Oscillations in an Ensemble of Noninteracting Oscillators

Edward B. Manoukian

Manuel Bojer, A. Cidrim, P. P. Abrantes +2 more

The authors investigate the photon statistics of an ensemble of coherently driven noninteracting two-level atoms in the weakly driven regime. They find emission characteristics that are strongly in contrast to the emission of classical oscillating dipoles, ranging from strong antibunching to superbunching.

Ana María Rey, Guido Pupillo, Charles W. Clark +1 more

We discuss interacting and noninteracting one dimensional atomic systems trapped in an optical lattice plus a parabolic potential. We show that, in the tight-binding approximation, the noninteracting problem is exactly solvable in terms of Mathieu functions. We use the analytic solutions to study the collective oscillations of ideal bosonic and fermionic ensembles induced by small displacements of the parabolic potential. We treat the interacting boson problem by numerical diagonalization of the Bose-Hubbard Hamiltonian. From analysis of the dependence upon lattice depth of the low-energy excitation spectrum of the interacting system, we consider the problems of ``fermionization'' of a Bose gas, and the superfluid-Mott insulator transition. The spectrum of the noninteracting system turns out to provide a useful guide to understanding the collective oscillations of the interacting system, throughout a large and experimentally relevant parameter regime.

V. V. Dodonov

F. Suekane

Е. А. Титов

Exact expressions for the statistical sum of the grand canonical ensemble and the one-particle density matrix are derived based on the definition of the density matrix for a system of N identical noninteracting Bose particles in an oscillator potential as a sum with respect to the symmetric exchange of the density matrix coordinates of distinguishable particles. A quasi-classical scenario is analyzed in detail.