Coherent Two-Dimensional Terahertz Magnetic Resonance Spectroscopy of Collective Spin Waves

Canted spin order as a platform for ultrafast conversion of magnons

Traditionally, magnetic solids are divided into two main classes-ferromagnets and antiferromagnets with parallel and antiparallel spin orders, respectively. Although normally the antiferromagnets have zero magnetization, in some of them an additional antisymmetric spin-spin interaction arises owing to a strong spin-orbit coupling and results in canting of the spins, thereby producing net magnetization. The canted antiferromagnets combine antiferromagnetic order with phenomena typical of ferromagnets and hold great potential for spintronics and magnonics1-5. In this way, they can be identified as closely related to the recently proposed new class of magnetic materials called altermagnets6-9. Altermagnets are predicted to have strong magneto-optical effects, terahertz-frequency spin dynamics and degeneracy lifting for chiral spin waves10 (that is, all of the effects present in the canted antiferromagnets11,12). Here, by utilizing these unique phenomena, we demonstrate a new functionality of canted spin order for magnonics and show that it facilitates mechanisms converting a magnon at the centre of the Brillouin zone into propagating magnons using nonlinear magnon-magnon interactions activated by an ultrafast laser pulse. Our experimental findings supported by theoretical analysis show that the mechanism is enabled by the spin canting.

Re-order parameter of interacting thermodynamic magnets

Phase diagrams of materials are typically based on a static order parameter, but it faces challenges when distinguishing subtle phase changes, such as re-ordering. Here, we report a dynamic nonequilibrium order parameter termed re-order parameter to determine subtle phases and their transitions in interacting magnets. The dynamical precession of magnetization, so-called magnon, premises as a reliable re-order parameter of strong spin-orbit coupled magnets. We employ orthoferrites YFeO3 and its Mn-doped variations, where diverse magnetic phases, including canted antiferromagnetic (Γ4) and collinear antiferromagnetic (Γ1) states, have been well-established. Low-energy magnon uncovers the spin-orbit coupling-induced subtle magnetic structures, resulting in distinct terahertz emissions. The temporal and spectral parameters of magnon emission exhibit characteristics akin to BCS-type order parameters, constructing the magnetic phase diagram of Mn-doped YFeO3. This approach further reveals a concealed ferrimagnetic phase within the Γ1 state, underscoring its potential to search for hidden phases of materials, completing their phase diagrams.

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.

Capturing Coherent Magnons by Tip-Assisted Terahertz Spectroscopy

Our study highlights the versatility of tip-assisted terahertz spectroscopy in probing coherent magnons, the elementary quanta of spin waves in magnetic materials. We identify two distinct coherent magnon types in canted antiferromagnet YFeO3. The remarkable consistency with far-field terahertz spectroscopy in crucial magnon parameters, such as coherence time and resonance frequency, firmly establishes the credibility of tip-assisted terahertz spectroscopy. Notably, we capture more coherent ferromagnetic magnons near the sample surface, underscoring the strength of the technique. This approach paves the way for local, free-standing, and real-space investigations of spin waves in solid magnets.

Signatures of Fractional Statistics in Nonlinear Pump-Probe Spectroscopy

We show that the presence of anyons in the excitation spectrum of a two-dimensional system can be inferred from nonlinear spectroscopic quantities. In particular, we consider pump-probe spectroscopy, where a sample is irradiated by two light pulses with an adjustable time delay between them. The relevant response coefficient exhibits a universal form that originates from the statistical phase acquired when anyons created by the first pulse braid around those created by the second. This behavior is shown to be qualitatively unchanged by nonuniversal physics including nonstatistical interactions and small nonzero temperatures. In magnetic systems, the signal of interest can be measured using currently available terahertz-domain probes, highlighting the potential usefulness of nonlinear spectroscopic techniques in the search for quantum spin liquids.

