We compare the semiclassical and quantum predictions for the unitary dynamics of a two-level atom interacting with a single-mode electromagnetic field under parametric modulation of the atomic parameters in the regime of multiphoton atom–field resonances. We derive approximate analytic solutions for the semiclassical Rabi model when the atomic transition frequency and the atom–field coupling strength undergo harmonic external modulations. These solutions are compared to the predictions of the quantum Rabi model, which we solve numerically for an initial coherent state with a large average photon number (on the order of 104), in the regime of three-photon resonance. We show that, for short enough times and sufficiently intense coherent states, the semiclassical dynamics agrees quite well with the quantum dynamics, although it inevitably fails at longer times due to the absence of collapse–revival behavior. Furthermore, we describe how the field state evolves throughout the interaction, presenting numerical results for the average photon number, entropies (related to atom–field entanglement), and other quantities characterizing the photon number statistics of the electromagnetic field.
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.
Continuous monitoring can convert a dissipative channel into a resource for accelerating otherwise slow multiphoton transitions. We consider a three-level atom in a
Λ configuration and condition the evolution on the absence of photon emission through an auxiliary monitored decay channel. The resulting no-jump dynamics is governed by a non-Hermitian Rabi-type Hamiltonian. Using Floquet theory and Brillouin--Wigner projection-operator perturbation method, we derive effective two-state descriptions of odd-multiphoton resonances in the semiclassical and quantum Rabi models. The effective population-transfer rate, defined as the inverse of the time required for the first complete transfer between the atomic states, is maximized at an exceptional point, where its enhancement factor approaches
π/2, corresponding to an approximately
57% increase over the Hermitian value. Numerical results for three- and five-photon resonances closely reproduce the analytical transition times and yield non-negligible postselection probabilities. By contrast, the complete unconditioned dissipative evolution does not exhibit the same population-transfer enhancement. These results demonstrate a speed--success trade-off for measurement-conditioned multiphoton state transfer.