Abstract
The proximity effect in hybrid superconducting–normal-metal structures is shown to affect strongly the
coherent oscillations of the superconducting order parameter $\Delta$ known as the Higgs modes. The standard Higgs
mode at frequency $2\Delta$ is damped exponentially by the quasiparticle leakage from the primary superconductor.
Two new Higgs modes with the frequencies depending on both the primary and induced gaps in the hybrid
structure are shown to appear due to the coherent electron transfer between the superconductor and the normal
metal. Altogether, these three modes determine the long-time asymptotic behavior of the superconducting
order parameter disturbed either by the electromagnetic pulse or the quench of the system parameters and
thus are of crucial importance for the dynamical properties and restrictions on the operating frequencies for
superconducting devices based on the proximity effect used, e.g., in quantum computing, in particular, with
topological low-energy excitations.
