Breathing oscillations and quasi-low-dimensional shell-structures of fermion condensates in super-anisotropic traps

Abstract

Takushi Nishimura ∗ and Tomoyuki Maruyama 3, 4, † Division of Advanced Sciences, Ochadai Academic Production, Ochanomizu University, Otsuka, Bunkyo, Tokyo 112-8610, Japan College of Bioresource Sciences, Nihon University, Fujisawa 252-8510, Japan Advanced Science Research Center, Japan Atomic Energy Research Institute,Tokai 319-1195, Japan Department of Physics, Tokyo Metropolitan University, Hachioji, Tokyo 192-0397, Japan Abstract We theoretically investigate breathing oscillations of fermion condensates in anisotropic harmonic oscillator traps. When anisotropy of the trap is not large, the Fermi gases behave as threedimensional (3D) gases, and those breathing oscillations are studied in the previous work [1]; when the trap is super-anisotropic, the fermions show quasi-low-dimensional (QLD) properties differently from the 3D gases because of variation of one-particle energy-level densities, which exhibit specific types of shell-structures, QLD shell-structures, in super-anisotropic systems. In the present work, we study the effects of the QLD shell-structures on the breathing oscillations of the week-interacting fermion condensates with same number densities. The QLD shell-structures are described in the semi-classical Thomas-Fermi approximation (TFA) extended to the super-anisotropic systems, and the collective frequencies of the breathing oscillations are estimated in the scaling and sum-rule methods with the perturbation theory and extended TFA up to the first order in a coupling constant of inter-atomic interaction. As a result, we reveal that the effects of the QLD shell-structures on the collective frequencies disappear in transverse modes in both of the oblate and prolate deformed traps, and appear only in longitudinal modes with hierarchic structures associated with the trap anisotropy. We also demonstrate time-evolution of the oscillations in the present framework.