Terahertz 2D coherent spectroscopy (THz-2DCS) is an emerging technique that brings multidimensional resolution to the ultrafast spectral–temporal dynamics of non-equilibrium quantum phases of matter, enabling new capabilities for precise coherent control in many-body dynamics and multiorder correlations. By mapping and disentangling complex excitation and detection pathways across distinct time and frequency dimensions, THz-2DCS provides a form of coherence tomography of light-induced quantum matter — revealing multiquantum coherences, separating nonlinear response functions and capturing collective modes and quantum kinetics on ultrafast THz timescales. This Perspective discusses the technical capabilities of THz-2DCS, provides a comparison to other multidimensional and coherent transient spectroscopies and looks ahead towards opportunities for advancing THz-2DCS instrumentation and experimental strategies towards new frontier discoveries. Terahertz 2D coherent spectroscopy can be used to probe phase-resolved, multidimensional spectra of quantum materials. This Perspective discusses the capabilities of this method and provides a comparison with other multidimensional spectroscopies.

Ultrafast spectroscopy under simultaneous high pressure and magnetic field provides a versatile approach for investigating pressure-driven electronic instabilities and correlated phases, and for probing potential bulk superconducting behavior under extreme conditions. However, such an experimental platform has yet to be implemented, standing as a roadblock to a fuller understanding of nonequilibrium superconductivity and vortex-controlled quasi-particle (QP) dynamics. Here, we bridge this capability gap by developing high pressure (up to 40 GPa), high magnetic field (up to 7 T), cryogenic (down to 5 K) femtosecond spectroscopy, and using it to probe magneto-pressure evolution of quasiparticle dynamics in the trilayer nickelate Pr_4Ni_3O_10. We observe pronounced critical slowing down of QP relaxation at the charge-density-wave transition, which collapses under applied pressure. At higher pressures, the relaxation instead lengthens at low temperature, consistent with incipient superconducting correlations. However, the negligibel magnetic-field-dependence up to 7 T and absence of vortex-induced pre-bottleneck dynamics–robust signatures observed in our controlled bulk superconducting samples–indicates that any superconducting state under the present pressure conditions is likely non-bulk, filamentary, or strongly inhomogeneous. The magneto-pressure ultrafast capability opens a new avenue for resolving outstanding questions surrounding pressure-induced superconductivity and intertwined orders in correlated quantum materials.

Coherent control of quantum materials has progressed along two major fronts: nonlinear phononics, which reshapes lattices to induce emergent states, and Floquet engineering, which tailors electronic band reconstruction via time-periodic driving. Both mechanisms face fundamental limitations at terahertz (THz) frequencies: phononic nonlinearities are intrinsically weak in standard lattices, while electronic Floquet states are often constrained by rapid decoherence upon light-off and by a scarcity of coherence-resolved, multi-correlation probes beyond (quasi-)stationary band structures. Here we report an extreme THz nonlinear-phononics mechanism in Ta_2NiSe_5, where a highly susceptible non-equilibrium electronic correlation bath dramatically amplifies lattice nonlinearities under coherent driving. Utilizing THz two-dimensional spectroscopy as a coherence-tomography tool, we resolve an exceptionally rich landscape of approximately 30 distinct multi-order quantum pathways, including high-harmonic phonon generation, multi-quantum coherences, and multi-wave anharmonic cross-mode mixing. The density and complexity of this extreme manifold establishes a new benchmark for THz nonlinear phononics, as the multi-order quantum pathways surpass the limits of conventional lattice responses. These high-order signals collapse above 100 K, defining an electronic correlation scale of a coherence-imprinted hybrid electronic-phonon order that governs the sustainability of high-order quantum correlations and nonlinear pathways beyond linear and equilibrium responses. Our results establish a route for correlation-boosted, phonon-anchored periodic Hamiltonian engineering and for certifying such periodically-driven states via multi-correlation coherence tomography.

