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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.

A grand challenge underlies the entire field of topology-enabled quantum logic and information science: how to establish topological control principles driven by quantum coherence and understand the time dependence of such periodic driving. Here we demonstrate a few-cycle THz-pulse-induced phase transition in a Dirac semimetalZrTe5that is periodically driven by vibrational coherence due to excitation of the lowest Raman active mode. Above a critical THz-pump field threshold, there emerges a long-lived metastable phase, approximately 100 ps, with unique Raman phonon-assisted topological switching dynamics absent for optical pumping. The switching also manifests itself by distinct features: nonthermal spectral shape, relaxation slowing near the Lifshitz transition where the critical Dirac point occurs, and diminishing signals at the same temperature that the Berry-curvature-induced anomalous Hall effect magnetoresistance vanishes. These results, together with first-principles modeling, identify a mode-selective Raman coupling that drives the system from strong to weak topological insulators with a Dirac semimetal phase established at a critical atomic displacement controlled by the phonon coherent pumping. Harnessing of vibrational coherence can be extended to steer symmetry-breaking transitions, i.e., Dirac to Weyl ones, with implications for THz topological quantum gate and error correction applications.

The electronic and structural components of charge density waves occurring in layered transition metal dichalcogenides are known to be interdependent, yet have only been probed in separate measurements. Now, a broadband terahertz spectroscopy approach that monitors the evolution of these two order parameters simultaneously is demonstrated. The simultaneous ordering of different degrees of freedom in complex materials undergoing spontaneous symmetry-breaking transitions often involves intricate couplings that have remained elusive in phenomena as wide ranging as stripe formation 1 , unconventional superconductivity 1 , 2 , 3 , 4 , 5 , 6 , 7 or colossal magnetoresistance 1 , 8 . Ultrafast optical, X-ray and electron pulses can elucidate the microscopic interplay between these orders by probing the electronic and lattice dynamics separately 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , but a simultaneous direct observation of multiple orders on the femtosecond scale has been challenging. Here we show that ultrabroadband terahertz pulses can simultaneously trace the ultrafast evolution of coexisting lattice and electronic orders. For the example of a charge density wave (CDW) in 1 T -TiSe 2 , we demonstrate that two components of the CDW order parameter—excitonic correlations and a periodic lattice distortion (PLD)—respond very differently to 12-fs optical excitation. Even when the excitonic order of the CDW is quenched, the PLD can persist in a coherently excited state. This observation proves that excitonic correlations are not the sole driving force of the CDW transition in 1 T -TiSe 2 , and exemplifies the sort of profound insight that disentangling strongly coupled components of order parameters in the time domain may provide for the understanding of a broad class of phase transitions.

‘Sudden’ quantum quench and prethermalization have become a cross-cutting theme for discovering emergent states of matter1–4. Yet this remains challenging in electron matter5–9, especially superconductors10–14. The grand question of what is hidden underneath superconductivity (SC)15 appears universal, but poorly understood. Here we reveal a long-lived gapless quantum phase of prethermalized quasiparticles (QPs) after a single-cycle terahertz (THz) quench of a Nb3Sn SC gap. Its conductivity spectra is characterized by a sharp coherent peak and a vanishing scattering rate that decreases almost linearly towards zero frequency, which is most pronounced around the full depletion of the condensate and absent for a high-frequency pump. Above a critical pump threshold, such a QP phase with coherent transport and memory persists as an unusual prethermalization plateau, without relaxation to normal and SC thermal states for an order of magnitude longer than the QP recombination and thermalization times. Switching to this metastable ‘quantum QP fluid’ signals non-thermal quench of coupled SC and charge-density-wave (CDW)-like orders and hints quantum control beneath the SC.

The Higgs mechanism, i.e., spontaneous symmetry breaking of the quantum vacuum, is a cross-disciplinary principle, universal for understanding dark energy, antimatter and quantum materials, from superconductivity to magnetism. Unlike one-band superconductors (SCs), a conceptually distinct Higgs amplitude mode can arise in multi-band, unconventional superconductors  via strong interband Coulomb interaction, but is yet to be accessed. Here we discover such hybrid Higgs mode and demonstrate its quantum control by light in iron-based high-temperature SCs. Using terahertz (THz) two-pulse coherent spectroscopy, we observe a tunable amplitude mode coherent oscillation of the complex order parameter from coupled lower and upper bands. The nonlinear dependence of the hybrid Higgs mode on the THz driving fields is distinct from any known SC results: we observe a large reversible modulation of resonance strength, yet with a persisting mode frequency. Together with quantum kinetic modeling of a hybrid Higgs mechanism, distinct from charge-density fluctuations and without invoking phonons or disorder, our result provides compelling evidence for a light-controlled coupling between the electron and hole amplitude modes assisted by strong interband quantum entanglement. Such light-control of Higgs hybridization can be extended to probe many-body entanglement and hidden symmetries in other complex systems. A collective excitation called Higgs mode may arise in multi-band superconductors via strong interband interaction, but it is yet to be accessed. Here, the authors observe a tunable coherent amplitude oscillation of the order parameter in Ba(Fe 1− x Co x ) 2 As 2 , suggesting appearance and control of the Higgs mode by light tuning interband interaction.

