The dynamical properties of partially coherent Bose-Einstein condensates in double wells are investigated in three typical regimes. In the extreme Fock regime, the time evolution of the degree of coherence is shown to decay rapidly. In the Rabi regime, a relation between the amplitude of Rabi oscillation and the degree of coherence is obtained, which is expected to determine the degree of coherence by measuring the amplitude of Rabi oscillation. The study on the self-trapping phenomena in the Josephson regime exhibits that both the degree of coherence and the initial relative phase can affect the final particle distribution.
The superconducting flux qubit has two quantum states with opposite currents which generate different magnetic fields. Environment of nuclear spins can find out the magnetic field after a decoherence time ${\ensuremath{\tau}}_{0}$ inversely proportional to the magnetic field and the square root of the number of spins. When the Hamiltonian of the qubit drives fast coherent Rabi oscillations between the states with opposite current, then the magnetic field is flipped at a constant rate $\ensuremath{\omega}$ and the decoherence time $\ensuremath{\tau}=\ensuremath{\omega}{\ensuremath{\tau}}_{0}^{2}$ is much longer than ${\ensuremath{\tau}}_{0}$. However, on closer inspection decoherence actually takes place on two time scales. The long time $\ensuremath{\tau}$ is a time of full decoherence but a part of quantum coherence is lost already after the much shorter time $\ensuremath{\pi}∕\ensuremath{\omega}$. This fast partial decoherence biases coherent flux oscillations towards the initial flux direction and it can affect performance of the superconducting devices as qubits.
In this paper the dynamics of wave fields in a cavity, part of which is filled with a dielectric, are investigated. The wave equation is solved approximately using the method of multiple time scales. Phase modulations of the cavity modes in an adiabatic case are given up to the first order. A simple effective field Hamiltonian operator is derived and then used to analyze the interaction of radiation with a two-level atom passing through the cavity. Corrections to the Rabi oscillations due to the time-dependent frequency of the cavity photons are investigated. It is shown that adiabatic time dependence of the refractive index of the dielectric can lead to suppression of the Rabi oscillations of atomic inversion.