Terahertz Second-Harmonic Generation from Lightwave Acceleration of Symmetry-Breaking Nonlinear Supercurrents

Magnetic parity violation and parity-time-reversal-symmetric magnets

Parity-time-reversal symmetry (PTsymmetry), a symmetry for the combined operations of space inversion (P) and time reversal (T), is a fundamental concept of physics and characterizes the functionality of materials as well asPandTsymmetries. In particular, thePT-symmetric systems can be found in the centrosymmetric crystals undergoing the parity-violating magnetic order which we call the odd-parity magnetic multipole order. While this spontaneous order leavesPTsymmetry intact, the simultaneous violation ofPandTsymmetries gives rise to various emergent responses that are qualitatively different from those allowed by the nonmagneticP-symmetry breaking or by the ferromagnetic order. In this review, we introduce candidates hosting the intriguing spontaneous order and overview the characteristic physical responses. Various off-diagonal and/or nonreciprocal responses are identified, which are closely related to the unusual electronic structures such as hidden spin-momentum locking and asymmetric band dispersion.

Extreme terahertz magnon multiplication induced by resonant magnetic pulse pairs

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.

Tracing the dynamics of superconducting order via transient terahertz third-harmonic generation

Ultrafast optical control of quantum systems is an emerging field of physics. In particular, the possibility of light-driven superconductivity has attracted much of attention. To identify nonequilibrium superconductivity, it is necessary to measure fingerprints of superconductivity on ultrafast timescales. Recently, nonlinear THz third-harmonic generation (THG) was shown to directly probe the collective degrees of freedoms of the superconducting condensate, including the Higgs mode. Here, we extend this idea to light-driven nonequilibrium states in superconducting La2-xSrxCuO4, establishing an optical pump-THz-THG drive protocol to access the transient superconducting order-parameter quench and recovering on few-picosecond timescales. We show in particular the ability of two-dimensional TH spectroscopy to disentangle the effects of optically excited quasiparticles from the pure order-parameter dynamics, which are unavoidably mixed in the pump-driven linear THz response. Benchmarking the gap dynamics to existing experiments shows the ability of driven THG spectroscopy to overcome these limitations in ordinary pump-probe protocols.

A universal route to efficient non-linear response via Thomson scattering in linear solids

Non-linear materials are cornerstones of modern optics and electronics. Strong dependence on the intrinsic properties of particular materials, however, inhibits the at-will extension of demanding non-linear effects, especially those second-order ones, to widely adopted centrosymmetric materials (for example, silicon) and technologically important burgeoning spectral domains (for example, terahertz frequencies). Here we introduce a universal route to efficient non-linear responses enabled by exciting non-linear Thomson scattering, a fundamental process in electrodynamics that was known to occur only in relativistic electrons in metamaterial composed of linear materials. Such a mechanism modulates the trajectory of charges, either intrinsically or extrinsically provided in solids, at twice the driving frequency, allowing second-harmonic generation at terahertz frequencies on crystalline silicon with extremely large non-linear susceptibility in our proof-of-concept experiments. By offering a substantially material- and frequency-independent platform, our approach opens new possibilities in the fields of on-demand non-linear optics, terahertz sources, strong field light-solid interactions and integrated photonic circuits.

Field-resolved THz-pump laser-probe measurements with CEP-unstable THz light sources

Radiation sources with a stable carrier-envelope phase (CEP) are highly demanded tools for field-resolved studies of light-matter interaction, providing access both to the amplitude and phase information of dynamical processes. At the same time, many coherent light sources, including those with outstanding power and spectral characteristics lack CEP stability, and so far could not be used for this type of research. In this work, we present a method enabling linear and non-linear phase-resolved terahertz (THz) -pump laser-probe experiments with CEP-unstable THz sources. THz CEP information for each pulse is extracted using a specially designed electro-optical detection scheme. The method correlates the extracted CEP value for each pulse with the THz-induced response in the parallel pump-probe experiment to obtain an absolute phase-resolved response after proper sorting and averaging. As a proof-of-concept, we demonstrate experimentally field-resolved THz time-domain spectroscopy with sub-cycle temporal resolution using the pulsed radiation of a CEP-unstable infrared free-electron laser (IR-FEL) operating at 13 MHz repetition rate. In spite of the long history of IR-FELs and their unique operational characteristics, no successful realization of CEP-stable operation has been demonstrated yet. Being CEP-unstable, IR-FEL radiation has so far only been used in non-coherent measurements without phase resolution. The technique demonstrated here is robust, operates easily at high-repetition rates and for short THz pulses, and enables common sequential field-resolved time-domain experiments. The implementation of such a technique at IR-FEL user end-stations will facilitate a new class of linear and non-linear experiments for studying coherent light-driven phenomena with increased signal-to-noise ratio.

