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Optical drives at terahertz and mid-infrared frequencies in quantum materials are increasingly used to reveal the nonlinear dynamics of collective modes in correlated many-body systems and their interplay with electromagnetic waves. Recent experiments demonstrated several surprising optical properties of transient states induced by driving, including the appearance of photo-induced edges in the reflectivity in cuprate superconductors, observed both below and above the equilibrium transition temperature. Furthermore, in other driven materials, reflection coefficients larger than unity have been observed. In this paper we demonstrate that unusual optical properties of photoexcited systems can be understood from the perspective of a Floquet system; a system with periodically modulated system parameters originating from pump-induced oscillations of a collective mode. We present a general phenomenological model of reflectivity from Floquet materials, which takes into account parametric generation of excitation pairs. We find a universal phase diagram of drive induced features in reflectivity which evidence a competition between driving and dissipation. To illustrate our general analysis we apply our formalism to two concrete examples motivated by recent experiments: a single plasmon band, which describes Josephson plasmons in layered superconductors, and a phonon-polariton system, which describes upper and lower polaritons in materials such as insulating SiC. Finally we demonstrate that our model can be used to provide an accurate fit to results of phonon-pump - terahertz-probe experiments in the high temperature superconductor $\rm{YBa_2Cu_3O_{6.5}}$. Our model explains the appearance of a pump-induced edge, which is higher in energy than the equilibrium Josephson plasmon edge, even if the interlayer Josephson coupling is suppressed by the pump pulse., Comment: 14 pages, 6 figures

Nonlinear phononics relies on the resonant optical excitation of infrared-active lattice vibrations to coherently induce targeted structural deformations in solids. This form of dynamical crystal-structure design has been applied to control the functional properties of many interesting systems, including magneto-resistive manganites, magnetic materials, superconductors, and ferroelectrics. However, phononics has so far been restricted to protocols in which structural deformations occur locally within the optically excited volume, sometimes resulting in unwanted heating. Here, we extend nonlinear phononics to propagating polaritons, effectively separating in space the optical drive from the functional response. Mid-infrared optical pulses are used to resonantly drive an 18 THz phonon at the surface of ferroelectric LiNbO3. A time-resolved stimulated Raman scattering probe reveals that the ferroelectric polarization is reduced over the entire 50 micron depth of the sample, far beyond the ~ micron depth of the evanescent phonon field. We attribute the bulk response of the ferroelectric polarization to the excitation of a propagating 2.5 THz soft-mode phonon-polariton. For the highest excitation amplitudes, we reach a regime in which the polarization is reversed. In this this non-perturbative regime, we expect that the polariton model evolves into that of a solitonic domain wall that propagates from the surface into the materials at near the speed of light.

Non-linear interactions between collective modes play a definitive role in far out of equilibrium dynamics of strongly correlated electron systems. Understanding and utilizing these interactions is crucial to photo-control of quantum many-body states. One of the most surprising examples of strong mode coupling is the interaction between apical oxygen phonons and Josephson plasmons in bilayer YBa$_2$Cu$_3$O$_{6+x}$ superconductors. Experiments by Hu et al (2014). and Kaiser et al. (2014) showed that below Tc, photo-excitation of phonons leads to enhancement and frequency shifts of Josephson plasmon edges, while aboveTc, photo-excited phonons induce plasmon edges even when there are no discernible features in the equilibrium reflectivity spectrum. Recent experiments by Van Hoegen et al. (2019) also observed parametric generation of Josephson plasmons from photo-excited phonons both below Tc and in the pseudogap phase. In this paper we present a theoretical model of phonon-plasmon three wave interaction arising from coupling between the oxygen motion and the in-plane superfluid stiffness. Analysis of the parametric instability of plasmons based on this model gives frequencies of the most unstable plasmons that are in agreement with experimental observations. We also discuss how strong parametric excitation of Josephson plasmons can explain pump induced changes in the TeraHertz reflectivity of YBa$_2$Cu$_3$O$_{6+x}$ in the superconducting state, including frequency shifts and sharpening of Josephson plasmon edges, as well as appearance of a new peak around 2THz. An interesting feature of this model is that overdamped Josephson plasmons do not give any discernible features in reflectivity in equilibrium, but can develop plasmon edges when parametrically excited. We suggest that this mechanism explains photo-induced plasmon edges in the pseudogap phase of YBa$_2$Cu$_3$O$_{6+x}$., Comment: 21 papers, 17 figures

