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Acta Physica Sinica

Variational-method analysis of stability of Bose-Fermi mixture

Chen Hai-Jun, Li Gao-Qing, Xue Ju-Kui

Published Jan 1, 2011• 2 citations
Publisher

Abstract

In one-dimensional trapped Bose-Fermi mixture, described by time-dependent one-dimensional nonlinear equations that are derived from a three-dimensional Bose-Fermi system, we study the effect of atom-interactions on stability using a Gaussian Variational approach. We investigate the stable and the unstable conditions as functions of the atoms number and s-wave scattering length. We find that the interaction between the different species of atoms has significant effect on the stability of Bose-Fermi mixture. We also give critical conditions of the atoms number and s-wave scattering length for both special and general cases.

DOI
10.7498/aps.60.040304.1

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In one-dimensional trapped Bose-Fermi mixture, described by time-dependent one-dimensional nonlinear equations that are derived from a three-dimensional Bose-Fermi system, we study the effect of atom-interactions on stability using a Gaussian Variational approach. We investigate the stable and the unstable conditions as functions of the atoms number and s-wave scattering length. We find that the interaction between the different species of atoms has significant effect on the stability of Bose-Fermi mixture. We also give critical conditions of the atoms number and s-wave scattering length for both special and general cases.
The influence of boson-boson and boson-fermion interactions on the stability of a binary mixture of bosonic and fermionic atoms is investigated. The density profiles of the trapped mixture are obtained from direct numerical solution of a modified Gross-Pitaevskii equation that is self-consistently coupled to the mean field generated by the interaction with the fermionic species, the fermions which in turn feel the mean field created by the bosons are treated in the Thomas-Fermi approximation. We study the effects of different combinations of signs of the boson-boson and the boson-fermion scattering lengths and determine explicit expressions for critical particle numbers as a function of these scattering lengths.
We consider the stability of a mixture of degenerate Bose and Fermi gases. Even though the bosons effectively repel each other, the mixture can still collapse provided the Bose and Fermi gases attract each other strongly enough. For a given number of atoms and the strengths of the interactions between them, we find the geometry of a maximally compact trap that supports the stable mixture. We compare a simple analytical estimation for the critical axial frequency of the trap with results based on the numerical solution of hydrodynamic equations for the Bose–Fermi mixture.
The stability of Bose-Fermi gases trapped in an isotropic potentials at ultracold temperature is strongly influenced by the interaction between the fermions and the bosons. At zero temperature, the stability criterion is given in this paper using variation method, the results show that whether a fermion-boson mixture is stable depends mainly on the interaction between the fermions and the bosons. For finite temperature, however, the stability is not only related to the coupling constants, but also to the temperature. The stability conditions for finite temperature are also derived and discuss in details in this paper.
We study a Bose–Fermi mixture within the framework of the mean-field theory, including three possible regimes for the fermionic species: fully polarized, BCS, and unitarity. Starting from the 3D description and using the variational approximation (VA), we derive one-dimensional and two-dimensional systems of equations, under the corresponding confining potentials. This method produces a pair of nonlinear Schrödinger equations coupled to algebraic equations for the transverse widths of the confined state. The equations incorporate interactions between atoms of the same species and between the species, assuming that the latter can be manipulated by means of the Feshbach resonance. As an application, we explore spatial density correlations in the ground state (GS) between the species, concluding that they strongly depend on the sign and strength of the inter-species interaction. Also studied are the dynamics of the mixture in a vicinity of the GS and the corresponding spatiotemporal inter-species correlation. The correlations are strongly affected by the fermionic component, featuring the greatest variation in the unitary regime. Results produced by the VA are verified by comparison with full numerical solutions.
In three-dimensional trapped Bose-Einstein condensate (BEC), described by the time-dependent Gross-Pitaevskii-Ginzburg equation, we study the effect of initial conditions on stability using a Gaussian variational approach and exact numerical simulations. We also discuss the validity of the criterion for stability suggested by Vakhitov and Kolokolov. The maximum initial chirp (initial focusing defocusing of cloud) that can lead a stable condensate to collapse even before the number of atoms reaches its critical limit is obtained for several specific cases. When we consider two- and three-body nonlinear terms, with negative cubic and positive quintic terms, we have the conditions for the existence of two phases in the condensate. In this case, the magnitude of the oscillations between the two phases are studied considering sufficient large initial chirps. The occurrence of collapse in a BEC with repulsive two-body interaction is also shown to be possible.