In the past decade, photo-induced superconducting-like behaviors have been reported in a number of materials driven by intense pump fields. Of particular interest is the high-Tc cuprate YBCO, where such effect has been reported up to the so-called pseudogap temperature T* 300-400 K. In a recent experiment, a transient magnetic field which is proportional to and in the same direction of an applied field has been observed outside the sample, suggestive of flux exclusion due to the Meissner effect. In this paper, we present an alternative interpretation of these experiments based on a mechanism that we term the flux-Floquet instability of the sine-Gordon (SG) model. We take as our premise the model of preformed Cooper pairs in the pseudogap phase. Starting from the local superconducting order parameter in equilibrium, we introduce an extended SG model to describe the dynamics of the relative phase between the layers of a bilayer. We demonstrate that a combination of external magnetic field and strong terahertz drive used in experiments by Fava et al. results in a novel Floquet instability in the model. This instability leads to currents at the edges of the bilayer formed by defects or grain boundaries, with the current flowing in the opposite direction of the equilibrium screening current, producing a giant paramagnetic magnetization in the same direction as the applied field. We show how this scenario can fit most of the available data. To the extent that this model can account for the data, we conclude that the experiments have the important consequence of revealing the presence of local pairing in the pseudogap phase. More broadly our results reveal a new instability in the SG equation that is of fundamental interest, with potential applications such as providing a mechanism for generating large magnetic fields at ultrafast time scales in Josephson devices.

We discuss terahertz pump-probe experiments in hBN from the perspective of Floquet optical materials and photonic time crystals. Anisotropic nature of this material results in a large separation of frequencies of in-plane and out-of-plane optical phonons and leads to several branches of phonon-polariton excitations. We consider a slab of finite thickness pumped at the frequency of middle polaritons, around 25 THz. We theoretically analyze properties of the pump induced state and identify several interesting features, including possible light amplification and parametric instability at 2 THz. We relate these features to resonant pair scattering processes of polaritons excited by the pump pulse. We show that amplification/instability frequency ranges depend on both the pump intensity and the slab thickness. We point out that this setup can be used utilized to strongly enhance optical nonlinearities at terahertz frequencies. Richness and tunability of this system suggests that it holds promise for practical applications in terahertz technology.

Pump-probe experiments performed on K_3C_60 have unveiled both optical and transport signatures of metastable light-induced superconductivity up to room temperature, far above T_c. Recent experiments have uncovered that excitation in the vicinity of 50 meV enables the observation of high temperature light-induced superconductivity at significantly lower fluences. Inspired by these experiments we develop a mechanism which can explain such a giant resonant enhancement of light-induced superconductivity. Within a minimal non-linear Holstein model, we show that resonantly driving optical Raman modes leads to a time-dependent electron-phonon coupling. Such a coupling then modulates the effective electron-electron attraction, with the strongest modulations occurring when the drive is resonant with the phonon frequency. These dynamical modulations of the pairing interactions lead to Floquet-BCS instabilities at temperatures far exceeding equilibrium T_c, as observed in experiments. We conclude by discussing the implications of our general analysis on the K_3C_60 experiments specifically and suggesting experimental signatures of our mechanism.

Van der Waals heterostructures host many-body quantum phenomena that are tunable in situ using electrostatic gates. Their constituent two-dimensional materials and gates can naturally form plasmonic self-cavities, confining light in standing waves of current density due to finite-size effects. The plasmonic resonances of typical graphite gates fall in the gigahertz to terahertz range, corresponding to the same microelectronvolt to millielectronvolt energy scale as the phenomena in van der Waals heterostructures that they electrically control. This raises the possibility that the built-in cavity modes of graphite gates are relevant for shaping the low-energy physics of these heterostructures. However, probing these cavity-coupled electrodynamics is challenging as devices are notably smaller than the diffraction limit at the relevant wavelengths. Here we report on the intrinsic cavity conductivity of gate-tunable graphene heterostructures. As the carrier density is tuned, we observe coupling and spectral weight transfer between graphene and graphite plasmonic cavity modes in the ultrastrong coupling regime. We present an analytical model to describe the results and provide general principles for cavity design. Our findings show that intrinsic cavity effects are important for understanding the low-energy electrodynamics of van der Waals heterostructures and open a pathway for useful functionality through cavity control.

