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.
Multiphoton resonant excitation of a three-state quantum system (a qutrit) with a single-mode photonic field is considered in the ultrastrong coupling regime, when the qutrit–photonic field coupling rate is comparable to appreciable fractions of the photon frequency. For ultrastrong couplings, the obtained solutions of the Schrödinger equation that reveal multiphoton Rabi oscillations in qutrits with the interference effects leading to the collapse and revival of atomic excitation probabilities at the direct multiphoton resonant transitions.
We consider the multiphoton dynamics of a quantum system composed of a three-state atom (a qutrit) and a single-mode photonic field in the ultrastrong and deep strong coupling regimes, when the coupling strength is comparable to or larger than the oscillator energy scale. We assume a qutrit to be in a L configuration, where an upper level is coupled to a twofold degenerate lower level. Direct multiphoton resonant transitions revealing generalized Rabi oscillations, collapse, and revivals in atomic excitation probabilities for the ultrastrong couplings are studied. In the deep strong coupling regime, particular emphasis is placed on the ground state of the considered system which strictly exhibits nonclassical properties.
A two-level system driven by a classical single frequency field in rotating-wave approximation is a basic model for resonance in quantum optics. The probability of making a transition depends sinusoidally on time with a characteristic frequency called the Rabi frequency. The Jaynes-Cummings model (JCM) consists of a two-level atomic system driven by a single quantized electromagnetic field mode. The field entropy in the case of an atom interacting with an initially coherent field is expected to reflect the collapse and revival of Rabi oscillations. The photon statistics of the JCM are examined and the entropy concepts are used to describe the apparently disordered collapses. A density matrix method is used to describe the influence of photon statistics in the JCM. The quantum generalization defines entropy through where the trace is taken over a convenient basis set. The thermal field JCM shows enhanced photon variances as expected for an initially Bose-Einstein field with large fluctuations.
Within the Rabi quantum model, it has been shown theoretically that a two-level atom ultrastrongly coupled to an electromagnetic field generates or absorbs photons. Photons can be generated if the field is initially in the vacuum state. Under certain initial states of the atom + field system, the absorption of photons is possible in the field mode in the ultrastrong atom–field coupling regime. If the atom is initially in the ground (unexcited) state and the field is in the vacuum state, photons can be generated under resonance condition ωa ≈ ωf or ξ ≡ ωa/ωf ≈ 1, where ωa and ωf are the atomic transition and field frequencies, respectively, in the ultrastrong coupling regime. At the negative detuning when ξ
≪ 1 or ωa
≪ ωf, Rabi oscillations of the average number of photons
⟨n^⟩t with
0⩽⟨n^⟩t⩽nmax≫1 are observed in the case of the ultrastrong coupling with the atom–field coupling constant
g~≡|g|/ωf∼1 ; in this case, the population of the excited atomic state is Pe(t) ≈ 0.5. At a large positive detuning when ξ
≫ 1, photons are not generated, i.e.,
⟨n^⟩≈0 , and the atom remains in the initial state, i.e., Pe(t) ≈ 0. The statistics of photons in the generation regime is nearly chaotic: the variance of photons is much larger than the level of the coherent field state (i.e., is super-Poisson). Field photons are absorbed without the excitation of the atom in the ultrastrong coupling regime in the case of the coherent initial state of the field
(⟨n^(t=0⟩>0) for certain positive detuning values. In this case, the field becomes sub-Poisson.
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.