Fig. 1. Application of terahertz spectroscopy in the research of quantum materials

Fig. 2. Terahertz ultrafast spectroscopy and its study in high temperature superconductors

Fig. 3. Schematic of THz-TDS experimental setup

Fig. 4. Schematic of TES experimental setup

Fig. 5. Schematic of OPTP experimental setup

Fig. 6. Measurement of terahertz conductivity in YBCO superconductors. (a) Terahertz complex conductivity of YBa₂Cu₃O_7-δ^[97]; (b) terahertz complex conductivity of YBa₂Cu₃O_7-δ as a function of temperature, where the circles represent real part of complex conductivity, and the black dots represent imaginary part of complex conductivity^[97]; (c) real part of terahertz conductivity of optimally doped YBa₂Cu₃O_6.95 and underdoped YBa₂Cu₃O_6.60 at room temperature (295 K), near the Tc (70 K), and below the Tc (10 K), and the inset shows frequency dependent scattering rate^[98]

Fig. 7. Terahertz optical properties of magnesium diboride (MgB₂) superconductor^[99]. (a) Real part σ1 and imaginary part σ2 of complex conductivity for MgB₂ at 45 K; (b) temperature dependent surface resistance of MgB₂ under different terahertz frequencies, where solid line represents temperature dependent resistance of copper under different terahertz frequencies

Fig. 8. Error analysis of terahertz conductivity of Tl₂Ba₂CaCu₂O_8+x thin film^[100]. (a) Real part σRe and (b) imaginary part σIm of terahertz conductivity based on THz-TDS data of Tl₂Ba₂CaCu₂O_8+x thin films at different temperatures; frequency dependence of (c) real part σRe and (d) imaginary part σIm at different temperatures after thickness error correction

Fig. 9. Terahertz conductivity of La_2-xSr_xCuO₄ (x=0.16) thin film with Tc=41 K^[101]. (a) Real part σRe(ω) and (b) imaginary part σIm(ω) of terahertz conductivity at different temperatures; (c) real part σRe and (d) imaginary part σIm of temperature dependent terahertz conductivity under different frequencies

Fig. 10. Photoinduced quasiparticle dynamics. (a) Superconducting gap dynamics of NbN extracted from σ1, and the illustration shows temperature dependent variation of terahertz transmittance^[102]; (b) photoinduced transient terahertz conductivity of Bi₂Sr₂CaCu₂O_8+δ with pump fluence of 0.7 μJ/cm2 and temperature of 6 K, where blue circle on the left and red circle on the right represent frequency dependence of real part ∆σ1 and imaginary part ∆σ2 of transient terahertz conductivity at different time delays t respectively, the illustration shows the relationship between photoinduced transient terahertz conductivity and pump probe delayt, the photon energy at the center frequency of terahertz probe pulse is 5.5 meV^[103]; (c) schematic diagram of photoinduced quasiparticles relax to Cooper pairs^[56]

Fig. 11. TPTP spectral measurement results of NbN^[104]. (a) Temporal evolution of ∆Eprobe(t) at 4 K for various terahertz pump intensities; (b) real part σ1 and (c) imaginary part σ2of terahertz conductivity at about 20 ps after excitation of terahertz pump, where dotted line is real part of terahertz conductivity in the normal metal state (16 K)

Fig. 12. TPTP spectral measurement results of La_1.84Sr_0.16CuO₄^[105]. (a) Real and imaginary parts of terahertz conductivity of La_1.84Sr_0.16CuO₄ measured along c-axis as functions of pump‒probe time delay and frequency; (b) real and imaginary parts of terahertz conductivity of La_1.84Sr_0.16CuO₄ measured along a-b-plane as functions of pump‒probe time delay and frequency; (c) real and imaginary parts of terahertz conductivity measured along c-axis as functions of frequency at 1.25 ps and 1.55 ps, respectively

Fig. 13. Higgs mode detection in Bi₂Sr₂CaCu₂O_8+x^[109]. (a) Terahertz pulse-induced transient reflectivity change ΔR/R as a function of delay time at different temperatures with probe polarization angle θprobe= 0° (OP90 denotes optimally doping and Tc=90 K, the top red line shows the waveform of squared terahertz pump pulse field); (b) peak of ΔR/Ras a function of probe polarization angle θprobe at different temperatures with terahertz pump polarization angle θpump=0° (circles denote raw data and lines denote fitting curves); (c) A1g and B1g components of ΔR/R as functions of delay time at 10 K; (d) A1g decaying component, A1g terahertz Kerr component, and B1g terahertz Kerr component as functions of temperature

Fig. 14. Non-equilibrium optical response of YBa₂Cu₃O_6.55 for near-infrared pump excitation under normal conditions^[113]. (a) Pump‒probe relaxation process of the system; (b)(c) changes in terahertz electric field reflected by samples with different delay time after pumping in both time- and frequency-domains; (d)‒(f) non-equilibrium optical properties under different delay time

Fig. 15. Transient terahertz conductivity of photoexcited FeSe_0.5Te_0.5 below Tc^[60]. (a)(b) Real part and imaginary part of time evolution of pump-induced terahertz conductivity; (c)(d) transient terahertz conductivities at 1.4 ps and corresponding imaginary part of terahertz conductivity

Fig. 16. TES of YBCO superconductors. (a) Typical waveforms of terahertz emission from YBCO thin film dipole antennas, and the inset shows Fourier transformed spectra of terahertz pulse^[118]; (b) terahertz emission waveform from YBCO with different carrier concentrations^[119]

Fig. 17. TES of La_2-xSr_xCuO₄ and La_2-xBa_xCuO₄^[120]. (a)‒(d) Phase diagrams of La_2-xSr_xCuO₄ and La_2-xBa_xCuO₄ under different doping concentrations; (e)‒(h) terahertz time-domain signals of doped samples selected from Fig. 17(a)‒(d) at different temperatures