We present a novel theoretical approach for computing and analyzing two-dimensional spectroscopy of bosonic collective excitations in disordered many-body systems. Specifically, we employ the Keldysh formalism to derive, within a non-pertubative treatment of disorder effects, the third-order nonlinear response and obtain two-dimensional spectroscopy maps. In the weak nonlinear regime of our formalism, we demonstrate the ability of the echo peak to distinguish between elastic and inelastic scattering processes, in perfect agreement with the intuition developed in isolated two-level systems. Furthermore, we discuss unique many-body effects on the echo peak signature arising from interaction induced quantum fluctuations. In particular, we show that these quantum fluctuations induce a finite nonrephasable broadening and examine how the echo peak is influenced by the attractive or repulsive nature of the collective excitations.

Inspired by the striking discovery of metastable superconductivity in K3C60 at 100K, far above Tc = 20 K, we discuss possible mechanisms for long-lived, photo-induced superconductivity. Starting from a model of optically-driven Raman phonons coupled to inter-band electronic transitions, we develop a microscopic mechanism for photo-controlling the pairing interaction. Leveraging this mechanism, we first investigate long-lived superconductivity arising from the thermodynamic metastable trapping of the driven phonon. We then propose an alternative route, where the superconducting gap created by an optical drive leads to a dynamical bottleneck in the equilibration of quasi-particles. We conclude by discussing the implications of both scenarios for experiments that can be used to discriminate between them. Our work provides falsifiable explanations for the nanosecond-scale photo-induced superconductivity found in K3C60, while simultaneously offering a theoretical basis for exploring metastable superconductivity in other quantum materials.

Engineering phases of matter in cavities requires effective light-matter coupling strengths that are on the same order of magnitude as the bare system energetics, coined the ultrastrong coupling regime. For models of itinerant electron systems, which do not have discrete energy levels, a clear definition of this regime has been lacking to date. Here, we argue that a change of the electronic mass exceeding 10% of its bare value may serve as such a definition. We propose a quantitative computational scheme for obtaining the electronic mass in relation to its bare vacuum value and show that coupling to surface polariton modes can induce such mass changes. Our results have important implications for cavity design principles that enable the engineering of electronic properties with quantum light.

Motivated by recent experiments that observed low-frequency second-order optical responses in doped striped superconductors, here we investigate the nonlinear electrodynamics of systems exhibiting a charge density wave (CDW) order parameter. Due to the Bragg scattering off the CDW order, an incoming spatially homogeneous electric field in addition to zero momentum current generates Umklapp currents that are modulated in space at momenta of the reciprocal CDW lattice. In particular, here we predict and microscopically evaluate the Umklapp shift current, a finite momentum analog of the regular shift current which represents the second-order optical process that downconverts homogeneous AC electric field into low-frequency, zero momentum current. Specifically, we evaluate real-time response functions within mean-field theory via the Keldysh technique and use the Peierls substitution to compute observables at finite momenta in lattice models. We find that systems with certain lattice symmetries (such as inversion symmetry), where the regular shift current is disallowed, may give rise to the Umklapp one. We apply our framework to investigate lattice symmetries in layered materials with helical-like stripes and show that both types of shift currents provide insight into the nature of intertwined phases of matter. Finally, we discuss the relation of our findings to recent experiments in striped superconductors.

