Probing amplified Josephson plasmons in YBa₂Cu₃O_6+x by multidimensional spectroscopy

The nonlinear driving of collective modes in quantum materials can lead to a number of striking non-equilibrium functional responses, which merit a comprehensive exploration of underlying dynamics. However, the coherent coupling between nonlinearly-driven modes frequently involves multiple mode coordinates at once, and is often difficult to capture by one-dimensional pump probe spectroscopy. One example is phonon-mediated amplification of Josephson plasmons in YBa₂Cu₃O_6+x, a phenomenon likely associated with the mysterious superconducting-like optical response observed in this material. Here, we report two-dimensional nonlinear spectroscopy measurements in driven YBa₂Cu₃O_6+x. We excite apical oxygen phonons with pairs of mutually-delayed carrier envelope phase stable mid-infrared pump pulses, and detect time-modulated second-order nonlinear optical susceptibility. We find that the driven phonons parametrically amplify coherent pairs of fluctuating opposite-momentum Josephson plasma polaritons, corresponding to a squeezed state of the Josephson plasma.