Parametrically amplified Josephson plasma waves in YBa_2Cu_3O_(6+x): evidence for local superconducting fluctuations up to the pseudogap temperature $T^*$

A number of experiments have reported evidence for the existence of the lower Josephson plasmon mode in underdoped YBCO up to the pseudogap temperature scale when the sample is subject to intense terahertz pulses. Evidences include the observation of a reflectivity edge that resembles that of the superconducting state, and the second harmonic generation of a probe optical pulse that is modulated at a frequency similar the reflectivity feature. Since the lower Josephson plasmon mode is often associated with coherent oscillations between bilayers in the YBCO structure, these experiments have led to the suggestion that the intense pump has created pair coherence up to 350K. In this paper, we propose an alternative explanation of these experiments based on the model of short ranged superconducting correlations in the equilibrium state and using the Floquet perspective to analyze optical responses of the photoexcited state. Our model only requires local pairing with phase correlations that can be very short ranged when the system is at equilibrium at a temperature above Tc but below the pseudo-gap temperature T*. Within this assumption there is no phase coherence between bilayers. On the other hand the relative phase between members of the bilayer has a longer in-plane correlation which leads locally to a finite Josephson current. We show that the nonlinearity afforded by the local intra-bilayer Josephson current is sufficient to explain both the reflectivity and second harmonic generation data. The key point is that in the lower Josephson plasmon, the coupling between bilayers is mainly capacitive: the Josepson current between bilayers can be set to zero without affecting the parametric amplification process. The implication is that while superconducting coherence may not be created by the pump, the pseudogap phase must possess a local pairing amplitude at equilibrium.