Quantum materials are characterized by a macroscopic behavior that does not have a clear classical counterpart. Among the experimental probes capable of exploring the exotic properties of quantum materials, ultrafast laser pulses can offer a perspective that is not readily accessible with other conventional techniques. With extremely short pulses (10~100 fs), the strength of electric field is strong enough to cause nonlinear optical phenomena in which the frequency of response is different from that of the input. In this thesis, we discuss how second harmonic generation (SHG) and time and angle-resolved photoemission spectroscopy (tr-ARPES) based on high harmonic generation can offer a unique pathway toward studying quantum materials in the context of broken symmetries and nonequilibrium electronic structure, respectively. In particular, we measured the hidden magnetism buried at a topological insulator ferromagnet interface with SHG, and developed a tr-ARPES setup with 16 and 30 meV energy resolutions using 11 and tunable 24~33 eV photons, respectively. Such high photon energy laser pulses allow us to map the nonequilibrium band structure of a large number of quantum materials, as the setup is capable of probing a much wider momentum range compared to previous tr-ARPES experiments. The capability of our setup is demonstrated through the nonequilibrium band structure of ZrTe5, the quasiparticle recombination dynamics of Bi2Sr2CaCu2O8+[delta], and the dynamics of photoinduced replica bands in WSe2.;
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