Higgs mode mediated enhancement of interlayer transport in high- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>T</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:math> cuprate superconductors

We put forth a mechanism for enhancing the interlayer transport in cuprate superconductors, by optically driving plasmonic excitations along $c$ axis with frequency that is blue-detuned from Higgs frequency. The induce collective oscillation of field which induces parametric enhancement superconducting response, as we demonstrate minimal analytical model. Furthermore, perform simulations particle-hole symmetric $U(1)$ lattice gauge theory and find good agreement our prediction. map out renormalization coupling function parameters optical mode mediated can be larger than $50%$.