The symmetry-topology interplay dictates how to define order parameters and classify material ordered phases. However, current understanding of this interplay has been predominately approached from a one-sided perspective, with topological states being classified within the constraints imposed by specific fixed symmetries. Here we complete this full circle by demonstrating spontaneous symmetry breaking that results from a periodic alteration of topological phases induced by light in a centrosymmetric Dirac material ZrTe5. The distinguishing feature is the observation of robust correlation and striking anomalies in the fluence and temperature dependence of key transport parameters. First, both shift current Js and displacement current Jd, arising from interband transition and infrared phonon driving, respectively, along with charge carrier pumping, exhibit similar behaviors. Second, they all peak at similar low pump fluence, followed by a subsequent reduction as the fluence further increases. This behavior cannot be explained by conventional energetically allowed, direct excitations. Third, all the three observables exhibit anomalies when they approach the topological phase transition temperature. These results highlight the unique low-energy pumping behaviors in ZrTe5, characterized by reversible fluence dependence and a "hinge-like" interaction that connects various electronic and lattice observables, including phonons, charge carriers, and currents. Our findings, supported by model analysis, provide key insights into the fragility of crystalline (inversion) and time-reversal symmetries during the dynamics of topological phase transitions. This fragility drives spontaneous symmetry breaking, evidenced by the synchronized emergence of off-resonant infrared phonons and broken-symmetry photocurrents.

The symmetry-topology interplay dictates how to define order parameters and classify material ordered phases. However, current understanding of this interplay has been predominately approached from a one-sided perspective, with topological states being classified within the constraints imposed by specific fixed symmetries. Here we complete this full circle by demonstrating spontaneous symmetry breaking that results from a periodic alteration of topological phases induced by light in a centrosymmetric Dirac material ZrTe_5. The distinguishing feature is the observation of robust correlation and striking anomalies in the fluence and temperature dependence of key transport parameters.First, both shift current J_s and displacement current J_d, arising from interband transition and infrared phonon driving, respectively, along with charge carrier pumping, exhibit similar behaviors. Second, they all peak at similar low pump fluence, followed by a subsequent reduction as the fluence further increases. This behavior cannot be explained by conventional energetically allowed, direct excitations. Third, all the three observables exhibit anomalies when they approach the topological phase transition temperature. These results highlight the unique low-energy pumping behaviors in ZrTe_5, characterized by reversible fluence dependence and a 'hinge-like' interaction that connects various electronic and lattice observables, including phonons, charge carriers, and currents. Our findings, supported by model analysis, provide key insights into the fragility of crystalline (inversion) and time-reversal symmetries during the dynamics of topological phase transitions. This fragility drives spontaneous symmetry breaking, evidenced by the synchronized emergence of off-resonant infrared phonons and broken-symmetry photocurrents.

Detecting photon echoes from superconducting Higgs modes is challenging due to the necessity of preserving and retrieving phase coherence encoded in multiple Higgs and quasiparticle (QP) excitations. Here, we demonstrate the emergence of a Higgs echo in niobium superconductors. This approach disentangles unique quantum pathways involving the Higgs mode and QP excitations. Using Higgs echo spectroscopy, we also uncover unconventional echo formation caused by inhomogeneous broadening and "soft" QP bands, which dynamically evolve under terahertz (THz) driving. Specifically, THz pulse pairs modulate the superconducting gap, imprinting coherence and forming a temporal "Higgs grating." This grating produces echoes with distinctive characteristics: (i) echo rephasing spectral peaks at superconducting gap frequencies, (ii) asymmetric echo formation delays unlike those observed in atoms or semiconductors, and (iii) negative-time echo signals stemming from Higgs-QP anharmonic interactions. Combined with advanced time-frequency analysis, these findings distinguish Higgs from QP responses and clarify their intricate interactions in THz-driven superconductivity.

The interplay between electronic topology and superconductivity is the subject of great current interest in condensed matter physics. For example, superconductivity induced on the surface of topological insulators is predicted to be triplet in nature, while the interplay between electronic correlations and topology may lead to unconventional superconductivity as in twisted bilayer graphene. Here, we unveil an unconventional two-dimensional superconducting state in the recently discovered Dirac nodal line semimetal ZrAs2 which is exclusively confined to the top and bottom surfaces within the crystal's ab plane. As a remarkable consequence of this emergent state, we observe a Berezinskii-Kosterlitz-Thouless (BKT) transition, the hallmark of two-dimensional superconductivity. Notably, this is the first observation of a BKT transition on the surface of a three-dimensional system. Furthermore, employing angle-resolved photoemission spectroscopy and first-principles calculations, we find that these same surfaces also host a two-dimensional van Hove singularity near the Fermi energy. The proximity of van Hove singularity to the Fermi level leads to enhanced electronic correlations contributing to the stabilization of superconductivity at the surface of ZrAs2, a unique phenomenon among topological semimetals. The surface-confined nature of the van Hove singularity, and associated superconductivity, realized for the first time, opens new avenues to explore the interplay between low-dimensional quantum topology, correlations, and superconductivity in a bulk material without resorting to the superconducting proximity effect.

