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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. Yet, Higgs…
We present a gauge-invariant density matrix description of non-equilibrium superconductor (SC) states with spatial and temporal correlations driven by intense terahertz (THz) lightwaves. We derive superconductor Bloch--Maxwell equations of…
Ultrafast optical control of quantum systems is an emerging field of physics. In particular, the possibility of light-driven superconductivity with ultrashort laser pulses has attracted much of attention. To identify non-equilibrium…
We present a comprehensive theory of light-controlled multi-band superconductivity and apply it to predict distinctive signatures of light-driven superconducting (SC) states in terahertz multi-dimensional coherent spectroscopy (THz-MDCS)…
We report terahertz (THz) second harmonic generation (SHG) in superconductors (SC) with inversion symmetric equilibrium states that forbid even-order nonlinearities. Such SHG signal is observed in single-pulse emission by periodic driving…
Overcoming the decoherence bottleneck remains a central challenge for advancing coherent superconducting quantum device and information technologies. Solitons -- non-dispersive wave packets stabilized by the collective synchronization of…
Higgs spectroscopy is a new field in which Higgs modes in nonequilibrium superconductors are analyzed to gain information about the ground state. One experimental setup in which the Higgs mode in s-wave superconductors was observed is…
2H-NbSe2 is an archetypal system in which superconductivity and charge-density-wave (CDW) coexist and compete macroscopically with each other. In particular, this interplay also manifests in their dynamical fluctuations. As a result, the…
The study of interaction between different degrees of freedom in solids is of fundamental importance to understand the functionalities of materials. One striking example of such interaction is the intertwined coupling or competition between…
Terahertz two-dimensional coherent spectroscopy (THz-2DCS) is transforming our ability to probe, visualize, and control quantum materials far from equilibrium. This emerging technique brings multi-dimensional resolution to the ultrafast…
Motivated by the recent development of terahertz pump-probe experiments, we investigate the short-time dynamics in superconductors with multiple attractive pairing channels. Studying a single-band square lattice model with spin-spin…
Lifshitz invariant is a symmetry invariant composed of multiple order parameters that contain a single spatial derivative in a Ginzburg-Landau (GL) free energy, which may induce a nonuniform configuration of the order parameters. In…
Unconventional superconductors have been long sought for their potential applications in quantum technologies and devices. A key challenge impeding this effort is the difficulty associated with probing and characterizing candidate materials…
Driving superconductors out of equilibrium is a promising avenue to study their equilibrium properties as well as to control the superconducting state. Non-equilibrium superconductors are often studied using time resolved optical…
We show that the amplitude, or Higgs mode of a superconductor with strong spin-orbit coupling and an exchange field, couples linearly to the electromagnetic field. Furthermore, by coupling such a superconductor to an LC resonator, we…
Superconductivity (SC) in so-called "unconventional superconductors" is nearly always found in the vicinity of another ordered state, such as antiferromagnetism, charge density wave (CDW), or stripe order. This suggests a fundamental…
Coherent control of quantum materials has progressed along two major fronts: nonlinear phononics, which reshapes lattices to induce emergent states, and Floquet engineering, which tailors electronic band reconstruction via time-periodic…
As pointed out by Nambu&Goldstone, continuous symmetry breaking gives rise to gapless bosonic excitation. In superconductors, continuous local U(1) gauge symmetry is broken. The gapless excitation thus created is the collective phase mode…
Development of ultrafast lasers and non-linear optical techniques over the last two decades provides tools to access real-time dynamics of low energy excitations in superconductors. For example, time-resolved THz spectroscopy and time- and…
We report a fully self-consistent calculation of the complex renormalization by exchange interactions and hence the complete phase diagram of conventional $s$-wave superconductors with magnetic impurities as well as the related physical…