title: Homoclinic chaos in vacuum rabi oscillations of moving two-level atoms
abstract: We study analytically and numerically vacuum Rabi oscillations of N identical two-level atoms moving through a single-mode lossless cavity. Equations of motion which take into account the atomic quantum correlations are obtained for the quantum mechanical expectation values in the strong-coupling, rotating-wave, pointlike, and Raman-Nath approximations. It is shown that moving atoms may demonstrate an unusual type of spontaneous emission, the chaotic vacuum Rabi oscillations. This manifestation of quantum dynamical chaos in the matter-vacuum interaction is caused by a spatial inhomogeneity of the cavity mode that modulates the vacuum Rabi frequency of moving atoms. For small values of the depth of this modulation we use the Melnikov method and show analytically the presence of homoclinic chaos in this interaction. Transition to global chaos and global phase space stochasticity under conditions of the strong modulation are studied numerically by computing the maximal Lyapunov exponent lambda of the atom-field dynamical system as a function of the number and velocity of atoms and detuning. We find a curious structure of the lambda(N) dependence reflecting an intermittent route to global chaos. The strength of chaos depends strongly on the initial state preparation of atoms just before injecting into a cavity. It is shown that initially fully inverted atoms, which are in a superfluorescent Dicke state, demonstrate much stronger chaos (under other equal conditions) than the atoms prepared initially in a superradiant state with macroscopic polarization. A maser operating with two-level Rydberg atoms to be injected into a high-Q superconducting microwave cavity seems to be a realistic device for observing some manifestations of the chaotic vacuum Rabi oscillations.
authors.affiliation: Laboratory of Nonlinear Dynamical Systems, Pacific Oceanological Institute of the Russian Academy of Sciences, 690041 Vladivostok, Russia.
authors.initials: SV
authors.lastname: Prants
authors.initials: LE
authors.lastname: Kon'kov