The dynamics of driven-dissipative Kerr nonlinear oscillators in the large photon number limit

Abstract We investigate the dynamics of dissipative Kerr nonlinear oscillator with single-photon drive, focusing on the phase diagram in the large photon number limit and phase-space dynamics. We find that the dimension of the parameter space can be reduced significantly by proper scaling and the fixed-point phase diagram can be obtained exactly, i.e. both the phase boundaries and the critical points can be solved in closed form. The various phases are distinguished by two numbers: the number of stable fixed points and the number of unstable fixed points, and hence phase transitions show up as bifurcations. Furthermore, we study the dynamical behavior in phase space, focusing on the basin of attraction in multistable phases and the emergence of limit cycles in phases with no stable fixed point. Our results reveal the rich physics induced by the interplay between dissipation and nonlinearity in Kerr nonlinear oscillator.