Recent Development of Ultrafast Optical Characterizations for Quantum Materials

The advent of intense ultrashort optical pulses spanning a frequency range from terahertz to the visible has opened a new era in the experimental investigation and manipulation of quantum materials. The generation of strong optical field in an ultrashort time scale enables the steering of quantum materials nonadiabatically, inducing novel phenomenon or creating new phases which may not have an equilibrium counterpart. Ultrafast time-resolved optical techniques have provided rich information and played an important role in characterization of the nonequilibrium and nonlinear properties of solid systems. Here, some of the recent progress of ultrafast optical techniques and their applications to the detection and manipulation of physical properties in selected quantum materials are reviewed. Specifically, the new development in the detection of the Higgs mode and photoinduced nonequilibrium response in the study of superconductors by time-resolved terahertz spectroscopy are discussed.

Spintronic terahertz emission with manipulated polarization (STEMP)

Highly efficient generation and arbitrary manipulation of spin-polarized terahertz (THz) radiation will enable chiral lightwave driven quantum nonequilibrium state regulation, induce new electronic structures, consequently provide a powerful experimental tool for investigation of nonlinear THz optics and extreme THz science and applications. THz circular dichromic spectroscopy, ultrafast electron bunch manipulation, as well as THz imaging, sensing, and telecommunication, also need chiral THz waves. Here we review optical generation of circularly-polarized THz radiation but focus on recently emerged polarization tunable spintronic THz emission techniques, which possess many advantages of ultra-broadband, high efficiency, low cost, easy for integration and so on. We believe that chiral THz sources based on the combination of electron spin, ultrafast optical techniques and material structure engineering will accelerate the development of THz science and applications.

Petahertz charge dynamics in a correlated organic superconductor

We report an observation of stimulated emission induced by a nearly single-cycle 6 fs near infrared electric field of 10 MV/cm in an organic superconductor (κ-(h-ET)2Cu[N(CN)2]Br). The stimulated emission is...

Broadband micro-transient absorption spectroscopy enabled by improved lock-in amplification

Recent breakthroughs in material development have increased the demand for characterization methods capable of probing nanoscale features on ultrafast time scales. As the sample reduces to atomically thin levels, an extremely low-level signal limits the feasibility of many experiments. Here, we present an affordable and easy-to-implement solution to expand the maximum sensitivity of lock-in detection systems used in transient absorption spectroscopy by multiple orders of magnitude. By implementation of a tuned RC circuit to the output of an avalanche photodiode, electric pulse shaping allows for vastly improved lock-in detection. Furthermore, a carefully designed "peak detector" circuit provides additional pulse shaping benefits, resulting in even more lock-in detection signal enhancement. We demonstrate the improvement of lock-in detection with each of these schemes by performing benchmark measurements of a white-light continuum signal and micro-transient absorption spectroscopy on a few-layer transition metal dichalcogenide sample. Our results show the practicality of ultrafast pump-probe spectroscopy for many high-sensitivity experimental schemes.

Coherent control of asymmetric spintronic terahertz emission from two-dimensional hybrid metal halides

Next-generation terahertz (THz) sources demand lightweight, low-cost, defect-tolerant, and robust components with synergistic, tunable capabilities. However, a paucity of materials systems simultaneously possessing these desirable attributes and functionalities has made device realization difficult. Here we report the observation of asymmetric spintronic-THz radiation in Two-Dimensional Hybrid Metal Halides (2D-HMH) interfaced with a ferromagnetic metal, produced by ultrafast spin current under femtosecond laser excitation. The generated THz radiation exhibits an asymmetric intensity toward forward and backward emission direction whose directionality can be mutually controlled by the direction of applied magnetic field and linear polarization of the laser pulse. Our work demonstrates the capability for the coherent control of THz emission from 2D-HMHs, enabling their promising applications on the ultrafast timescale as solution-processed material candidates for future THz emitters.

Terahertz radiation has wide array of potential uses, however, finding robust and tunable sources of terahertz radiation has been challenging. Here, Cong et al demonstrate a room temperature terahertz source composed of a two-dimensional hybrid metal halide and ferromagnetic heterostructure.

A light-induced phononic symmetry switch and giant dissipationless topological photocurrent in ZrTe5

Dissipationless currents from topologically protected states are promising for disorder-tolerant electronics and quantum computation. Here, we photogenerate giant anisotropic terahertz nonlinear currents with vanishing scattering, driven by laser-induced coherent phonons of broken inversion symmetry in a centrosymmetric Dirac material ZrTe₅. Our work suggests that this phononic terahertz symmetry switching leads to formation of Weyl points, whose chirality manifests in a transverse, helicity-dependent current, orthogonal to the dynamical inversion symmetry breaking axis, via circular photogalvanic effect. The temperature-dependent topological photocurrent exhibits several distinct features: Berry curvature dominance, particle-hole reversal near conical points and chirality protection that is responsible for an exceptional ballistic transport length of ~10 μm. These results, together with first-principles modelling, indicate two pairs of Weyl points dynamically created by B_1u phonons of broken inversion symmetry. Such phononic terahertz control breaks ground for coherent manipulation of Weyl nodes and robust quantum transport without application of static electric or magnetic fields.

