Coupled breathing oscillations of two-component fermion condensates in deformed traps

Abstract

We investigate collective excitations coupled with monopole and quadrupole oscillations in twocomponent 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.

Shell Effects in the First Sound Velocity of an Ultracold Fermi Gas

“…In fact, due to the large anisotropy, transverse modes are decoupled from the axial sound modes. 31 As previously stressed the Fermi gas is strictly 1D only for 0 ≤ n 1 < 2 3/2 /(πa ⊥ ), i.e. for 0 ≤ µ <hω ⊥ .…”

Breathing Oscillations and Quasi-Low-Dimensional Structures of Weakly-Interacting Degenerate Fermi Gases in Highly-Anisotropic Traps

“…Especially in spherical systems, they indicate the monopole oscillations in terms of the multipole expansion. However, in anisotropic systems, the monopole oscillations are inseparably mixed with incompressive oscillations, e.g., the quadrupole oscillations [1] and then it is necessary to redefine the breathing oscillations as mixtures of those oscillations. In the present paper, we adopt the later definition for the anisotropic systems.…”

“…In theory, those collective excitations can be treated in the time-dependent mean-field theory for weakly-correlated systems and random-phase approximation (RPA) for small amplitude excitations [23][24][25]. Especially for pure collective excitations, simpler methods can be adopted to calculate collective frequencies of the minimal oscillations, e.g., the sumrule method [26] and scaling method [1,[27][28][29]. Note that the sum-rule and scaling methods are related to each other as explained in appendix A.…”

“…In another previous paper [1], furthermore, we study the breathing oscillations of the two-component degenerate Fermi gases in anisotropic harmonic oscillator traps with various trap frequencies and obtain the coupled collective frequencies of the longitudinal and transverse oscillations. At that time, we assume the usual trap anisotropy and apply the conventional Thomas-Fermi approximation (TFA) to the 3D gases in order to predict the collective frequencies in the sum-rule-scaling method.…”

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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 [1]; 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.

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