Two-dimensional coherent spectroscopy of a THz quantum cascade laser: observation of multiple harmonics

Field-resolved high-order sub-cycle nonlinearities in a terahertz semiconductor laser

The exploitation of ultrafast electron dynamics in quantum cascade lasers (QCLs) holds enormous potential for intense, compact mode-locked terahertz (THz) sources, squeezed THz light, frequency mixers, and comb-based metrology systems. Yet the important sub-cycle dynamics have been notoriously difficult to access in operational THz QCLs. Here, we employ high-field THz pulses to perform the first ultrafast two-dimensional spectroscopy of a free-running THz QCL. Strong incoherent and coherent nonlinearities up to eight-wave mixing are detected below and above the laser threshold. These data not only reveal extremely short gain recovery times of 2 ps at the laser threshold, they also reflect the nonlinear polarization dynamics of the QCL laser transition for the first time, where we quantify the corresponding dephasing times between 0.9 and 1.5 ps with increasing bias currents. A density-matrix approach reproducing the emergence of all nonlinearities and their ultrafast evolution, simultaneously, allows us to map the coherently induced trajectory of the Bloch vector. The observed high-order multi-wave mixing nonlinearities benefit from resonant enhancement in the absence of absorption losses and bear potential for a number of future applications, ranging from efficient intracavity frequency conversion, mode proliferation to passive mode locking.

Two-dimensional terahertz spectroscopy of condensed-phase molecular systems

Nonlinear terahertz (THz) spectroscopy relies on the interaction of matter with few-cycle THz pulses of electric field amplitudes up to megavolts/centimeter (MV/cm). In condensed-phase molecular systems, both resonant interactions with elementary excitations at low frequencies such as intra- and intermolecular vibrations and nonresonant field-driven processes are relevant. Two-dimensional THz (2D-THz) spectroscopy is a key method for following nonequilibrium processes and dynamics of excitations to decipher the underlying interactions and molecular couplings. This article addresses the state of the art in 2D-THz spectroscopy by discussing the main concepts and illustrating them with recent results. The latter include the response of vibrational excitations in molecular crystals up to the nonperturbative regime of light-matter interaction and field-driven ionization processes and electron transport in liquid water.

Graphene-Coupled Terahertz Semiconductor Lasers for Enhanced Passive Frequency Comb Operation

Optical frequency combs, consisting of well-controlled equidistant frequency lines, have been widely used in precision spectroscopy and metrology. Terahertz combs have been realized in quantum cascade lasers (QCLs) by employing either an active mode-locking or phase seeding technique, or a dispersion compensator mirror. However, it remains a challenge to achieve the passive comb formation in terahertz semiconductor lasers due to the insufficient nonlinearities of conventional saturable absorbers. Here, a passive terahertz frequency comb is demonstrated by coupling a multilayer graphene sample into a QCL compound cavity. The terahertz modes are self-stabilized with intermode beat note linewidths down to a record of 700 Hz and the comb operation of graphene-coupled QCLs is validated by on-chip dual-comb measurements. Furthermore, the optical pulse emitted from the graphene-coupled QCL is directly measured employing a terahertz pump-probe technique. The enhanced passive frequency comb operation is attributed to the saturable absorption behavior of the graphene-integrated saturable absorber mirror, as well as the dispersion compensation introduced by the graphene sample. The results provide a conceptually different graphene-based approach for passive comb formation in terahertz QCLs, opening up intriguing opportunities for fast and high-precision terahertz spectroscopy and nonlinear photonics.

Ultrafast two-dimensional field spectroscopy of terahertz intersubband saturable absorbers

Intersubband (ISB) transitions in semiconductor multi-quantum well (MQW) structures are promising candidates for the development of saturable absorbers at terahertz (THz) frequencies. Here, we exploit amplitude and phase-resolved two-dimensional (2D) THz spectroscopy on the sub-cycle time scale to observe directly the saturation dynamics and coherent control of ISB transitions in a metal-insulator MQW structure. Clear signatures of incoherent pump-probe and coherent four-wave mixing signals are recorded as a function of the peak electric field of the single-cycle THz pulses. All nonlinear signals reach a pronounced maximum for a THz electric field amplitude of 11 kV/cm and decrease for higher fields. We demonstrate that this behavior is a fingerprint of THz-driven carrier-wave Rabi flopping. A numerical solution of the Maxwell-Bloch equations reproduces our experimental findings quantitatively and traces the trajectory of the Bloch vector. This microscopic model allows us to design tailored MQW structures with optimized dynamical properties for saturable absorbers that could be used in future compact semiconductor-based single-cycle THz sources.