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.

The d-wave pairing symmetry in newly discovered infinite-layer nickelates remains highly debated compared to the widely accepted d-wave superconductivity in cuprates, despite recent intense efforts using equilibrium optical and electrical transport measurements. A complementary approach involves characterizing THz coherent nonlinear responses, which is currently lacking but needed, as it would offer new insights into the superconducting gap structure by characterizing Higgs modes and quasiparticle excitations. Here, we report THz 2D coherent spectroscopy (THz-2DCS) responses from the superconducting state in an infinite-layer nickelate. The 2D spectra clearly demonstrate the absence of hallmark signatures of s-wave pairing symmetry, such as resonant 2A peaks at superconducting gaps. Instead, we observe gapless 2D spectra in the nickelate, centered around the THz driving frequency, with no noticeable shift as the temperature increases. These findings closely resemble the nodal superconductivity behavior expected in cuprates. Together with our simulations, these findings suggest that 2A signatures in the 2D spectra of d-wave gap structures can be obscured by significant nodal quasiparticle excitations at arbitrarily low energies. This contrasts with the long-lived Higgs modes, observed as distinct 2A peaks in a controlled THz-2DCS experiment on niobium, a representative example of dirty-limit s-wave superconductors. Our results have implications for understanding the unconventional superconductivity in nickelates and highlight the need to explore their coherent nonlinear dynamics.

We report quantum beating via Floquet-like periodic driving of superfluid momentum. Using two-dimensional terahertz pump-probe interference spectroscopy signals, we identify a characteristic signature from the interplay between the driving and the intrinsic Higgs mode frequency.

Even in the quantum limit, non-equilibrium quasiparticle (QP) populations induce QP poisoning that irreversibly relaxes the quantum state and significantly degrades the coherence of transmon qubits. A particularly detrimental yet previously unexplored mechanism arises from QP multiplication facilitated by vortex trapping in superconducting quantum circuits, where a high-energy QP relaxes by breaking additional Cooper pairs and amplifying the QP population due to the locally reduced excitation gap and enhanced quantum confinement within the vortex core. Here we directly resolve this elusive QP multiplication process by revealing vortex-controlled QP self-generation in a highly nonequilibrium regime preceding the phonon bottleneck of QP relaxation. At sufficiently low fluence, femtosecond-resolved magneto-reflection spectroscopy directly reveals a continuously increasing QP population that is strongly dependent on magnetic-field-tuned vortex density and absent at higher excitation fluences. Quantitative analysis of the emergent QP pre-bottleneck dynamics further reveals that, although the phonon population saturates within $\simeq$10~ps, both free and trapped QPs continue to grow in a self-sustained manner--hallmarks of the long-anticipated QP-vortex interactions in nonequilibrium superconductivity. We estimate a substantial increase of $\sim$34\% in QP density at vortex densities of $\sim$ 100 magnetic flux quanta per $\mathrm{μm^{2}}$. Our findings establish a powerful spectroscopic tool for uncovering QP multiplication and reveal vortex-assisted QP relaxation as a critical materials bottleneck whose mitigation will be essential for resolving QP poisoning and enhancing coherence in superconducting qubits.

The discovery of superconductivity in infinite-layer nickelates establishes a new category of unconventional superconductors that share structural and electronic similarities with cuprates. Despite exciting advances, such as the establishment of a cuprate-like phase diagram and the observation of charge order and short-range antiferromagnetic fluctuation, the key issues of superconducting pairing symmetry, gap amplitude, and superconducting fluctuation remain elusive. In this work, we utilize static and ultrafast terahertz spectroscopy to address these outstanding problems. We demonstrate that the equilibrium terahertz conductivity and nonequilibrium terahertz responses of an optimally Sr-doped nickelate film ($T_c$ = 17 K) are in line with the electrodynamics of $d$-wave superconductivity in the dirty limit. The gap-to-$T_c$ ratio 2$\Delta/k_\mathrm{B}T_\mathrm{c}$ is extracted to be 3.4, indicating the superconductivity falls in the weak-coupling regime. In addition, we observed significant superconducting fluctuation near $T_\mathrm{c}$, while it does not extend into the deep normal state as optimally hole-doped cuprates. Our result highlights a new $d$-wave system which closely resembles the electron-doped cuprates, expanding the family of unconventional superconductivity in oxides.

