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arXiv:cond-mat/0601350 · Physical Review A

Bright solitons in Bose-Fermi mixtures

Tomasz Karpiuk, Mirosław Brewczyk, Kazimierz Rza̧żewski

Published May 3, 2006• 38 citations
arXivHTMLPDF

Abstract

We consider the formation of bright solitons in a mixture of Bose and Fermi degenerate gases confined in a three-dimensional elongated harmonic trap. The Bose and Fermi atoms are assumed to effectively attract each other whereas bosonic atoms repel each other. Strong enough attraction between bosonic and fermionic components can change the character of the interaction within the bosonic cloud from repulsive to attractive making thus possible the generation of bright solitons in the mixture. On the other hand, such structures might be in danger due to the collapse phenomenon existing in attractive gases. We show, however, that under some conditions (defined by the strength of the Bose-Fermi components attraction) the structures which neither spread nor collapse can be generated. For elongated enough traps the formation of solitons is possible even at the ``natural'' value of the mutual Bose-Fermi ($^{87}\mathrm{Rb}\text{\ensuremath{-}}^{40}\mathrm{K}$ in our case) scattering length.

DOI
10.1103/physreva.73.053602

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We consider the formation of bright solitons in a mixture of Bose and Fermi degenerate gases confined in a three-dimensional elongated harmonic trap. The Bose and Fermi atoms are assumed to effectively attract each other whereas bosonic atoms repel each other. Strong enough attraction between bosonic and fermionic components can change the character of the interaction within the bosonic cloud from repulsive to attractive making thus possible the generation of bright solitons in the mixture. On the other hand, such structures might be in danger due to the collapse phenomenon existing in attractive gases. We show, however, that under some conditions (defined by the strength of the Bose-Fermi components attraction) the structures which neither spread nor collapse can be generated. For elongated enough traps the formation of solitons is possible even at the ``natural'' value of the mutual Bose-Fermi (87Rb\ensuremath-40K^{87}\mathrm{Rb}\text{\ensuremath{-}}^{40}\mathrm{K}87Rb\ensuremath-40K in our case) scattering length.
We theoretically consider the formation of bright solitons in a mixture of Bose and Fermi degenerate gases. While we assume the forces between atoms in a pure Bose component to be effectively repulsive, their character can be changed from repulsive to attractive in the presence of fermions provided the Bose and Fermi gases attract each other strongly enough. In such a regime the Bose component becomes a gas of effectively attractive atoms. Hence, generating bright solitons in the bosonic gas is possible. Indeed, after a sudden increase of the strength of attraction between bosons and fermions (realized by using a Feshbach resonance technique or by firm radial squeezing of both samples) soliton trains appear in the Bose-Fermi mixture.
We use a time-dependent dynamical mean-field-hydrodynamic model to study the formation of fermionic bright solitons in a trapped degenerate Fermi gas mixed with a Bose-Einstein condensate in a quasi-one-dimensional cigar-shaped geometry. Due to a strong Pauli-blocking repulsion among spin-polarized fermions at short distances there cannot be bright fermionic solitons in the case of repulsive boson-fermion interactions. However, we demonstrate that stable bright fermionic solitons can be formed for a sufficiently attractive boson-fermion interaction in a boson-fermion mixture. We also consider the formation of fermionic solitons in the presence of a periodic axial optical-lattice potential. These solitons can be formed and studied in the laboratory with present technology.
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.
It is shown that a Bose-Fermi mixture of a degenerate gas of spin-polarized fermions, whose number significantly exceeds the number of bosons, embedded in a strongly anisotropic trap, is described by the one-dimensional coupled nonlinear Schr\"odinger equation for the boson component and the wave equation with external source for the fermion component. Depending on the type of boson-fermion interaction, the system may display modulational instability and the existence of solitons in the fermion and boson components, respectively. Such solitons represent either a local decrease (increase) of the density of both the components or a decrease of the density in one component and an increase of the density in the other component. It is shown that the type of the effective interactions can be easily managed by varying the trap geometry or by means of Feshbach resonance.
The recent experimental realisation of Bose–Fermi superfluid mixtures of dilute ultracold atomic gases has opened new perspectives in the study of quantum many-body systems. Depending on the values of the scattering lengths and the amount of bosons and fermions, a uniform Bose–Fermi mixture is predicted to exhibit a fully mixed phase, a fully separated phase or, in addition, a purely fermionic phase coexisting with a mixed phase. The occurrence of this intermediate configuration has interesting consequences when the system is nonuniform. In this work we theoretically investigate the case of solitonic solutions of coupled Bogoliubov–de Gennes and Gross–Pitaevskii equations for the fermionic and bosonic components, respectively. We show that, in the partially separated phase, a dark soliton in Fermi superfluid is accompanied by a broad bosonic component in the soliton, forming a dark–bright soliton which keeps full spatial coherence.
We explore bright soliton solutions of ultracold Bose-Fermi gases, showing that the presence of ppp-wave interactions can remove the usual collapse instability and support stable soliton solutions that are global energy minima. A variational model that incorporates the relevant sss- and ppp-wave interactions in the system is established analytically and solved to probe the dependencies of the soliton stationary states on key experimental parameters. Under attractive sss-wave interactions, bright solitons exist only as metastable states susceptible to collapse. Remarkably, the presence of repulsive ppp-wave interactions alleviates this collapse instability. This dramatically widens the range of experimentally achievable soliton solutions and indicates greatly enhanced robustness. While we focus specifically on the boson-fermion pairing of 87{}^{87}87Rb and 40{}^{40}40K, the stabilization inferred by repulsive ppp-wave interactions should apply to the wider remit of ultracold Bose-Fermi mixtures.