Response in a Molecular Crystal

“…The THz field transmitted through the sample held at a temperature of 80 K is detected in amplitude and phase as a function of real time t by freespace electro-optic sampling. The field E NL ðt; τÞ emitted by the nonlinear polarization of the sample is extracted as E NL ðt; τÞ ¼ E AB ðt; τÞ − E A ðt; τÞ − E B ðtÞ where E AB ðt; τÞ is the transmitted field with both pulses A and B interacting with the sample, E A (E B ) being the transmitted field measured with only pulse A (B) [17][18][19][20][21]. The two THz pulses are generated by optical rectification of 25 fs pulses at 800 nm in two GaSe crystals (200 and 300 μm thickness).…”