Quantum collapses and revivals in a nonlinear Jaynes-Cummings model

Nonclassical effects of a two-level spin system interacting with a two-mode cavity field via two-photon transition

The interaction of a two-level cyclic XY n-spin model with a two-mode cavity field involving two-photon transitions is investigated through a generalized Jaynes-Cummings model in the rotating-wave approximation. The two-photon interacting Hamiltonian becomes from the replacement of each single-mode field in the one-photon interacting Hamiltonian with the second-harmonic generation. It was assumed that initially the correlated field modes are in disentangled coherent states having the same photon distribution and that the spin system is in an excited state. At any time t > 0, the spin system and the field are in an entangled state, in this case, via a unitary time evolution operator. Thus, the spontaneous decay of a spin level was treated by considering the interaction of the two-level spin system with the modes of the universe in the vacuum state. The different cases of interest, characterized in terms of a detuning parameter for each mode, which emerge from nonvanishing commutation relations, were analytically implemented and numerically discussed for various values of the initial mean photon number and spin-photon coupling constants. Photon distribution, time evolution of the spin population inversion, as well as the statistical properties of the field leading to the possible production of nonclassical states, such as antibunched light, violations of the Cauchy-Schwartz inequality, and second- and fourth-order squeezing, are examined. The case of zero detuning of both modes was treated in terms of a linearization of the expansion of the time evolution operator, while in other three cases, the computations were conducted via second- and third-order Dyson perturbation expansion of the time evolution operator matrix elements for the excited and ground states of the spin system, respectively.

Strong confinement and oscillations in two-component bose-einstein condensates

We present a new model of Bose-Einstein condensate dynamics based on strong confinement near the ground state. The model is based on a combined particle-wave view of the condensate and predicts oscillations in a two-component condensate, based on interference of nonspreading wave packets moving within a pair of tilted nearly square potentials. The oscillations are similar to those recently reported for a magnetically trapped 87Rb condensate, and the model's predictions give good quantitative agreement with the experiments.