Abstract
We present a summary of some recent theoretical results for matter-wave patterns in Fermi and Bose–Fermi degenerate gases, obtained in the framework of the quasi-mean-field approximation. We perform a dimensional reduction from the three-dimensional (3D) equations of motion to 2D and 1D effective equations. In both cases, comparison of the low-dimensional reductions to the full model is performed, showing very good agreement for ground-state solutions. Some complex dynamical regimes are reported too for the corresponding 1D systems.
Highlights
Ultracold atomic gases have been widely explored from both experimental and theoretical point of view due to their ability to emulate many effects from condensed-matter physics and create novel states of quantum matter
We show that the attractive interaction of fermions with bosons in a state different from the ground state (GS) eventually generates a gas of dark solitons
The results demonstrate that the variational approximation (VA) profiles are very similar to their counterparts produced by the 3D simulations, the present approximation provides good accuracy and allows one to study dynamical features of the Bose-Fermi mixtures (BFMs) in a sufficiently simple form
Summary
Ultracold atomic gases have been widely explored from both experimental and theoretical point of view due to their ability to emulate many effects from condensed-matter physics and create novel states of quantum matter. For dark solitons in Fermi gases, several works have reported theoretical and experimental results [26,27,28,29,30,31,32]. The reduced 1D equation for Fermi gases was used for studies of interactions between dark solitons [21]. We address, in particular, dark solitons in the 7Li-6Li BFM, using the effective low-dimensional equations derived in Ref. Using the corresponding effective equations, we address various dynamical settings, such as dark solitons and their interactions. For the 1D situation, we address the formation of dark solitons in the mixture, and compare the corresponding 1D solution to results of the full numerical simulations, observing good agreement between them.
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