The interlayer terahertz response of strongly anisotropic superconductors such as high-TC cuprates is dominated, in the linear regime, by the Josephson Plasma Resonance. As soon as electric fields of the order of several tens of kV/cm, routinely generated in our laboratories, are applied, a highly nonlinear regime is turned on, characterized by a multitude of phenomena. Through a variety of experimental techniques including nonlinear terahertz reflectivity, terahertz pump-probe and emission spectroscopy, as well as second harmonic generation, our group has been able over the years to discover several effects and understand their origin. Among these we mention the ultrafast gating of interlayer transport, the opening of transparency windows in the spectrum, the parametric amplification of terahertz waves, as well as the generation of odd terahertz harmonics. Remarkably, some of these phenomena have been found to persist above TC, highlighting the ability of nonlinear spectroscopies to reveal superconducting fluctuations in the normal state that would otherwise be silent in linear response.


Nonlinear light–matter interaction at terahertz frequencies
D. Nicoletti and A. Cavalleri
Advances in Optics and Photonics, 8, 401-464 (2016)


Strong optical pulses at mid-infrared and terahertz frequencies have recently emerged as powerful tools to manipulate and control the solid state and especially complex condensed matter systems with strongly correlated electrons. The recent developments in high-power sources in the 0.1–30 THz frequency range, both from table-top laser systems and from free-electron lasers, have provided access to excitations of molecules and solids, which can be stimulated at their resonance frequencies. Amongst these, we discuss free electrons in metals, superconducting gaps and Josephson plasmons in layered superconductors, and vibrational modes of the crystal lattice (phonons), as well as magnetic excitations. This review provides an overview and illustrative examples of how intense terahertz transients can be used to resonantly control matter, with particular focus on strongly correlated electron systems and high-temperature superconductors.

Josephson plasmonics in layered superconductors
Y. Laplace & A. Cavalleri
Advances in Physics: X, 1, 387-411 (2016)

We review the optical physics of Josephson plasmons in cuprate superconductors. These coherent charge modes arise from tunneling of the superfluid between superconducting planes and exhibit strong nonlinearities and quantum coherent dynamics at THz frequencies. We summarize early transport and microwave experiments in Bi2Sr2CaCu2O8+δ (BSCCO) and discuss more recent work performed in La2−xSrxCuO4 (LSCO) and La2−xBaxCuO4 (LBCO) using nonlinear THz techniques. We cover THz-driven oscillations between superconducting and resistive states, optical excitation of solitonic breathers, and the parametric amplification of Josephson plasma waves. The last part of the review discusses some new research directions, including cooling of superconducting phase fluctuations with lasers and optical cavity control techniques.

Key publications

Amplification of Superconducting Fluctuations in Driven YBa2Cu3O6+x
A. von Hoegen, M. Fechner, M. Först, N. Taherian, E. Rowe, A. Ribak, J. Porras, B. Keimer, M. Michael, E. Demler, and A. Cavalleri
Physical Review X, 12, 031008 (2022)

In cuprate high-Tc superconductors, resonant excitation of certain lattice vibrations has been shown to induce transient terahertz reflectivity features suggestive of nonequilibrium superconductivity above the critical temperature Tc. A microscopic mechanism for these observations is still lacking. Here, timeresolved measurements of scattering-angle- and polarization-dependent second-harmonic generation in driven YBa2Cu3O6+x reveal a three-order-of-magnitude amplification of a 2.5-THz electronic mode, which is unique because of its symmetry, momentum, and temperature dependence. A theory for amplification of finite-momentum Josephson plasma polaritons, which are assumed to be well formed below Tc but incoherent throughout the pseudogap phase, explains all these observations. A theoretical solution for the Fresnel-Floquet reflection that starts from the coherently oscillating Josephson plasma polaritons provides a possible mechanism for the nonequilibrium superconductorlike terahertz reflectivity reported earlier. Beyond the immediate case of cuprates, this work underscores the role of nonlinear mode mixing to amplify fluctuating modes above the transition temperature in a wide range of materials.

Coherent emission from surface Josephson plasmons in striped cuprates
D. Nicoletti, M. Buzzi, M. Fechner, P. E. Dolgirev, M. H. Michael, J. B. Curtis, E. Demler, G. D. Gu, A. Cavalleri
PNAS, 119, e2211670119 (2022)

The interplay between charge order and superconductivity remains one of the central themes of research in quantum materials. In the case of cuprates, the coupling between striped charge fluctuations and local electromagnetic fields is especially important, as it affects transport properties, coherence, and dimensionality of superconducting correlations. Here, we study the emission of coherent terahertz radiation in single-layer cuprates of the La2-xBaxCuO4 family, for which this effect is expected to be forbidden by symmetry. We find that emission vanishes for compounds in which the stripes are quasi-static but is activated when c-axis inversion symmetry is broken by incommensurate or fluctuating charge stripes, such as in La1.905Ba0.095CuO4 and in La1.845Ba0.155CuO4. In this case, terahertz radiation is emitted by surface Josephson plasmons, which are generally dark modes, but couple to free space electromagnetic radiation because of the stripe modulation.

