  The dynamics of Higgs mode in superconductors, manifested as coherent
oscillations of the superconducting order parameter amplitude, provides vital
insights into the nature of the superconducting gap structure and symmetry.
Here we utilize two-dimensional terahertz coherent spectroscopy to investigate
Higgs dynamics of a newly discovered infinite-layer nickelate superconductor.
While we observe distinct nonlinear terahertz responses from the
superconducting state, well-defined long-lived Higgs modes, as commonly
observed in $s$-wave superconductors, are entirely absent in the nickelate
film. Instead, we find the coherent nonlinear terahertz response is dominated
by the quasiparticle excitations. These observations strongly indicate that the
Higgs mode in infinite-layer nickelates is heavily damped by the quasiparticle
excitations at arbitrarily low energies, which is a characteristic of $d$-wave
pairing symmetry. Additionally, by examining the temperature dependence of the
nonlinear terahertz response, we discover short-range superconducting
fluctuations in the vicinity of $T_\mathrm{c}$. Our findings provide proof of a
new $d$-wave system and establish a foundation for investigating the
unconventional superconductivity in nickelates.
