  Unconventional superconductivity in the cuprates emerges from, or coexists
with, other types of electronic order. However, these orders are sometimes
invisible because of their symmetry. For example, the possible existence of
superfluid charge stripes in the normal state of single layer cuprates cannot
be validated with infrared optics, because interlayer tunneling fluctuations
vanish on average. Similarly, it is not easy to establish if charge orders are
responsible for dynamical decoupling of the superconducting layers over broad
ranges of doping and temperatures. Here, we show that TeraHertz pulses can
excite nonlinear tunneling currents between linearly de-coupled charge-ordered
planes. A giant TeraHertz third harmonic signal is observed in
La1.885Ba0.115CuO4 far above Tc=13 K and up to the charge ordering temperature
TCO = 55 K. We model these results by considering large order-parameter-phase
oscillations in a pair density wave condensate, and show how nonlinear mixing
of optically silent tunneling modes can drive large dipole-carrying
super-current oscillations. Our results provide compelling experimental support
for the presence of hidden superfluid order in the normal state of cuprates.
These experiments also underscore the power of nonlinear TeraHertz optics as a
sensitive probe of frustrated excitations in quantum solids.

Superconductivity;Strongly Correlated Electrons