We investigate the effects of correlations on the properties of the ground state of the rotating harmonically trapped Bose gas by adding Bogoliubov fluctuations to the mean-field ground state of an
N-particle single-vortex system. We demonstrate that the fluctuation-induced correlations lower the energy compared to that of the mean-field ground state, that the vortex core is pushed slightly away from the center of the trap, and that an unstable mode with negative energy (for rotations slower than a critical frequency) emerges in the energy spectrum, thus pointing to a better state for slow rotation. We construct mean-field ground states of zero-, one-, and two-vortex states as a function of rotation rate and determine the critical frequencies for transitions between these states, as well as the critical frequency for appearance of a metastable state with an off-center vortex and its image vortex in the evanescent tail of the cloud.
To investigate the interaction of a mesoscopic Josephson junction with a single mode quantized electromagnetic field, the diagnonalizing process of the coupled system Hamiltonian was performed by using an unitary transformation. Zero? point energy and zero? point fluctuation of the coupled system were shown. For the ground state of the coupled system, the quantum fluctuations of the flux and charge operators in the field and junction subsystems can exhibit smaller quantum noise than the zero point fluctuations of the individual subsystems. Thus, when the coupled system is in its lowest energy state, which means that no radiation appear, the two subsystems exhibit nonclassical behavior.
We discuss the quantum phases and their diffusion in a spinor-1 atomic Bose-Einstein condensate. For ferromagnetic interactions, we obtain the exact ground state distribution of the phase fluctuations corresponding to the total atom number (N), the magnetization (M), and the alignment (or hypercharge) (Y) of the system. The mean-field ground state is shown to be stable against these fluctuations, which dynamically recover the two continuous symmetries associated with the conservation of N and M as in current experiments.