Correlations and synchronization in a Bose–Fermi mixture

Abstract

We study a Bose-Fermi mixture within the framework of the meanfield theory, including three possible regimes for the fermionic species: fully polarized, BCS, and unitarity. Starting from the 3D description and using the variational approximation (VA), we derive 1D and 2D systems of equations, under the corresponding confining potentials. This method produces a pair of nonlinear Schrödinger (NLS) equations coupled to algebraic equations for the transverse widths of the confined state. The equations incorporate interactions between atoms of the same species and between the species, assuming that the latter can be manipulated by means of the Feshbach resonance (FR). As an application, we explore spatial density correlations in the ground state (GS) between the species, concluding that they strongly depend on the sign and strength of the inter-species interaction. Also studied are the dynamics of the mixture in a vicinity of the GS and the corresponding spatiotemporal inter-species correlation. The correlations are strongly affected by the fermionic component, featuring the greatest variation in the unitary regime. Results produced by the VA are verified by comparison with full numerical solutions.

The Variational Reduction for Low-Dimensional Fermi Gases and Bose–Fermi Mixtures: A Brief Review

“…where L B and L F are the Lagrangian densities of the Bose and Fermi components, while L BF accounts for the interaction between them [58]:…”

“…In the next two subsections we reduce the full 3D system to the corresponding 2D and 1D effective systems, using the VA proposed in Ref. [58].…”

“…This figure is taken from Ref. [58]. three possible regimes are considered for the fermions: fully polarized, BCS, and unitarity.…”

“…Here, we address, in particular, dark solitons in the 7 Li- 6 Li BFM, using the effective low-dimensional equations derived in Ref. [58].…”

Two-dimensional composite solitons in a spin-orbit-coupled fermi gas in free space

“…remain stable when, respectively, the cross-or self-interaction is repulsive, the self-trapping being provided by the stronger self-(cross-) attraction for SVs (MMs) [55]. The aim of the present work is to obtain soliton solutions in the model of an oblate (quasi-2D) Fermi superfluid, based on the known 2D density-functional equations [34][35][36][37][38][39][40][41][42], to which SOC terms are added. We demonstrate that the system produces quiescent composite solitons in the free 2D space.…”