Approximate analytic solution of the dissipative semiclassical Rabi model under parametric multi-tone modulations

Abstract We present an analytic method for obtaining the dynamics of the dissipative time-modulated semiclassical Rabi model, which describes a two-level system (qubit) with time-dependent parameters, coupled to a single-mode bosonic field via the dipole-interaction and to a thermal reservoir. We consider the simultaneous harmonic modulations of the qubit transition frequency and the qubit-field coupling strength, with arbitrary frequencies, and obtain closed analytic expressions for the density operator under the coarse-graining approximation. Our approximate results are in excellent ageement with exact numerical data, and illustrate how the qubit state can be controlled in the dispersive regime by properly adjusting the system parameters.