Finite-Temperature Hole-Magnon Dynamics in an Antiferromagnet

Employing the numerically accurate multiple Davydov Ansatz in combination with the thermo-field dynamics approach, we delve into the interplay of the finite-temperature dynamics of holes and magnons in an antiferromagnet, which allows for scrutinizing previous predictions from the self-consistent Born approximation while offering, for the first time, accurate finite-temperature computation of detailed magnon dynamics as a response and a facilitator to the hole motion. The study also uncovers a pronounced temperature dependence of the magnon and hole populations, pointing to the feasibility of potential thermal manipulation and control of hole dynamics. Our methodology can be applied not only to the calculation of steady-state angular-resolved photoemission spectra but also to the simulation of femtosecond terahertz pump-probe and other nonlinear signals for the characterization of antiferromagnetic materials.

Accelerating Quantum Materials Development with Advances in Transmission Electron Microscopy

Quantum materials are driving a technology revolution in sensing, communication, and computing, while simultaneously testing many core theories of the past century. Materials such as topological insulators, complex oxides, superconductors, quantum dots, color center-hosting semiconductors, and other types of strongly correlated materials can exhibit exotic properties such as edge conductivity, multiferroicity, magnetoresistance, superconductivity, single photon emission, and optical-spin locking. These emergent properties arise and depend strongly on the material's detailed atomic-scale structure, including atomic defects, dopants, and lattice stacking. In this review, we describe how progress in the field of electron microscopy (EM), including in situ and in operando EM, can accelerate advances in quantum materials and quantum excitations. We begin by describing fundamental EM principles and operation modes. We then discuss various EM methods such as (i) EM spectroscopies, including electron energy loss spectroscopy (EELS), cathodoluminescence (CL), and electron energy gain spectroscopy (EEGS); (ii) four-dimensional scanning transmission electron microscopy (4D-STEM); (iii) dynamic and ultrafast EM (UEM); (iv) complementary ultrafast spectroscopies (UED, XFEL); and (v) atomic electron tomography (AET). We describe how these methods could inform structure-function relations in quantum materials down to the picometer scale and femtosecond time resolution, and how they enable precision positioning of atomic defects and high-resolution manipulation of quantum materials. For each method, we also describe existing limitations to solve open quantum mechanical questions, and how they might be addressed to accelerate progress. Among numerous notable results, our review highlights how EM is enabling identification of the 3D structure of quantum defects; measuring reversible and metastable dynamics of quantum excitations; mapping exciton states and single photon emission; measuring nanoscale thermal transport and coupled excitation dynamics; and measuring the internal electric field and charge density distribution of quantum heterointerfaces- all at the quantum materials' intrinsic atomic and near atomic-length scale. We conclude by describing open challenges for the future, including achieving stable sample holders for ultralow temperature (below 10K) atomic-scale spatial resolution, stable spectrometers that enable meV energy resolution, and high-resolution, dynamic mapping of magnetic and spin fields. With atomic manipulation and ultrafast characterization enabled by EM, quantum materials will be poised to integrate into many of the sustainable and energy-efficient technologies needed for the 21st century.

Revealing the frequency-dependent oscillations in the nonlinear terahertz response induced by the Josephson current

Nonlinear responses of superconductors to intense terahertz radiation has been an active research frontier. Using terahertz pump-terahertz probe spectroscopy, we investigate the c-axis nonlinear optical response of a high-temperature superconducting cuprate. After excitation by a single-cycle terahertz pump pulse, the reflectivity of the probe pulse oscillates as the pump-probe delay is varied. Interestingly, the oscillatory central frequency scales linearly with the probe frequency, a fact widely overlooked in pump-probe experiments. By theoretically solving the nonlinear optical reflection problem on the interface, we show that our observation is well explained by the Josephson-type third-order nonlinear electrodynamics, together with the emission coefficient from inside the material into free space. The latter results in a strong enhancement of the emitted signal whose physical frequency is around the Josephson plasma edge. Our result offers a benchmark for and new insights into strong-field terahertz spectroscopy of related quantum materials.