Photonic time crystals refer to materials whose dielectric properties are periodic in time, analogous to a photonic crystal whose dielectric properties is periodic in space. Here, we theoretically investigate photonic time-crystalline behaviour initiated by optical excitation above the electronic gap of the excitonic insulator candidate Ta2NiSe5. We show that after electron photoexcitation, electron-phonon coupling leads to an unconventional squeezed phonon state, characterised by periodic oscillations of phonon fluctuations. Squeezing oscillations lead to photonic time crystalline behaviour. The key signature of the photonic time crystalline behaviour is terahertz (THz) amplification of reflectivity in a narrow frequency band. The theory is supported by experimental results on Ta2NiSe5 where photoexcitation with short pulses leads to enhanced THz reflectivity with the predicted features. We explain the key mechanism leading to THz amplification in terms of a simplified electron-phonon Hamiltonian motivated by ab-initio DFT calculations. Our theory suggests that the pumped Ta2NiSe5 is a gain medium, demonstrating that squeezed phonon noise may be used to create THz amplifiers in THz communication applications.

Condensates are a hallmark of emergence in quantum materials with superconductors and charge density wave as prominent examples. An excitonic insulator (EI) is an intriguing addition to this library, exhibiting spontaneous condensation of electron-hole pairs. However, condensate observables can be obscured through parasitic coupling to the lattice. Time-resolved terahertz (THz) spectroscopy can disentangle such obscurants through measurement of the quantum dynamics. We target $Ta_{2}NiSe_{5}$, a putative room-temperature EI where electron-lattice coupling dominates the structural transition ($T_{c}$=326 K), hindering identification of excitonic correlations. A pronounced increase in the THz reflectivity manifests following photoexcitation and exhibits a BEC-like temperature dependence. This occurs well below the $T_{c}$, suggesting a novel approach to monitor exciton condensate dynamics. Nonetheless, dynamic condensate-phonon coupling remains as evidenced by peaks in the enhanced reflectivity spectrum at select infrared-active phonon frequencies. This indicates that parametric reflectivity enhancement arises from phonon squeezing, validated using Fresnel-Floquet theory and density functional calculations. Our results highlight that coherent dynamics can drive parametric stimulated emission with concomitant possibilities, including entangled THz photon generation.

Optical driving of materials has emerged as a versatile tool to control their properties, with photo-induced superconductivity being among the most fascinating examples. In this work, we show that light or lattice vibrations coupled to an electronic interband transition naturally give rise to electron-electron attraction that may be enhanced when the underlying boson is driven into a non-thermal state. We find this phenomenon to be resonantly amplified when tuning the boson's frequency close to the energy difference between the two electronic bands. This result offers a simple microscopic mechanism for photo-induced superconductivity and provides a recipe for designing new platforms in which light-induced superconductivity can be realized. We discuss two-dimensional heterostructures as a potential test ground for light-induced superconductivity concretely proposing a setup consisting of a graphene-hBN-SrTiO3 heterostructure, for which we estimate a superconducting Tc that may be achieved upon driving the system.

Parametric resonances and amplification have led to extraordinary photo-induced phenomena in pump-probe experiments. While these phenomena manifest themselves in out-of-equilibrium settings, here, we present the striking result of parametric amplification in equilibrium. In particular, we demonstrate that quantum and thermal fluctuations of a Raman-active mode amplifies light inside a cavity, at equilibrium, when the Raman mode frequency is twice the cavity mode frequency. This noise-driven amplification leads to the creation of an unusual parametric Raman polariton, intertwining the Raman mode with cavity squeezing fluctuations, with smoking gun signatures in Raman spectroscopy. In the resonant regime, we show the emergence of not only quantum light amplification but also localization and static shift of the Raman mode. Apart from the fundamental interest of equilibrium parametric amplification our study suggests a resonant mechanism for controlling Raman modes and thus matter properties by cavity fluctuations. We conclude by outlining how to compute the Raman-cavity coupling, and suggest possible experimental realization

