Deformation Dependence of Breathing Oscillations in Bose - Fermi Mixtures at Zero Temperature

We study the breathing oscillations in bose-fermi mixtures in the axially-symmetric deformed trap of prolate, spherical and oblate shapes, and clarify the deformation dependence of the frequencies and the characteristics of collective oscillations. The collective oscillations of the mixtures in deformed traps are calculated in the scaling method. In largely-deformed prolate and oblate limits and spherical limit, we obtain the analytical expressions of the collective frequencies. The full calculation shows that the collective oscillations become consistent with the analytically-obtained frequencies when the system is deformed into both prolate and oblate regions. The complicated changes of oscillation characters are shown to occur in the transcendental regions around the spherically-deformed region. We find that these critical changes of oscillation characters are explained by the level crossing behaviors of the intrinsic oscillation modes. The approximate expressions are obtained for the level crossing points that determine the transcendental regions. We also compare the results of the scaling methods with those of the dynamical approach.

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.

Free Expansion of a Weakly-interacting Dipolar Fermi Gas

We theoretically investigate a polarized dipolar Fermi gas in free expansion. The inter-particle dipolar interaction deforms phase-space distribution in trap and also in the expansion. We exactly predict the minimal quadrupole deformation in the expansion for the high-temperature Maxwell-Boltzmann and zero-temperature Thomas-Fermi gases in the Hartree-Fock and Landau-Vlasov approaches. In conclusion, we provide a proper approach to develop the time-of-flight method for the weakly-interacting dipolar Fermi gas and also reveal a scaling law associated with the Liouvilles theorem in the long-time behaviors of the both gases.

Breathing oscillations and quasi-low-dimensional structures of weakly-interacting degenerate Fermi gases in highly-anisotropic traps

We theoretically investigate breathing oscillations of weakly-interacting degenerate Fermi gases in highly-anisotropic harmonic oscillator traps. If the traps are not highly anisotropic, the fermions behave as three-dimensional (3D) gases and exhibit the coupled breathing oscillations as studied in a previous paper [T. Maruyama and T. Nishimura, Phys. Rev. A 75 (2007) 033611]; Otherwise the fermions exhibit quasi-low-dimensional (QLD) properties derived from specific structures in their single-particle spectrum, called QLD structures. In the present paper, we focus on effects of the QLD structures on the breathing oscillations of the two-component fermions with symmetric population densities. Here we develop the semi-classical Thomas-Fermi approximation extended to the highly-anisotropic systems and obtain the collective frequencies in the sum-rule-scaling method and perturbation theory. As a result, we reveal that the effects of the QLD structures can not be seen in the transverse modes in the first-order perturbation and appear only in the longitudinal modes with hierarchies reflecting the QLD structures. We also demonstrate time-evolution of the oscillations in the present framework.

Coupled Breathing Oscillations of Two-Component Fermion Condensates in Deformed Traps

We investigate collective excitations coupled with monopole and quadrupole oscillations in two-component fermion condensates in deformed traps. The frequencies of monopole and dipole modes are calculated using Thomas-Fermi theory and the scaling approximation. When the trap is largely deformed, these collective motions are decoupled to the transverse and longitudinal breathing oscillation modes. As the trap approaches becoming spherical, however, they are coupled and show complicated behaviors.