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arXiv:0907.1096 · Physical Review A

Two-dimensional boson-fermion mixtures

A. Levent Subaşı, S. Sevinçli, Patrizia Vignolo, B. Tanatar

Published Jun 30, 2009• 7 citations
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Abstract

Using mean-field theory, we study the equilibrium properties of boson-fermion mixtures confined in a harmonic pancake-shaped trap at zero temperature. When the modulus of the $s$-wave scattering lengths are comparable to the mixture thickness, two-dimensional scattering events introduce a logarithmic dependence on density in the coupling constants, greatly modifying the density profiles themselves. We show that, for the case of a negative boson-fermion three-dimensional $s$-wave scattering length, the dimensional crossover stabilizes the mixture against collapse and drives it toward spatial demixing.

DOI
10.1103/physreva.79.063632

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Using mean-field theory, we study the equilibrium properties of boson-fermion mixtures confined in a harmonic pancake-shaped trap at zero temperature. When the modulus of the sss-wave scattering lengths are comparable to the mixture thickness, two-dimensional scattering events introduce a logarithmic dependence on density in the coupling constants, greatly modifying the density profiles themselves. We show that, for the case of a negative boson-fermion three-dimensional sss-wave scattering length, the dimensional crossover stabilizes the mixture against collapse and drives it toward spatial demixing.
We investigate the equilibrium properties of boson-fermion mixtures consisting of a Bose condensate and spin-polarized Fermi gas confined in a harmonic two-dimensional (2D) trap using mean-field theory. Boson-boson and boson-fermion coupling constants have a logarithmic dependence on the density because of the two-dimensional scattering events when the s -wave scattering lengths are on the order of mixture thickness. We show that this modifies the density profiles significantly. It is also shown that the dimensional crossover stabilizes the mixture against collapse and spatial demixing is observed for the case of a negative boson-fermion scattering length.
We evaluate in a mean-field model the equilibrium stability conditions of a gaseous mixture of bosonic and spin-polarized fermionic atoms inside a pancake-shaped or a cigar-shaped harmonic trap, under conditions such that the trap thickness approaches the magnitude of the s -wave scattering lengths but the atoms still experience collisions in three dimensions. With decreasing dimensionality, the Fermi pressure plays an increasingly dominant role. Full demixing in the case of repulsive boson-fermion interactions can be induced by squeezing the thickness of the clouds in a pancake-shaped trap or by lowering the number of trapped fermions in a cigar-shaped trap. Collapse under attractive interspecies interaction in quasi-one-dimensional confinement is inhibited within the range of validity of a mean-field model.
Two-dimensionality of the scattering events in a Bose-Einstein condensate introduces a logarithmic dependence on density in the coupling constant entering a mean-field theory of the equilibrium density profile, which becomes dominant as the s-wave scattering length gets larger than the condensate thickness. We analyze quantitatively the role of the form of the coupling constant in determining the transverse profile of a condensate confined in a harmonic pancake-shaped trap at zero temperature. We trace the regions of experimentally accessible system parameters for which the cross-over between different dimensionality behaviors may become observable through in situ imaging of the condensed cloud with varying trap anisotropy and scattering length.
The structure of trapped binary mixtures of bosonic and fermionic atoms at zero temperature is studied using a modified Gross-Pitaevskii equation for the bosons which self-consistently includes the mean-field interaction generated by the fermionic cloud. The density of the fermionic component is described within the Thomas-Fermi approximation. The influence of the boson-boson and the boson-fermion s-wave interaction on the density profiles and the stability of the mixture is investigated systematically. Critical particle numbers for the mean-field collapse caused either by attractive boson-boson or by attractive boson-fermion interactions and for the onset of spatial component separation are discussed. It is shown that the interplay between the boson-boson and the boson-fermion interaction generates a rich and complex phase diagram. Finally, the specific properties and prospects of the boson-fermion mixtures available in present experiments are addressed.
We present mean-field calculations of the equilibrium state in a gaseous mixture of bosonic and spin-polarized fermionic atoms with repulsive or attractive interspecies interactions, confined inside a cigar-shaped trap under conditions such that the radial thickness of the two atomic clouds is approaching the magnitude of the s-wave scattering lengths. In this regime the kinetic pressure of the fermionic component is dominant. Full demixing under repulsive boson-fermion interactions can occur only when the number of fermions in the trap is below a threshold, and collapse under attractive interactions is suppressed within the range of validity of the mean-field model. Specific numerical illustrations are given for values of system parameters obtaining in 7Li-6Li clouds.
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.