Terahertz Néel spin-orbit torques drive nonlinear magnon dynamics in antiferromagnetic Mn2Au

Antiferromagnets have large potential for ultrafast coherent switching of magnetic order with minimum heat dissipation. In materials such as Mn2Au and CuMnAs, electric rather than magnetic fields may control antiferromagnetic order by Néel spin-orbit torques (NSOTs). However, these torques have not yet been observed on ultrafast time scales. Here, we excite Mn2Au thin films with phase-locked single-cycle terahertz electromagnetic pulses and monitor the spin response with femtosecond magneto-optic probes. We observe signals whose symmetry, dynamics, terahertz-field scaling and dependence on sample structure are fully consistent with a uniform in-plane antiferromagnetic magnon driven by field-like terahertz NSOTs with a torkance of (150 ± 50) cm2 A-1 s-1. At incident terahertz electric fields above 500 kV cm-1, we find pronounced nonlinear dynamics with massive Néel-vector deflections by as much as 30°. Our data are in excellent agreement with a micromagnetic model. It indicates that fully coherent Néel-vector switching by 90° within 1 ps is within close reach.

Empowering Control of Antiferromagnets by THz-Induced Spin Coherence

Finding efficient and ultrafast ways to control antiferromagnets is believed to be instrumental in unlocking their potential for magnetic devices operating at THz frequencies. Still, it is challenged by the absence of net magnetization in the ground state. Here, we show that the magnetization emerging from a state of coherent spin precession in antiferromagnetic iron borate FeBO_{3} can be used to enable the nonlinear coupling of light to another, otherwise weakly susceptible, mode of spin precession. This nonlinear mechanism can facilitate conceptually new ways of controlling antiferromagnetism.

Generation of third-harmonic spin oscillation from strong spin precession induced by terahertz magnetic near fields

The ability to drive a spin system to state far from the equilibrium is indispensable for investigating spin structures of antiferromagnets and their functional nonlinearities for spintronics. While optical methods have been considered for spin excitation, terahertz (THz) pulses appear to be a more convenient means of direct spin excitation without requiring coupling between spins and orbitals or phonons. However, room-temperature responses are usually limited to small deviations from the equilibrium state because of the relatively weak THz magnetic fields in common approaches. Here, we studied the magnetization dynamics in a HoFeO₃ crystal at room temperature. A custom-made spiral-shaped microstructure was used to locally generate a strong multicycle THz magnetic near field perpendicular to the crystal surface; the maximum magnetic field amplitude of about 2 T was achieved. The observed time-resolved change in the Faraday ellipticity clearly showed second- and third-order harmonics of the magnetization oscillation and an asymmetric oscillation behaviour. Not only the ferromagnetic vector M but also the antiferromagnetic vector L plays an important role in the nonlinear dynamics of spin systems far from equilibrium.

Large Photogalvanic Spin Current by Magnetic Resonance in Bilayer Cr Trihalides

Spin current is a key to realizing various phenomena and functionalities related to spintronics. Recently, the possibility of generating spin current through a photogalvanic effect of magnons was pointed out theoretically. However, neither a candidate material nor a general formula for calculating the photogalvanic spin current in materials is known so far. In this Letter, we develop a general formula for the photogalvanic spin current through a magnetic resonance process. This mechanism involves a one-magnon excitation process in contrast to the two-particle processes studied in earlier works. Using the formula, we show that GHz and THz waves create a large photogalvanic spin current in the antiferromagnetic phase of bilayer CrI_{3} and CrBr_{3}. The large spin current arises from an optical process involving two magnon bands, which is a contribution unknown to date. This spin current appears only in the antiferromagnetic ordered phase and is reversible by controlling the order parameter. These results open a route to material design for the photogalvanic effect of magnetic excitations.

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.

Quench-drive spectroscopy of cuprates

Cuprates are d-wave superconductors which exhibit a rich phase diagram: they are characterized by superconducting fluctuations even above the critical temperature, and thermal disorder can reduce or suppress the phase...

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.

Enabling high-power, broadband THz generation with 800-nm pump wavelength

The organic terahertz (THz) generation crystal BNA has recently gained traction as a source for producing broadband THz pulses. When pumped with 100 fs pulses, the thin BNA crystals can produce relatively high electric fields with frequency components out to 5 THz. However, the THz output with 800-nm pump wavelength is limited by the damage threshold of the material, particularly when using a 1 kHz or higher repetition rate laser. Here, we report that the damage threshold of BNA THz generation crystals can be significantly improved by bonding BNA to a high-thermal conductivity sapphire window. When pumped with 800-nm light from an amplified Ti:sapphire laser system, this higher damage threshold enables generation of 2.5× higher electric field strengths compared to bare BNA crystals. We characterize the average damage threshold for bare BNA and BNA-sapphire, measure peak-to-peak electric field strengths and THz waveforms, and determine the nonlinear transmission in BNA. Pumping BNA bonded to sapphire with 3 mJ 800-nm pulses results in peak-to-peak electric fields exceeding 1 MV/cm, with broadband frequency components >3 THz. This high-field, broadband THz source is a promising alternative to tilted pulse front LiNbO₃ THz sources, enabling many research groups without optical parametric amplifiers to perform high-field, broadband THz spectroscopy.

