Enhancing spin-phonon and spin-spin interactions utilizing the linear resources in a hybrid quantum system*

Improving the spin-phonon and spin-spin couplings in hybrid quantum systems remains a crucial challenge. Here, we propose an experimentally feasible and simple method for exponentially enhancing the spin-phonon and the spin-spin interactions in a hybrid spin-mechanical setup, using only linear resources. Through modulating the spring constant of the cantilever with a time-dependent pump, we can acquire a tunable and nonlinear drive to the mechanical mode, thus amplifying the mechanical zero-point fluctuations and directly enhancing the spin-phonon coupling. This method allows the spin-mechanical system to be driven from the weak-coupling regime to the strong-coupling regime, and even the ultra-strong coupling regime. This method also gives rise to a large enhancement of the phonon-mediated spin-spin interactions between distant solid-state spins, typically two orders of magnitude larger than that without modulation.