Terahertz phase slips in striped La2−xBaxCuO4
D. Fu, D. Nicoletti, M. Fechner, M. Buzzi, G. D. Gu, A. Cavalleri
Physical Review B 05, L020502 (2022)

Interlayer transport in high-TC cuprates is mediated by superconducting tunneling across the CuO2 planes. For this reason, the terahertz frequency optical response is dominated by one or more Josephson plasma resonances and becomes highly nonlinear at fields for which the tunneling supercurrents approach their critical value IC. These large terahertz nonlinearities are in fact a hallmark of superconducting transport. Surprisingly, however, they have been documented in La2−xBaxCuO4 (LBCO) also above TC for doping values near x = 1/8 and interpreted as an indication of superfluidity in the stripe phase. Here, electric-field-induced second harmonic is used to study the dynamics of time-dependent interlayer voltages when LBCO is driven with large-amplitude terahertz pulses, in search of other characteristic signatures of Josephson tunneling in the normal state. We show that this method is sensitive to the voltage anomalies associated with 2π Josephson phase slips, which near x = 1/8 are observed both below and above TC. These results document a regime of nonlinear transport that shares features of fluctuating stripes and superconducting phase dynamics.

Probing optically silent superfluid stripes in cuprates
S. Rajasekaran, J. Okamoto, L. Mathey, M. Fechner, V. Thampy, G. D. Gu, A. Cavalleri
Science, 369, 575-579 (2018)

Unconventional superconductivity in the cuprates coexists with other types of electronic order. However, some of these orders are invisible to most experimental probes because of their symmetry. For example, the possible existence of superfluid stripes is not easily validated with linear optics, because the stripe alignment causes interlayer superconducting tunneling to vanish on average. Here we show that this frustration is removed in the nonlinear optical response. A giant terahertz third harmonic, characteristic of nonlinear Josephson tunneling, is observed in La1.885Ba0.115CuO4 above the transition temperature Tc = 13 kelvin and up to the charge-ordering temperature Tco = 55 kelvin. We model these results by hypothesizing the presence of a pair density wave condensate, in which nonlinear mixing of optically silent tunneling modes drives large dipole-carrying supercurrents.

Parametric amplification of a superconducting plasma wave
S. Rajasekaran, E. Casandruc, Y. Laplace, D. Nicoletti, G. D. Gu, S. R. Clark, D. Jaksch & A. Cavalleri
Nature Physics, 12, 1012–1016 (2016)

Many applications in photonics require all-optical manipulation of plasma waves1, which can concentrate electromagnetic energy on sub-wavelength length scales. This is dicult in metallic plasmas because of their small optical nonlinearities. Some layered superconductors support Josephson plasma waves, involving oscillatory tunnelling of the superfluid between capacitively coupled planes. Josephson plasmawaves are also highly nonlinear and exhibit striking phenomena such as cooperative emission of coherent terahertz radiation superconductor–metal oscillations and soliton formation. Here, we show that terahertz Josephson plasma waves can be parametrically amplified through the cubic tunnelling nonlinearity in a cuprate superconductor. Parametric amplification is sensitive to the relative phase between pump and seed waves, and may be optimized to achieve squeezing of the order-parameter phase fluctuations9 or terahertz single-photon devices.

Optical excitation of Josephson plasma solitons in a cuprate superconductor
A. Dienst, E. Casandruc, D. Fausti, L. Zhang, M. Eckstein, M. Hoffmann, V. Khanna, N. Dean, M. Gensch, S. Winnerl, W. Seidel, S. Pyon, T. Takayama, H. Takagi & A. Cavalleri
Nature Materials, 12, 535-541 (2013)

Josephson plasma waves are linear electromagnetic modes that propagate along the planes of cuprate superconductors, sustained by interlayer tunnelling supercurrents. For strong electromagnetic fields, as the supercurrents approach the critical value, the electrodynamics become highly nonlinear. Josephson plasma solitons (JPSs) are breather excitations predicted in this regime, bound vortex–antivortex pairs that propagate coherently without dispersion. We experimentally demonstrate the excitation of a JPS in La1.84Sr0.16CuO4, using intense narrowband radiation from an infrared free-electron laser tuned to the 2-THz Josephson plasma resonance. The JPS becomes observable as it causes a transparency window in the opaque spectral region immediately below the plasma resonance. Optical control of magnetic-flux-carrying solitons may lead to new applications in terahertz-frequency plasmonics, in information storage and transport and in the manipulation of high-Tc superconductivity.

Bi-directional ultrafast electric-field gating of interlayer charge transport in a cuprate superconductor
A. Dienst, M. C. Hoffmann, D. Fausti, J. C. Petersen, S. Pyon, T. Takayama, H. Takagi and A. Cavalleri
Nature Photonics, 5, 485-488 (2011)

In cuprate superconductors, tunnelling between planes makes three-dimensional superconductive transport possible. However, the interlayer tunnelling amplitude is reduced when an order-parameter-phase gradient between planes is established. As such, interlayer superconductivity along the c-axis can be weakened if a strong electric field is applied along the c-axis. In this Letter, we use high-field single-cycle terahertz pulses to gate interlayer coupling in La1.84Sr0.16CuO4. We induce ultrafast oscillations between superconducting and resistive states and switch the plasmon response on and off, without reducing the density of Cooper pairs. In-plane superconductivity remains unperturbed, revealing a non-equilibrium state in which the dimensionality of the superconductivity is time-dependent. The gating frequency is determined by the electric field strength. Non-dissipative, bi-directional gating of superconductivity is of interest for device applications in ultrafast nanoelectronics and represents an example of how nonlinear terahertz physics can benefit nanoplasmonics and active metamaterials.