We present a comprehensive theory of light-controlled multiband superconductivity, and apply it to predict distinctive signatures of light-driven superconducting (SC) states in terahertz multidimensional coherent spectroscopy (THz-MDCS) experiments. We first derive gauge-invariant Maxwell-Bloch equations for multiband BCS superconductors with spatial fluctuations. We consider driving electromagnetic fields determined self-consistently by Maxwell's equations. By calculating the THz-MDCS spectra measured experimentally in the clean SC limit, we identify unique signatures of finite-momentum Cooper-pairing states that live longer than the laser pulse. They are controlled by a pair of THz laser pulses with well-defined relative phase (pulse pair). The pseudospin oscillators that describe the properties of these SC states are parametrically driven by both finite-momentum Cooper pairing and by time oscillations of the order-parameter relative phase. We show that such strong parametric driving leads to drastic changes in the THz-MDCS spectral shape from the predictions of third-order nonlinear susceptibility calculations. These spectral changes strongly depend on the interband-to-intraband interaction ratio and on the collective modes of the light-driven state. For negligible interband interaction, the spectra show a transition with increasing field, from traditional pump-probe, four-wave-mixing, and third-harmonic generation peaks determined by the laser frequency to sidebands determined by the excitations of the driven system. These sidebands emerge from difference-frequency Raman processes in the nonequilibrium SC state. For interband couplings weaker than the intraband pairing, we show that the Leggett phase collective mode leads to harmonic sidebands around the traditional pump-probe peaks. Additional Higgs collective mode peaks result from light-induced inversion-symmetry breaking in a thin-film geometry. For strong interband coupling, we find a transition from a nonequilibrium finite Cooper-pair momentum state characterized by hybrid-Higgs amplitude mode peaks in THz-MDCS spectra to a driven state identified experimentally by the emergence of Floquet-type sidebands at bi-Higgs frequencies. Those dominant bi-Higgs-frequency satellites are manifestations of a new order parameter relative phase collective mode that characterizes the nonequilibrium SC state. The predicted interaction- and field-dependent transitions in the spectral profile allow us to propose THz-MDCS experiments for quantum tomography of light-driven superconductivity.

Nonlinear interactions of spin-waves and their quanta, magnons, have emerged as prominent candidates for interference-based technology, ranging from quantum transduction to antiferromagnetic spintronics. Yet magnon multiplication in the terahertz (THz) spectral region represents a major challenge. Intense, resonant magnetic fields from THz pulse-pairs with controllable phases and amplitudes enable high order THz magnon multiplication, distinct from non-resonant nonlinearities such as the high harmonic generation by below-band gap electric fields. Here, we demonstrate exceptionally high-order THz nonlinear magnonics. It manifests as 7th-order spin-wave-mixing and 6th harmonic magnon generation in an antiferromagnetic orthoferrite. We use THz two-dimensional coherent spectroscopy to achieve high-sensitivity detection of nonlinear magnon interactions up to six-magnon quanta in strongly-driven many-magnon correlated states. The high-order magnon multiplication, supported by classical and quantum spin simulations, elucidates the significance of four-fold magnetic anisotropy and Dzyaloshinskii-Moriya symmetry breaking. Moreover, our results shed light on the potential quantum fluctuation properties inherent in nonlinear magnons. The authors demonstrate high-order terahertz nonlinear magnonics using two-dimensional coherent spectroscopy, revealing the emergence of seventh-order spin-wave mixing and sixth harmonic magnon generation within an antiferromagnetic orthoferrite.

