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arXiv:1211.5616 · Physical Review A

Faraday waves in quasi-one-dimensional superfluid Fermi-Bose mixtures

F. Kh. Abdullaev, Magnus Ögren, Mads Peter Sørensen

Published Feb 15, 2013• 32 citations
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Abstract

The generation of Faraday waves in superfluid Fermi-Bose mixtures in elongated traps is investigated. The generation of waves is achieved by periodically changing a parameter of the system in time. Two types of modulations of parameters are considered: a variation of the fermion-boson scattering length and the boson-boson scattering length. We predict the properties of the generated Faraday patterns and study the parameter regions where they can be excited.

DOI
10.1103/physreva.87.023616

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The generation of Faraday waves in superfluid Fermi-Bose mixtures in elongated traps is investigated. The generation of waves is achieved by periodically changing a parameter of the system in time. Two types of modulations of parameters are considered: a variation of the fermion-boson scattering length and the boson-boson scattering length. We predict the properties of the generated Faraday patterns and study the parameter regions where they can be excited.
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Abstract Faraday waves (FW) are studied in mixtures of Bose gases by taking into account quantum fluctuations beyond the GP mean-field formalism with the Lee-Huang-Yang term, with both inter-and intra-species scattering lengths periodically varying in time. In this case, the effect of periodic modulations on the system is studied, with nonlinear resonances shown to be excited in the oscillation widths of quantum droplets. It was shown that the period of the Faraday patterns is quite sensitive to the estimated value obtained by the beyond mean-field contribution, which can be used to measure quantum fluctuations in the ground state of the quasi-one-dimensional mixture. Variational predictions are confirmed by full numerical simulations. We also add an analysis of quantum droplets and quantum fluctuation contributions when considering three-body interactions.
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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 ($^{87}\mathrm{Rb}\text{\ensuremath{-}}^{40}\mathrm{K}$ in our case) scattering length.
Collective oscillations of superfluid mixtures of ultracold fermionic and bosonic atoms are investigated while varying the fermion-boson scattering length. We study the dynamics with respect to excited center of mass modes and breathing modes in the mixture. Parametric resonances are also analyzed when the scattering length varies periodically in time, by comparing partial differential equation models and ordinary differential equation models for the dynamics. An application to the recent experiment with fermionic 6Li^{6}\mathrm{Li}6Li and bosonic 7Li^{7}\mathrm{Li}7Li atoms, which approximately have the same masses, is discussed.
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.