Nonlinear rotational spectroscopy reveals many-body interactions in water molecules

Because of their central importance in chemistry and biology, water molecules have been the subject of decades of intense spectroscopic investigations. Rotational spectroscopy of water vapor has yielded detailed information about the structure and dynamics of isolated water molecules, as well as water dimers and clusters. Nonlinear rotational spectroscopy in the terahertz regime has been developed recently to investigate the rotational dynamics of linear and symmetric-top molecules whose rotational energy levels are regularly spaced. However, it has not been applied to water or other lower-symmetry molecules with irregularly spaced levels. We report the use of recently developed two-dimensional (2D) terahertz rotational spectroscopy to observe high-order rotational coherences and correlations between rotational transitions that were previously unobservable. The results include two-quantum (2Q) peaks at frequencies that are shifted slightly from the sums of distinct rotational transitions on two different molecules. These results directly reveal the presence of previously unseen metastable water complexes with lifetimes of 100 ps or longer. Several such peaks observed at distinct 2Q frequencies indicate that the complexes have multiple preferred bimolecular geometries. Our results demonstrate the sensitivity of rotational correlations measured in 2D terahertz spectroscopy to molecular interactions and complexation in the gas phase.

Hydrodynamic nonlinear response of interacting integrable systems

We develop a formalism for computing the nonlinear response of interacting integrable systems. Our results are asymptotically exact in the hydrodynamic limit where perturbing fields vary sufficiently slowly in space and time. We show that spatially resolved nonlinear response distinguishes interacting integrable systems from noninteracting ones, exemplifying this for the Lieb-Liniger gas. We give a prescription for computing finite-temperature Drude weights of arbitrary order, which is in excellent agreement with numerical evaluation of the third-order response of the XXZ spin chain. We identify intrinsically nonperturbative regimes of the nonlinear response of integrable systems.

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.

Theory of Two-Dimensional Nonlinear Spectroscopy for the Kitaev Spin Liquid

Unambiguous identification of fractionalized excitations in quantum spin liquids has been a long-standing issue in correlated topological phases. Conventional spectroscopic probes, such as the dynamical spin structure factor, can only detect composites of fractionalized excitations, leading to a broad continuum in energy. Lacking a clear signature in conventional probes has been the biggest obstacle in the field. In this work, we theoretically investigate what kinds of distinctive signatures of fractionalized excitations can be probed in two-dimensional nonlinear spectroscopy by considering the exactly solvable Kitaev spin liquids. We demonstrate the existence of a number of salient features of the Majorana fermions and fluxes in two-dimensional nonlinear spectroscopy, which provide crucial information about such excitations.

Nonlinear Magnetization Dynamics Driven by Strong Terahertz Fields

We present a comprehensive experimental and numerical study of magnetization dynamics in a thin metallic film triggered by single-cycle terahertz pulses of ∼20  MV/m electric field amplitude and ∼1  ps duration. The experimental dynamics is probed using the femtosecond magneto-optical Kerr effect, and it is reproduced numerically using macrospin simulations. The magnetization dynamics can be decomposed in three distinct processes: a coherent precession of the magnetization around the terahertz magnetic field, an ultrafast demagnetization that suddenly changes the anisotropy of the film, and a uniform precession around the equilibrium effective field that is relaxed on the nanosecond time scale, consistent with a Gilbert damping process. Macrospin simulations quantitatively reproduce the observed dynamics, and allow us to predict that novel nonlinear magnetization dynamics regimes can be attained with existing tabletop terahertz sources.

