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We demonstrate that parametric driving of suitable collective modes incuprate superconductors results in a reflectivity $R>1$ for frequencies in thelow terahertz regime. We propose to exploit this effect for the amplificationof coherent terahertz radiation in a laser-like fashion. As an example, weconsider the optical driving of Josephson plasma oscillations in a monolayercuprate at a frequency that is blue-detuned from the Higgs frequency.Analogously, terahertz radiation can be amplified in a bilayer cuprate bydriving a phonon resonance at a frequency slightly higher than the upperJosephson plasma frequency. We show this by simulating a driven-dissipative$U(1)$ lattice gauge theory on a three-dimensional lattice, encoding a bilayerstructure in the model parameters. We find a parametric amplification ofterahertz radiation at zero and nonzero temperature.

Terahertz amplifiers based on gain reflectivity in cuprate superconductors