Suppression of the horizon effect in pairing correlation functions of $t$-$J$ chains after a quantum quench

We investigate the time evolution of density, spin, and pairing correlation functions in one-dimensional $t$-$J$ models following a quantum quench using the time-dependent density matrix renormalization group (tDMRG). While density and spin correlation functions show the typical light-cone behavior over a wide range of parameters, in pairing correlation functions it is strongly suppressed. This is supported by time-dependent BCS theory, where the light-cone in the pairing correlation functions is found to be at least two orders of magnitude weaker than in the density correlator. These findings indicate that in global quantum quenches not all observables are affected by the excitations equally.