Direct space to time terahertz pulse shaping with nonlinear metasurfaces

We present a method for the generation of THz pulses with tailored temporal shape from nonlinear metasurfaces. The method is based on single-cycle THz emission by the metasurface inclusions. We show that the spatial amplitude and phase structure of the nonlinear response is mapped to the temporal shape of pulses emitted at certain angles. We specifically show a method for reconstruction of desired pulses, generation of few-cycles pulses with tailored carrier-envelope and all-optical control over the pulse shape by the pump pulse characteristics.

Resolving Continua of Fractional Excitations by Spinon Echo in THz 2D Coherent Spectroscopy

We show that the new technique of terahertz 2D coherent spectroscopy is capable of giving qualitatively new information about fractionalized spin systems. For the prototypical example of the transverse field Ising chain, we demonstrate theoretically that, despite the broad continuum of excitations in linear response, the 2D spectrum contains sharp features that are a coherent signature of a "spinon echo," which gives previously inaccessible information such as the lifetime of the two-spinon excited state. The effects of disorder and finite lifetime, which are practically indistinguishable in the linear optical or neutron response, manifest in dramatically different fashion in the 2D spectra. Our results may be directly applicable to model quasi-1D transverse field Ising chain systems such as CoNb_{2}O_{6}, but the concept can be applied to fractionalized spin systems in general.

2D THz spectroscopic investigation of ballistic conduction-band electron dynamics in InSb

Using reflective cross-polarized 2D THz time-domain spectroscopy in the range of 1-12 THz, we follow the trajectory of the out-of-equilibrium electron population in the low-bandgap semiconductor InSb. The 2D THz spectra show a set of distinct features at combinations of the plasma-edge and vibration frequencies. Using finite difference time domain simulations combined with a tight binding model of the band structure, we assign these features to electronic nonlinearities and show that the nonlinear response in the first picoseconds is dominated by coherent ballistic motion of the electrons. We demonstrate that this technique can be used to investigate the landscape of the band curvature near the Γ-point, as illustrated by the observation of anisotropy in the (100)-plane.

Distinguishing Nonlinear Terahertz Excitation Pathways with Two-Dimensional Spectroscopy

High-field terahertz (THz) spectroscopy is enabling the ultrafast study and control of matter in new and exciting ways. However, when intense electromagnetic pulses are used in any kind of pump-probe spectroscopy, several nonlinear excitation pathways can result, leading to scenarios that required the development of multidimensional spectroscopies to illuminate the observed dynamics. Here we demonstrate a clear example where two-dimensional (2D) THz vibrational spectroscopy is needed to distinguish between nonlinear-excitation pathways in CdWO_{4}. We nonlinearly excite a set of Raman-active vibrational modes in CdWO_{4} with broadband THz pulses, and 2D spectroscopy allows us to determine the dominant excitation pathway. We provide a general framework for 2D THz and multi-THz nonlinear phonon spectroscopy in solid systems, which has important implications in contributing needed clarity to the nascent field of nonlinear phononics.

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.

Efficient terahertz generation in highly nonlinear organic crystal HMB-TMS

We report on generation of strong and broadband terahertz (THz) pulses via collinearly phase-matched optical rectification of near-infrared femtosecond pulses in the organic nonlinear optical HMB-TMS (2-(4-hydroxy-3-methoxystyryl)-3-methylbenzo[d]thiazol-3-ium 2,4,6-trimethylbenzenesulfonate) single crystals which exhibit optimal molecular orientation and large macroscopic optical nonlinearity for efficient THz wave generation. Single-cycle THz pulses with a peak electric field strength of 0.66 MV/cm and a bandwidth from 0.1 to 5.4 THz are achieved from an HMB-TMS crystal with only a 2-mm clear aperture pumped by 1350 nm pulses at moderate fluences. The generated THz energy is about 1 µJ and the corresponding pump-to-THz energy conversion efficiency reaches 0.23%.

Observation of Dicke cooperativity in magnetic interactions

The interaction ofNtwo-level atoms with a single-mode light field is an extensively studied many-body problem in quantum optics, first analyzed by Dicke in the context of superradiance. A characteristic of such systems is the cooperative enhancement of the coupling strength by a factor of N. In this study, we extended this cooperatively enhanced coupling to a solid-state system, demonstrating that it also occurs in a magnetic solid in the form of matter-matter interaction. Specifically, the exchange interaction ofNparamagnetic erbium(III) (Er3+) spins with an iron(III) (Fe3+) magnon field in erbium orthoferrite (ErFeO3) exhibits a vacuum Rabi splitting whose magnitude is proportional to N. Our results provide a route for understanding, controlling, and predicting novel phases of condensed matter using concepts and tools available in quantum optics.

