Unlocking Quantum Control and Multi-Order Correlations via Terahertz Two-Dimensional Coherent Spectroscopy

Terahertz two-dimensional coherent spectroscopy (THz-2DCS) is transforming our ability to probe, visualize, and control quantum materials far from equilibrium. This emerging technique brings multi-dimensional resolution to the ultrafast dynamics of nonequilibrium phases of matter, enabling new capabilities demanding precise coherent control and measurement of many-body dynamics and multi-order correlations. By mapping complex excitations across time and frequency dimensions, THz-2DCS delivers coherence tomography of driven quantum matter, thus revealing hidden excitation pathways, measuring higher order nonlinear response functions, disentangling various quantum pathways, capturing collective modes on ultrafast timescales and at terahertz frequencies. These experimental features frequently remain obscured in traditional single particle measurements, ultrafast spectroscopy techniques, and equilibrium-based probes. This Review traces the early development of THz-2DCS and showcases significant recent progress in leveraging this technique to probe and manipulate quantum material properties, including nonequilibrium superconductivity, nonlinear magnonics, dynamical topological phases, and the detection of novel excitations and exotic collective modes with potential technological impact. Looking forward, we identify critical opportunities in advancing THz-2DCS instrumentation and experimental strategies that are shaping future applications in THz optoelectronics, quantum information processing, and sensing.

💡 Research Summary

This review provides a comprehensive overview of terahertz two‑dimensional coherent spectroscopy (THz‑2DCS), a rapidly emerging technique that adds a second frequency‑time dimension to ultrafast spectroscopy of quantum materials. The authors begin by positioning THz‑2DCS within the broader landscape of quantum information science (QIS) and condensed‑matter physics, emphasizing that conventional GHz‑scale superconducting circuits or cold‑atom simulators cannot access the high‑frequency, high‑temperature dynamics that THz photons can probe. By employing two phase‑locked THz pulses (denoted A and B) with a controllable inter‑pulse delay τ, and detecting the resulting nonlinear emission via phase‑resolved electro‑optic sampling (EOS), THz‑2DCS directly measures the third‑order (and higher) response function E_NL(t,τ)=E_A+B−E_A−E_B. The technique captures both amplitude and phase of the emitted field, allowing extraction of nonlinear conductivity σ_NL(t,τ) and permittivity ε_NL(t,τ).

Two complementary experimental protocols are described. The “full 2D scanning” protocol fixes τ and scans the gate time t, yielding a complete map E_NL(t,τ) that visualizes cross‑peaks associated with specific quantum pathways. The “pump‑probe (PP) scanning” protocol fixes t and scans τ (or the combined pump‑delay τ_pump), providing a clean view of population dynamics while avoiding artifacts such as perturbed free‑induction decay. Both approaches are shown to be mathematically transformable into each other, and their combined use enables unambiguous separation of coherent versus incoherent contributions.

The review then enumerates four major scientific advantages of THz‑2DCS. First, coherence tomography: 2D spectra separate overlapping excitations (e.g., Higgs amplitude mode, magnons, phonons) into distinct (ω_t, ω_τ) coordinates, revealing multi‑order correlations that are invisible to one‑dimensional pump‑probe or linear spectroscopies. Second, coherent control of collective currents: phase‑locked THz pulse pairs can impart momentum to the Cooper‑pair condensate, generating and steering a superfluid momentum p_s(t) that persists beyond the pulse duration, a mechanism that can be extended to dissipationless edge currents in topological phases. Third, enhanced sensing fidelity: background‑free spectral locations in the 2D plane allow selective detection of genuine nonlinear signals while suppressing spurious contributions, dramatically improving signal‑to‑noise ratios for weak collective modes. Fourth, broad applicability: the technique has been successfully applied to semiconductors, high‑Tc superconductors, antiferromagnets, topological semimetals, ferroelectrics, and even molecular liquids, each time revealing new nonlinear pathways such as 2ω, 3ω, and mixed‑frequency (2ω±Ω) peaks.

Table 1 in the paper compiles recent experimental demonstrations, listing the THz field strengths (1–10 MV cm⁻¹), photon energies (0.1–100 meV), pulse bandwidth (single‑cycle broadband vs multi‑cycle narrowband), and the specific collective excitations probed. Representative studies include: (i) observation of the Higgs mode and its coupling to quasiparticles in Fe‑based superconductors; (ii) nonlinear magnon‑phonon conversion and magnon‑mediated Raman processes in orthoferrites; (iii) detection of Josephson plasma oscillations and interlayer tunneling dynamics in cuprate superconductors; (iv) probing electron‑phonon coupling and bulk photovoltaic effects in Dirac semimetal Cd₃As₂; and (v) coherent rotational dynamics in small molecules using cross‑polarized THz pulses. In each case, the 2D spectra display well‑resolved cross‑peaks that directly map the underlying quantum pathways, enabling quantitative extraction of higher‑order susceptibilities χ^(n).

The theoretical framework is discussed in depth. The nonlinear response is expanded in powers of the applied fields, yielding multi‑point correlation functions χ^(2), χ^(3), etc. For non‑perturbative regimes, the authors invoke the Keldysh‑Kadanoff‑Baym nonequilibrium Green’s function formalism to capture the full time‑ordering of the two THz interactions and the subsequent evolution of the system’s density matrix. This approach naturally distinguishes between “coherent evolution” (τ shorter than the intrinsic dephasing time) and “population dynamics” (τ longer than dephasing), providing a rigorous basis for interpreting the observed 2D line shapes and peak intensities.

Looking forward, the review identifies three key challenges and opportunities. (1) Development of real‑time feedback loops that use the measured 2D signal to adaptively shape the THz waveform, creating a self‑optimizing “coherence tomography” that can steer the system toward desired quantum states. (2) Extension of THz‑2DCS to nanoscale and near‑field geometries, enabling spatially resolved spectroscopy of 2D materials, heterostructures, and device‑scale elements. (3) Exploration of extreme‑field regimes (>10 MV cm⁻¹) to drive systems across nonlinear critical points and investigate strong‑coupling phenomena such as light‑induced superconductivity or Floquet topological transitions. Successful advances in these directions are expected to impact THz‑based quantum information processing, ultrahigh‑sensitivity sensing, and next‑generation THz optoelectronic technologies.

In summary, the authors present THz‑2DCS as a versatile, high‑resolution tool that simultaneously visualizes, quantifies, and controls multi‑order quantum correlations in a wide array of materials. By bridging the gap between ultrafast optics and quantum many‑body physics, THz‑2DCS is poised to become a cornerstone technique for future discoveries in quantum materials science and emerging quantum technologies.