Non-linear Terahertz driving of plasma waves in layered cuprates

The hallmark of superconductivity is the rigidity of the quantum-mechanical phase of electrons, responsible for superfluid behavior and Meissner effect. The strength of the phase stiffness is set by the Josephson coupling, which is strongly anisotropic in layered cuprates. So far, THz light pulses have been used to achieve non-linear control of the out-of-plane Josephson plasma mode, whose frequency lies in the THz range. However, the high-energy in-plane plasma mode has been considered insensitive to THz pumping. Here, we show that THz driving of both low-frequency and high-frequency plasma waves is possible via a general two-plasmon excitation mechanism. The anisotropy of the Josephson couplings leads to markedly different thermal effects for the out-of-plane and in-plane response, linking in both cases the emergence of non-linear photonics across T_c to the superfluid stiffness. Our results show that THz light pulses represent a preferential knob to selectively drive phase excitations in unconventional superconductors.

Josephson coupling determines the superconducting phase stiffness and sets the energy scale of plasma waves. Here, the authors show that THz light can induce two-plasmon excitations of both out-of-plane and in-plane phase modes, leading however to markedly different resonant and thermal effects due to the strong anisotropy of the Josephson couplings.

Light quantum control of persisting Higgs modes in iron-based superconductors

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−xCo_x)₂As₂, suggesting appearance and control of the Higgs mode by light tuning interband interaction.

Observation of magneto-electric rectification at non-relativistic intensities

The subject of electromagnetism has often been called electrodynamics to emphasize the dominance of the electric field in dynamic light–matter interactions that take place under non-relativistic conditions. Here we show experimentally that the often neglected optical magnetic field can nevertheless play an important role in a class of optical nonlinearities driven by both the electric and magnetic components of light at modest (non-relativistic) intensities. We specifically report the observation of magneto-electric rectification, a previously unexplored nonlinearity at the molecular level which has important potential for energy conversion, ultrafast switching, nano-photonics, and nonlinear optics. Our experiments were carried out in nanocrystalline pentacene thin films possessing spatial inversion symmetry that prohibited second-order, all-electric nonlinearities but allowed magneto-electric rectification.

The role of the optical magnetic field is generally not considered at nonrelativistic light intensities. Here the authors show magneto-electric rectification, an optical nonlinear effect due to electric and magnetic field coupling, in a thin film of the organic semiconductor pentacene at non-relativistic intensities.

Nonreciprocal Terahertz Second-Harmonic Generation in Superconducting NbN under Supercurrent Injection

Giant second-harmonic generation in the terahertz (THz) frequency range is observed in a thin film of an s-wave superconductor NbN, where the time-reversal (T) and space-inversion (P) symmetries are simultaneously broken by supercurrent injection. We demonstrate that the phase of the second-harmonic signal flips when the direction of supercurrent is inverted; i.e., the signal is ascribed to the nonreciprocal response that occurs under broken P and T symmetries. The temperature dependence of the SH signal exhibits a sharp resonance, which is accounted for by the vortex motion driven by the THz electric field in an anharmonic pinning potential. The maximum conversion ratio η_{SHG} reaches ≈10^{-2} in a thin film NbN with the thickness of 25 nm after the field cooling with a very small magnetic field of ≈1  Oe, for a relatively weak incident THz electric field of 2.8  kV/cm at 0.48 THz.

Petahertz non-linear current in a centrosymmetric organic superconductor

Charge acceleration during an intense light field application to solids attracts much attention as elementary processes in high-harmonic generation and photoelectron emission. For manipulating such attosecond dynamics of charge, carrier-envelope-phase (CEP: relative phase between carrier oscillation of light field and its envelope function) control has been employed in insulators, nanometal and graphene. In superconducting materials, collective control of charge motion is expected because of its strongly coherent nature of quasi-particles. Here we report that, in a layered organic superconductor, a non-linear petahertz current driven by a single-cycle 6 femtosecond near infrared field shows up as second harmonic generation (SHG), which is in contrast to the common belief that even harmonics are forbidden in the centrosymmetric system. The SHG represents a CEP sensitive nature and an enhancement near the superconducting temperature. The result and its quantum many-body analysis indicate that a polarized current is induced by non-linear acceleration of charge, which is amplified by superconducting fluctuations. This will lead to petahertz functions of superconductors and of strongly correlated systems.

Here the authors show second harmonic generation (SHG) from a centrosymmetric organic superconductor κ-(BEDT-TTF)₂Cu[N(CN)₂]Br. They find unusual temperature dependence and CEP-sensitive nature of the SHG which are explained in terms of nonlinear current.