Light engineering of correlated states in topological materials provides a new avenue of achieving exotic topological phases inaccessible by conventional tuning methods. Here we demonstrate a light control of correlation gaps in a model charge-density-wave (CDW) and polaron insulator (TaSe 4 ) 2 I recently predicted to be an axion insulator. Our ultrafast terahertz photocurrent spectroscopy reveals a two-step, non-thermal melting of polarons and electronic CDW gap via the fluence dependence of a longitudinal circular photogalvanic current. This helicity-dependent photocurrent reveals continuous ultrafast phase switches from the polaronic state to the CDW (axion) phase, and finally to a hidden Weyl phase as the pump fluence increases. Additional distinctive attributes aligning with the light-induced switches include: the mode-selective coupling of coherent phonons to the polaron and CDW modulation, and the emergence of a non-thermal chiral photocurrent above the pump threshold of CDW-related phonons. The demonstrated ultrafast chirality control of correlated topological states here holds large potentials for realizing axion electrodynamics and advancing quantum-computing applications.

We present a comprehensive theory of light-controlled multi-band superconductivity and apply it to predict distinctive signatures of light-driven superconducting (SC) states in terahertz multi-dimensional coherent spectroscopy (THz-MDCS) experiments. We first derive gauge-invariant Maxwell-Bloch equations for multi-band BCS superconductors. For this, we go beyond previously considered Anderson pseudo-spin precession models to include quantum transport effects. By calculating the THz-MDCS spectra measured experimentally, we then identify unique signatures of finite-momentum Cooper-pairing states that live longer than the laser pulse. These non-equilibrium SC states are characterized by long-lived canting of Anderson pseudo-spins. The pseudo-spin oscillators that describe the properties of these SC states are parametrically driven by both finite-momentum Cooper pairing and by time oscillations of the order parameter relative phase. We show that such strong parametric driving leads to drastic changes in the THz-MDCS spectral shape from the predictions of third-order nonlinear susceptibility calculations. These spectral changes strongly depend on the interband-to-intraband interaction ratio and on the collective modes of the light-driven state.

We report on an ultrafast nonequilibrium phase transition with a strikingly long-lived martensitic anomaly driven by above-threshold single-cycle terahertz pulses with a peak field of more than 1 MV/cm. A nonthermal, terahertz-induced depletion of low-frequency conductivity in Nb3Sn indicates increased gap splitting of high-energy Γ12 bands by removal of their degeneracies, which induces the martensitic phase above their equilibrium transition temperature. In contrast, optical pumping leads to a Γ12 gap thermal melting. Such light-induced nonequilibrium martensitic phase exhibits a substantially enhanced critical temperature up to ∼100 K, i.e., more than twice the equilibrium temperature, and can be stabilized beyond technologically relevant, nanosecond time scales. Together with first-principle simulations, we identify a compelling terahertz tuning mechanism of structural order via Γ12 phonons to achieve the ultrafast phase transition to a metastable electronic state out of equilibrium at high temperatures far exceeding those for equilibrium states.

Topologically protected surface current is highly promising for next-generation low-dissipation and disorder-tolerant quantum electronics and computing. Yet, electric transport from the co-existing bulk state dominates the responses of the Dirac surface state, especially at elevated temperatures relevant to technological applications. Here, we present an approach that convincingly showcases the generation, disentanglement, and precise control of enduring surface charge carriers on a topological insulator, Bi2Se3, with high bulk conductivity, all achieved at room temperature. By using pump–probe modulation spectroscopy under ultrabroadband driving tunable from 4 meV to 1.55 eV, we show the terahertz (THz) field-induced surface carriers by discovering their initial temporal responses dominant over high density trivial bulk carriers. Strikingly, the response of the induced surface carrier responses persists for more than ∼5 ps and is enhanced by reducing pump photon energy. The dynamics and lifetime of the distinct surface response manifest themselves as the enhanced THz pump-induced THz transmission, which directly correlates with the transient negative THz conductivity. Increasing the THz driving field reduces the induced surface carrier lifetime and identifies, particularly, an optimal pump field of Es ∼ 224 kV cm−1 for generating the dominant surface response relative to the bulk. This surface carrier dominant regime is suppressed by a joint effect of enhanced surface-bulk scattering and a more rapid saturation of surface excitation compared to the bulk that sets in above Es. The controllability of room temperature topologically surface carriers through pump photon energy offer compelling possibilities for extending this approach to other topological complex materials.