  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.
