Quantum Theory of Chaotic Rabi Oscillations

Alexander Alexandrovich Biryukov, B. V. Danilyuk

The object of the research are the quantum transitions of a many-level system between its stationary states under the influence of an alternating external electric field. The transition amplitudes and probabilities are calculated by the method of perturbation theory in the approximation of a classical external field. It is illustrated that in the case when the external field frequency is equal to the frequency of any quantum transition, then the probability of this transition fluctuate nearly the average value which is oscillating with Rabi frequency. Probabilities of other quantum transitions are very small and change chaotically with time.

Vyacheslav Shatokhin, S. Ya. Kilin

Leonid E. Kon’kov, Sergei V Prants

It is shown in numerical simulations with two-level atoms moving through a single-mode high- Q cavity that spontaneous emission of a new type — chaotic Rabi vacuum oscillations — arises in the strong atom-field coupling regime.

M. S. Santhanam

Lu Tie, Ju-Kui Xue

The nonlinear Landau-Zener tunneling and the nonlinear Rabi oscillations of superfluid Fermi gases between Bloch bands in an accelerating optical lattice are discussed. Within the hydrodynamic theory and a two-level model, the tunneling probability of superfluid Fermi gases between Bloch bands is obtained. We find that, as the system crosses from the Bose-Einstein condensation (BEC) side to the BCS side, the tunneling rate is closely related to the particle density: when the density is smaller (larger) than a critical value, the tunneling rate at unitarity is larger (smaller) than that in the BEC limit. This is well explained in terms of an effective interaction and an effective potential. Furthermore, the nonlinear Rabi oscillations of superfluid Fermi gases between the bands are discussed by imposing a periodic modulation on the level bias and the strength of the lattice. Analytical expressions of the critical density for suppressing or enhancing the Rabi oscillations are obtained. It is shown that, as the system crosses from the BEC side to the BCS side, the critical density strongly depends on the modulation parameters (i.e., the modulation amplitude and the modulation frequency). For a fixed density, a high-frequency or low-frequency modulation can suppress or enhance the Rabi oscillations both at unitarity and in the BEC limit. For an intermediate modulation frequency, the Rabi oscillations are chaotic along the entire BEC-BCS crossover, especially, on the BCS side. Interestingly, we find that the modulation of the lattice strength only with an intermediate modulation frequency has significant effect on the Rabi oscillations both in the BEC limit and at unitarity; that is, an intermediate-frequency modulation can enhance the Rabi oscillations, especially on the BCS side.

P. Lebœuf