Strain engineering is widely used to manipulate the electronic and magnetic properties of complex materials. An attractive route to control magnetism with strain is provided by the piezomagnetic effect, whereby the staggered spin structure of an antiferromagnet is decompensated by breaking the crystal field symmetry, which induces a ferrimagnetic polarization. Piezomagnetism is especially attractive because unlike magnetostriction it couples strain and magnetization at linear order, and allows for bi-directional control suitable for memory and spintronics applications. However, its use in functional devices has so far been hindered by the slow speed and large uniaxial strains required. Here, we show that the essential features of piezomagnetism can be reproduced with optical phonons alone, which can be driven by light to large amplitudes without changing the volume and hence beyond the elastic limits of the material. We exploit nonlinear, three-phonon mixing to induce the desired crystal field distortions in the antiferromagnet CoF$_2$. Through this effect, we generate a ferrimagnetic moment of 0.2 $\mu_B$ per unit cell, nearly three orders of magnitude larger than achieved with mechanical strain., Comment: 27 pages, 12 figures

Optical pulses are routinely used to drive dynamical changes in the properties of solids. In quantum materials, many new phenomena have been discovered, including ultrafast transitions between electronic phases, switching of ferroic orders and nonequilibrium emergent behaviors such as photo-induced superconductivity. Understanding the underlying non-equilibrium physics requires detailed measurements of multiple microscopic degrees of freedom at ultrafast time resolution. Femtosecond x-rays are key to this endeavor, as they can access the dynamics of structural, electronic and magnetic degrees of freedom. Here, we cover a series of representative experimental studies in which ultrashort x-ray pulses from free electron lasers have been used, opening up new horizons for materials research., Comment: 43 pages, 6 figures, 1 box, review paper

Femtosecond optical pulses at mid-infrared frequencies have opened up the nonlinear control of lattice vibrations in solids. So far, all applications have relied on second order phonon nonlinearities, which are dominant at field strengths near 1 MVcm-1. In this regime, nonlinear phononics can transiently change the average lattice structure, and with it the functionality of a material. Here, we achieve an order-of-magnitude increase in field strength, and explore higher-order lattice nonlinearities. We drive up to five phonon harmonics of the A1 mode in LiNbO3. Phase-sensitive measurements of atomic trajectories in this regime are used to experimentally reconstruct the interatomic potential and to benchmark ab-initio calculations for this material. Tomography of the Free Energy surface by high-order nonlinear phononics will impact many aspects of materials research, including the study of classical and quantum phase transitions.

We study the response of the one-dimensional charge density wave in K0.3MoO3 to different types of excitation with femtosecond optical pulses. We compare the response to direct excitation of the lattice at mid-infrared frequencies with that to the injection of quasi-particles across the low-energy charge density wave gap and to charge transfer excitations in the near infrared. For all three cases, we observe a fluence threshold above which the amplitude-mode oscillation frequency is softened and the mode becomes increasingly damped. We show that all the data can be collapsed onto a universal curve in which the melting of the charge density wave occurs abruptly at a critical lattice excursion. These data highlight the existence of a universal stability limit for a charge density wave, reminiscent of the empirical Lindemann criterion for the stability of a crystal lattice.

The ability to manipulate ferroelectrics at ultrafast speeds has long been an elusive target for materials research. Coherently exciting the ferroelectric mode with ultrashort optical pulses holds the promise to switch the ferroelectric polarization on femtosecond timescale, two orders of magnitude faster compared to what is possible today with pulsed electric fields. Here, we report on the demonstration of ultrafast optical reversal of the ferroelectric polarization in LiNbO3. Rather than driving the ferroelectric mode directly, we couple to it indirectly by resonant excitation of an auxiliary high-frequency phonon mode with femtosecond mid-infrared pulses. Due to strong anharmonic coupling between these modes, the atoms are directionally displaced along the ferroelectric mode and the polarization is transiently reversed, as revealed by time-resolved, phase-sensitive second-harmonic generation. This reversal can be induced in both directions, a key pre-requisite for practical applications.

To date, two types of coupling between electromagnetic radiation and a crystal lattice have been identified experimentally. One is direct, for infrared (IR)-active vibrations that carry an electric dipole. The second is indirect, it occurs through intermediate excitation of the electronic system via electron-phonon coupling, as in stimulated Raman scattering. Nearly 40 years ago, proposals were made of a third path, referred to as ionic Raman scattering (IRS). It was posited that excitation of an IR-active phonon could serve as the intermediate state for a Raman scattering process relying on lattice anharmonicity as opposed to electron phonon interaction. In this paper, we report an experimental demonstration of ionic Raman scattering and show that this mechanism is relevant to optical control in solids. The key insight is that a rectified phonon field can exert a directional force onto the crystal, inducing an abrupt displacement of the atoms from the equilibrium positions that could not be achieved through excitation of an IR-active vibration alone, for which the force is oscillatory. IRS opens up a new direction for the coherent control of solids in their electronic ground state, different from approaches that rely on electronic excitations., Comment: 10 manuscript pages, 3 figures