Periodic laser driving, known as Floquet engineering, is a powerful tool to manipulate the properties of quantum materials. Using circularly polarized light, artificial magnetic fields, called Berry curvature, can be created in the photon-dressed Floquet-Bloch states that form. This mechanism, when applied to 3D Dirac and Weyl systems, is predicted to lead to photon-dressed movement of Weyl nodes which should be detectable in the transport sector. The transport response of such a topological light-matter hybrid, however, remains experimentally unknown. Here, we report on the transport properties of the type-II Weyl semimetal T_d-MoTe_2 illuminated by a femtosecond pulse of circularly polarized light. Using an ultrafast optoelectronic device architecture, we observed injection currents and a helicity-dependent anomalous Hall effect whose scaling with laser field strongly deviate from the perturbative laws of nonlinear optics. We show using Floquet theory that this discovery corresponds to the formation of a magnetic Floquet-Weyl semimetal state. Numerical ab initio simulations support this interpretation, indicating that the light-induced motion of the Weyl nodes contributes substantially to the measured transport signals. This work demonstrates the ability to generate large effective magnetic fields (> 30T) with light, which can be used to manipulate the magnetic and topological properties of a range of quantum materials.

Two-dimensional terahertz spectroscopy (2DTS), a terahertz analogue of nuclear magnetic resonance, is a new technique poised to address many open questions in complex condensed matter systems. The conventional theoretical framework used ubiquitously for interpreting multidimensional spectra of discrete quantum level systems is, however, insufficient for the continua of collective excitations in strongly correlated materials. Here, we develop a theory for 2DTS of a model collective excitation, the Josephson plasma resonance in layered superconductors. Starting from a mean-field approach at temperatures well below the superconducting phase transition, we obtain expressions for the multidimensional nonlinear responses that are amenable to intuition derived from the conventional single-mode scenario. We then consider temperatures near the superconducting critical temperature $T_c$, where dynamics beyond mean-field become important and conventional intuition fails. As fluctuations proliferate near $T_c$, the dominant contribution to nonlinear response comes from an optical parametric drive of counter-propagating Josephson plasmons, which gives rise to 2D spectra that are qualitatively different from the mean-field predictions. As such, and in contrast to one-dimensional spectroscopy techniques, such as third harmonic generation, 2DTS can be used to directly probe thermally excited finite-momentum plasmons and their interactions. Our theory provides a clear interpretation of recent 2DTS measurements on cuprates, and we discuss implications beyond the present context of Josephson plasmons.

We report the existence of dissipationless currents in bilayer superconductors above the critical temperature $T_c$, assuming that the superconducting phase transition is dominated by phase fluctuations. Using a semiclassical $U(1)$ lattice gauge theory, we show that thermal fluctuations cause a transition from the superconducting state at low temperature to a resistive state above $T_c$, accompanied by the proliferation of unbound vortices. Remarkably, while the proliferation of vortex excitations causes dissipation of homogeneous in-plane currents, we find that counterflow currents, flowing in opposite direction within a bilayer, remain dissipationless. The presence of a dissipationless current channel above $T_c$ is attributed to the inhibition of vortex motion by local superconducting coherence within a single bilayer, in the presence of counterflow currents. Our theory presents a possible scenario for the pseudogap phase in bilayer cuprates.

The physics of driven collective modes in quantum materials underpin a number of striking non-equilibrium functional responses, which include enhanced magnetism, ferroelectricity and superconductivity. However, the coherent coupling between multiple modes at once are difficult to capture by single-pump probe (one-dimensional) spectroscopy, and often remain poorly understood. One example is phonon-mediated amplification of Josephson plasmons in YBa$_2$Cu$_3$O$_{6+x}$, in which at least three normal modes of the solid are coherently mixed as a source of enhanced superconductivity. Here, we go beyond previous pump-probe experiments in this system and acquire two-dimensional frequency maps using pairs of mutually delayed, carrier envelope phase stable mid-infrared pump pulses, combined with measurements of the time-modulated second-order nonlinear optical susceptibility. We find that the driven zone-center phonons amplify coherent pairs of opposite-momentum Josephson plasma polaritons, generating a squeezed state of interlayer phase fluctuations. The squeezed state is a potentially important ingredient in the microscopic physics of photo-induced superconductivity in this and other materials.

