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arXiv:1108.3453 · Physical Review A

p -wave stabilization of three-dimensional Bose-Fermi solitons

Nicholas G. Parker, David A. Smith

Published Jan 3, 2012• 7 citations
arXivHTMLPDF

Abstract

We explore bright soliton solutions of ultracold Bose-Fermi gases, showing that the presence of $p$-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 $s$- and $p$-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 $s$-wave interactions, bright solitons exist only as metastable states susceptible to collapse. Remarkably, the presence of repulsive $p$-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 ${}^{87}$Rb and ${}^{40}$K, the stabilization inferred by repulsive $p$-wave interactions should apply to the wider remit of ultracold Bose-Fermi mixtures.

DOI
10.1103/physreva.85.013604

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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 study an ultracold and dilute superfluid Bose-Fermi mixture confined in a strictly one-dimensional (1D) atomic waveguide by using a set of coupled nonlinear mean-field equations obtained from the Lieb-Liniger energy density for bosons and the Gaudin-Yang energy density for fermions. We consider a finite Bose-Fermi interatomic strength gbf{g}_{bf}gbf​ and both periodic and open boundary conditions. We find that with periodic boundary conditions---i.e., in a quasi-1D ring---a uniform Bose-Fermi mixture is stable only with a large fermionic density. We predict that at small fermionic densities the ground state of the system displays demixing if gbf>0{g}_{bf}>0gbf​>0 and may become a localized Bose-Fermi bright soliton for gbf<0{g}_{bf}<0gbf​<0. Finally, we show, using variational and numerical solutions of the mean-field equations, that with open boundary conditions---i.e., in a quasi-1D cylinder---the Bose-Fermi bright soliton is the unique ground state of the system with a finite number of particles, which could exhibit a partial mixing-demixing transition. In this case the bright solitons are demonstrated to be dynamically stable. The experimental realization of these Bose-Fermi bright solitons seems possible with present setups.