Macroscopic Magnetization Control by Symmetry Breaking of Photoinduced Spin Reorientation with Intense Terahertz Magnetic Near Field

We exploit an intense terahertz magnetic near field combined with femtosecond laser excitation to break the symmetry of photoinduced spin reorientation paths in ErFeO_{3}. We succeed in aligning macroscopic magnetization reaching up to 80% of total magnetization in the sample to selectable orientations by adjusting the time delay between terahertz and optical pump pulses. The spin dynamics are well reproduced by equations of motion, including time-dependent magnetic potential. We show that the direction of the generated magnetization is determined by the transient direction of spin tilting and the magnetic field at the moment of photoexcitation.

Recent advances in multidimensional ultrafast spectroscopy

Multidimensional ultrafast spectroscopies are one of the premier tools to investigate condensed phase dynamics of biological, chemical and functional nanomaterial systems. As they reach maturity, the variety of frequency domains that can be explored has vastly increased, with experimental techniques capable of correlating excitation and emission frequencies from the terahertz through to the ultraviolet. Some of the most recent innovations also include extreme cross-peak spectroscopies that directly correlate the dynamics of electronic and vibrational states. This review article summarizes the key technological advances that have permitted these recent advances, and the insights gained from new multidimensional spectroscopic probes.

Rapid and precise determination of zero-field splittings by terahertz time-domain electron paramagnetic resonance spectroscopy

Zero-field splitting (ZFS) parameters are fundamentally tied to the geometries of metal ion complexes. Despite their critical importance for understanding the magnetism and spectroscopy of metal complexes, they are not routinely available through general laboratory-based techniques, and are often inferred from magnetism data. Here we demonstrate a simple tabletop experimental approach that enables direct and reliable determination of ZFS parameters in the terahertz (THz) regime. We report time-domain measurements of electron paramagnetic resonance (EPR) signals associated with THz-frequency ZFSs in molecular complexes containing high-spin transition-metal ions. We measure the temporal profiles of the free-induction decays of spin resonances in the complexes at zero and nonzero external magnetic fields, and we derive the EPR spectra via numerical Fourier transformation of the time-domain signals. In most cases, absolute values of the ZFS parameters are extracted from the measured zero-field EPR frequencies, and the signs can be determined by zero-field measurements at two different temperatures. Field-dependent EPR measurements further allow refined determination of the ZFS parameters and access to the g-factor. The results show good agreement with those obtained by other methods. The simplicity of the method portends wide applicability in chemistry, biology and material science.

2D THz-THz-Raman Photon-Echo Spectroscopy of Molecular Vibrations in Liquid Bromoform

Fundamental properties of molecular liquids are governed by long-range interactions that most prominently manifest at terahertz (THz) frequencies. Here we report the detection of nonlinear THz photon-echo (rephasing) signals in liquid bromoform using THz-THz-Raman spectroscopy. Together, the many observed signatures span frequencies from 0.5 to 8.5 THz and result from couplings between thermally populated ladders of vibrational states. The strongest peaks in the spectrum are found to be multiquantum dipole and 1-quantum polarizability transitions and may arise from nonlinearities in the intramolecular dipole moment surface driven by intermolecular interactions.

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

Two-dimensional spectroscopy is performed on a terahertz (THz) frequency quantum cascade laser (QCL) with two broadband THz pulses. Gain switching is used to amplify the first THz pulse and the second THz pulse is used to probe the system. Fourier transforms are taken with respect to the delay time between the two THz pulses and the sampling time of the THz probe pulse. The two-dimensional spectrum consists of three peaks at (ω_τ = 0, ω_t = ω₀), (ω_τ = ω₀, ω_t = ω₀), and (ω_τ = 2ω₀, ω_t = ω₀) where ω₀ denotes the lasing frequency. The peak at ω_τ = 0 represents the response of the probe to the zero-frequency (rectified) component of the instantaneous intensity and can be used to measure the gain recovery.