Inhomogeneities crucially influence the properties of quantum materials, yet methods that can measure them remain limited and can access only a fraction of relevant observables. For example, local probes such as scanning tunnelling microscopy have documented that the electronic properties of cuprate superconductors are inhomogeneous over nanometre length scales. However, complementary techniques that can resolve higher-order correlations are needed to elucidate the nature of these inhomogeneities. Furthermore, local tunnelling probes are often effective only far below the critical temperature. Here we develop a two-dimensional terahertz spectroscopy method to measure Josephson plasmon echoes from an interlayer superconducting tunnelling resonance in a near-optimally doped cuprate. The technique allows us to study the multidimensional optical response of the interlayer Josephson coupling in the material and disentangle intrinsic lifetime broadening from extrinsic inhomogeneous broadening for interlayer superconducting tunnelling. We find that inhomogeneous broadening persists up to a substantial fraction of the critical temperature, above which this is overcome by the thermally increased lifetime broadening. By measuring terahertz photon echoes, multidimensional spectroscopy demonstrates that interlayer tunnelling in a cuprate superconductor remains largely unaffected by electronic disorder, even near the phase transition.

The excitonic insulator is an electronically driven phase of matter that emerges upon the spontaneous formation and Bose condensation of excitons. Detecting this exotic order in candidate materials is a subject of paramount importance, as the size of the excitonic gap in the band structure establishes the potential of this collective state for superfluid energy transport. However, the identification of this phase in real solids is hindered by the coexistence of a structural order parameter with the same symmetry as the excitonic order. Only a few materials are currently believed to host a dominant excitonic phase, Ta2NiSe5 being the most promising. Here, we test this scenario by using an ultrashort laser pulse to quench the broken-symmetry phase of this transition metal chalcogenide. Tracking the dynamics of the material's electronic and crystal structure after light excitation reveals spectroscopic fingerprints that are compatible only with a primary order parameter of phononic nature. We rationalize our findings through state-of-the-art calculations, confirming that the structural order accounts for most of the gap opening. Our results suggest that the spontaneous symmetry breaking in Ta2NiSe5 is mostly of structural character, hampering the possibility to realize quasi-dissipationless energy transport.

Inhomogeneities play a crucial role in determining the properties of quantum materials. Yet methods that can measure these inhomogeneities are few, and apply to only a fraction of the relevant microscopic phenomena. For example, the electronic properties of cuprate materials are known to be inhomogeneous over nanometer length scales, although questions remain about how such disorder influences supercurrents and their dynamics. Here, two-dimensional terahertz spectroscopy is used to study interlayer superconducting tunneling in near-optimally-doped La1.83Sr0.17CuO4. We isolate a 2 THz Josephson echo signal with which we disentangle intrinsic lifetime broadening from extrinsic inhomogeneous broadening. We find that the Josephson plasmons are only weakly inhomogeneously broadened, with an inhomogeneous linewidth that is three times smaller than their intrinsic lifetime broadening. This extrinsic broadening remains constant up to 0.7Tc, above which it is overcome by the thermally-increased lifetime broadening. Crucially, the effects of disorder on the Josephson plasma resonance are nearly two orders of magnitude smaller than the in-plane variations in the superconducting gap in this compound, which have been previously documented using Scanning Tunnelling Microscopy (STM) measurements. Hence, even in the presence of significant disorder in the superfluid density, the finite frequency interlayer charge fluctuations exhibit dramatically reduced inhomogeneous broadening. We present a model that relates disorder in the superfluid density to the observed lifetimes.

Recent experiments in the doped cuprates La_2-xBa_xCuO_4 have revealed the emission of anomalous terahertz radiation after impulsive optical excitation. Here, we theoretically investigate the nonlinear electrodynamics of such striped superconductors and explore the origin of the observed radiation. We argue that photoexcitation is converted into a photocurrent by a second-order optical nonlinearity, which is activated by the breaking of inversion symmetry in certain stripe configurations. We point out the importance of including Umklapp photocurrents modulated at the stripe periodicity itself, which impulsively drive surface Josephson plasmons and lead to a resonant structure of outgoing radiation, consistent with the experiments. We speculate on the utility of the proposed mechanism in the context of generating tunable terahertz radiation.