Lightwave terahertz quantum manipulation of nonequilibrium superconductor phases and their collective modes

Abstract

We present a gauge-invariant density matrix description of nonequilibrium superconductor (SC) states with spatial and temporal correlations driven by intense terahertz (THz) lightwaves. We derive superconductor Bloch-Maxwell equations of motion that extend Anderson pseudospin models to include the Cooper pair center-of-mass motion and electromagnetic propagation effects. We thus describe quantum control of dynamical phases, collective modes, quasiparticle coherence, and high nonlinearities during cycles of carrier wave oscillations, which relates to our recent experiments. Coherent photogeneration of a nonlinear supercurrent with a dc component, achieved via condensate acceleration by an effective lightwave field, dynamically breaks the equilibrium inversion symmetry. Experimental signatures include high harmonic light emission at equilibrium-symmetry-forbidden frequencies, Rabi-Higgs collective modes and quasiparticle coherence, and nonequilibrium moving condensate states tuned by few-cycle THz fields. We use such lightwaves as an oscillating accelerating force that drives strong nonlinearities and anisotropic quasiparticle populations to control and amplify different classes of collective modes, e.g., damped oscillations, persistent oscillations, and overdamped dynamics via Rabi flopping. Recent phase-coherent nonlinear spectroscopy experiments can be modeled by solving the full nonlinear quantum dynamics including self-consistent light-matter coupling.

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

“…To put the above hybrid Higgs mode findings on a rigorous footing, we calculate the THz coherent nonlinear spectra (Methods) by extending the gauge-invariant density matrix equations of motion theory of ref. 38 , as outlined in the Supplementary Note 6 . Using the results of these calculations, we propose a physical mechanism that explains the distinct differences of the Higgs mode resonance in the four-wave mixing spectra between the strong and weak interband interaction limits.…”

“…Using the results of these calculations, we propose a physical mechanism that explains the distinct differences of the Higgs mode resonance in the four-wave mixing spectra between the strong and weak interband interaction limits. For this, we calculate the APS and quantum transport nonlinearities 38 driven by two intense phase-locked THz E-field pulses for an effective 3-pocket BCS model of FeSCs 39 . This model includes both intraband and interband pairing interactions, as well as asymmetry between electron and hole pockets.…”

“…Third, the induced condensate momentum leads to a displacement of populations and coherences in momentum space by p S /2 in the equations of motion which is also neglected in the Anderson pseudo-spin model. While the linear coupling to the superconductor via the quantum transport terms dominate the driving of the Higgs modes in the perturbative excitation regime, the excitation of the hybrid Higgs mode in the non-perturbative regime is dominated by the quadratic -coupling known from the Anderson pseudo-spin model 38 .…”

“…Here, the calculated transmitted E -field is given by where E THz ( t ) is the applied THz electric field, n is the refractive index of the SC system, and is the current expressed in terms of the gauge-invariant density matrix ( 9 ). This result is obtained by solving Maxwell’s equations in a thin film geometry 38 . We then calculate the nonlinear differential transmission which is defined by Δ E = E pp ( t , τ ) − E pump ( t , τ ) − E probe ( t ) for the collinear pump–probe geometry used in the experiment.…”

Third harmonic generation from collective modes in disordered superconductors

“…A nonperturbative solution has been also recently discussed in Refs. [34,35] within either a kinetic equation or density-matrix approach in relation to the observation of second-harmonic generation in a superconductor in the presence of a finite dc component of the THz field [5,36]. As shown in details in Appendix A, the equations of motion (10) are fully equivalent to the equations of motions of the so-called Anderson pseudospins [2,21], that just represent a specific combinations of the density-matrix components.…”