Topology-protected surface transport of ultimate thinness in three-dimensional topological insulators (TIs) is breaking new ground in quantum science and technology. Yet a challenge remains on how to disentangle and selectively control surface helical spin transport from the bulk contribution. Here we use the mid-infrared and terahertz (THz) photoexcitation of exclusive intraband transitions to enable ultrafast manipulation of surface THz conductivity in Bi 2 Se 3 . The unique, transient electronic state is characterized by frequency-dependent carrier relaxations that directly distinguish the faster surface channel than the bulk with no complication from interband excitations or need for reduced bulk doping. We determine the topological enhancement ratio between bulk and surface scattering rates, i.e., γ BS / γ SS  ~3.80 in equilibrium. The ultra-broadband, wavelength-selective pumping may be applied to emerging topological semimetals for separation and control of the protected transport connected with the Weyl nodes from other bulk bands. It remains challenging on how to selectively control terahertz conductivity at surface from the bulk contribution in topological insulators. Here, Luo et al. discover and manipulate topologically enhanced surface transport due to helical spin structure using mid-infrared and terahertz ultrafast photoexcitations.

Light-induced supercurrents chart a path forward for the electromagnetic design of emergent materials phases and collective modes for quantum engineering applications. However, controlled spatial–temporal modulation of the complex order parameter characterizing such non-equilibrium macroscopic quantum states remains elusive. Such ultrafast phase-amplitude modulation can manifest via high harmonic modes beyond those allowed by equilibrium symmetries. Here, we drive moving condensate states via subcycle dynamical symmetry breaking achieved with nonlinear oscillating terahertz photocurrents. These non-equilibrium macroscopic quantum states with broken inversion symmetry are controlled via Cooper pair acceleration by asymmetric and multi-cycle terahertz photoexcitations. The observed supercurrent-carrying states evolve during a lightwave cycle and exhibit three distinguishing features: Anderson pseudo-spin precessions forbidden by equilibrium symmetry, strong high harmonic coherent oscillations assisted by pairing and long-lived gapless superfluidity with minimal condensate quench. Lightwave tuning of persistent photocurrents can be extended for quantum control of unconventional superconductors and topological matter, with implications on quantum gate and sensing functionalities.

The coupling between superconductors and oscillation cycles of light pulses, i.e., lightwave engineering, is an emerging control concept for superconducting quantum electronics. Although progress has been made towards terahertz-driven superconductivity and supercurrents, the interactions able to drive non-equilibrium pairing are still poorly understood, partially due to the lack of measurements of high-order correlation functions. In particular, the sensing of exotic collective modes that would uniquely characterize light-driven superconducting coherence, in a way analogous to the Meissner effect, is very challenging but much needed. Here we report the discovery of parametrically driven superconductivity by light-induced order-parameter collective oscillations in iron-based superconductors. The time-periodic relative phase dynamics between the coupled electron and hole bands drives the transition to a distinct parametric superconducting state out-of-equalibrium. This light-induced emergent coherence is characterized by a unique phase–amplitude collective mode with Floquet-like sidebands at twice the Higgs frequency. We measure non-perturbative, high-order correlations of this parametrically driven superconductivity by separating the terahertz-frequency multidimensional coherent spectra into pump–probe, Higgs mode and bi-Higgs frequency sideband peaks. We find that the higher-order bi-Higgs sidebands dominate above the critical field, which indicates the breakdown of susceptibility perturbative expansion in this parametric quantum matter.Multidimensional coherent spectroscopy measurements in iron-based superconductors demonstrate how the coupling between a superconductor and strong light pulses can drive the transition into a non-equilibrium superconducting state with distinct collective modes.

Topology-protected surface transport of ultimate thinness in three-dimensional topological insulators (TIs) is breaking new ground in quantum science and technology. Yet a challenge remains on how to disentangle and selectively control surface helical spin transport from the bulk contribution. Here we use the mid-infrared and terahertz (THz) photoexcitation of exclusive intraband transitions to enable ultrafast manipulation of surface THz conductivity in Bi Se . The unique, transient electronic state is characterized by frequency-dependent carrier relaxations that directly distinguish the faster surface channel than the bulk with no complication from interband excitations or need for reduced bulk doping. We determine the topological enhancement ratio between bulk and surface scattering rates, i.e., γ /γ  ~3.80 in equilibrium. The ultra-broadband, wavelength-selective pumping may be applied to emerging topological semimetals for separation and control of the protected transport connected with the Weyl nodes from other bulk bands.