Dynamical Properties of Quasi-One-Dimensional Boson-Fermion Mixtures of Atoms in a Toroidal Potential

We theoretically investigate quantum-mechanical dynamics of quasi-one-dimensional boson-fermion mixtures of atomic gases trapped in a toroidal potential, where effective inter-atomic interactions are tunable and affect the dynamics. We especially focus on effects of quantum statistics and many-body correlations beyond the Hartree-Fock (HF) mean-field approximation on the dynamics. In order to predict the dynamics, we utilize the numerical exact diagonalization method and also reproduce the calculation in the HF approximation for comparison. The toroidal gases originally have a rotational symmetry in the toroidal direction. We firstly prepare a deformed ground state as an initial state by adding a weak potential deformed in the toroidal direction, and then remove the potential to start the dynamics. In the dynamics, number densities of the deformed gases exhibit oscillations as demonstrated in the present paper. As a result, we find out that the bosons and fermions show quite different behaviors owing to quantum statistics. In particular, the bosons exhibit a low-frequency oscillation in the strong boson-boson attraction regime owing to the many-body correlations, and it can not be reproduced in the HF approximation. The oscillation of the fermions is strongly influenced by that of the bosons through the boson-fermion interaction as a forced oscillator. In addition, we also discuss a relationship between the low-frequency oscillation and restoration of the broken symmetry.

Phase Separation of Multi-Component Bose-Einstein Condensates of Trapped Atoms and Molecules with a Homonuclear Feshbach Resonance

We investigate phase separation of Bose-Einstein condensates (BECs) of two-component atoms and one-component molecules with a homonuclear Feshbach resonance. We develop a full model for dilute atomic and molecular gases including correlation of the Feshbach resonance and all kinds of interparticle interactions, and numerically calculate order parameters of the BECs in spherical harmonic oscillator traps at zero temperature with the Bogoliubovs classical field approximation. As a result, we find out that the Feshbach resonance can induce two types of phase separation. The actual phase structures and density profiles of the trapped gases are predicted in the whole parameter region, from the atom dominant regime to the molecule dominant regime. We focus on the role of the molecules in the phase separation. Especially in the atom dominant regime, the role of the molecules is described through effective interactions derived from our model. Furthermore we show that a perturbative and semi-classical limit of our model reproduces the conventional atomic BEC (single-channel) model.