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arXiv:1010.5800 · Physical Review A

Position swapping and pinching in Bose-Fermi mixtures with two-color optical Feshbach resonances

Sandeep Gautam, Paulsamy Muruganandam, D. Angom

Published Feb 10, 2011• 5 citations
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Abstract

We examine the density profiles of the quantum degenerate Bose-Fermi mixture of $^{174}\mathrm{Yb}$-$^{173}\mathrm{Yb}$, experimentally observed recently, in the mean-field regime. In this mixture there is a possibility of tuning the Bose-Bose and Bose-Fermi interactions simultaneously using two well-separated optical Feshbach resonances, and it is a good candidate to explore phase separation in Bose-Fermi mixtures. Depending on the Bose-Bose scattering length ${a}_{\mathrm{BB}}$, as the Bose-Fermi interaction is tuned the density of the fermions is pinched or swapping with bosons occurs.

DOI
10.1103/physreva.83.023605

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We study a dilute mixture of degenerate bosons and fermions across a Feshbach resonance of the Fermi-Fermi scattering length aF{a}_{F}aF​. This scattering length is renormalized by the boson-induced interaction between fermions and its value is crucial to determine the phase diagram of the system. For the mixture in a box and a positive Bose-Fermi scattering length, we show that there are three possibilities: A single uniform mixed phase, a purely fermionic phase coexisting with a mixed phase, and a purely fermionic phase coexisting with a purely bosonic one. As 1∕aF1∕{a}_{F}1∕aF​ is increased from a negative value to the Feshbach resonance (1∕aF=0)(1∕{a}_{F}=0)(1∕aF​=0), the region of pure separation increases and the other two regions are strongly reduced. Above the Feshbach resonance (1∕aF>0)(1∕{a}_{F}>0)(1∕aF​>0), pairs of Fermi atoms become Bose-condensed molecules. We find that these molecules are fully spatially separated from the bosonic atoms when 1∕aF1∕{a}_{F}1∕aF​ exceeds a critical value. For a negative Bose-Fermi scattering length we deduce the condition for collapse, which coincides with the onset of dynamical instability of the fully mixed phase. We consider also the mixture in a harmonic trap and determine the conditions for partial demixing, full demixing, and collapse. The experimental implications of our results are investigated by analyzing mixtures of $^{6}\mathrm{Li}\text{\ensuremath{-}}^{23}\mathrm{Na}$ and $^{40}\mathrm{K}\text{\ensuremath{-}}^{87}\mathrm{Rb}$ atoms.
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We control the interspecies interaction in a two-species atomic quantum mixture by tuning the magnetic field at a Feshbach resonance. The mixture is composed by fermionic 40K^{40}\mathrm{K}40K and bosonic 87Rb^{87}\mathrm{Rb}87Rb. We observe effects of the large attractive and repulsive interaction energy across the resonance, such as collapse or a reduced spatial overlap of the mixture, and we accurately locate the resonance position and width. Understanding and controlling instabilities in this mixture opens the way to a variety of applications, including formation of heteronuclear molecular quantum gases.
ENGLISH ABSTRACT: We present a theoretical approach that allows for the description of trapped Bose-Fermi mixtures with a tunable interspecies interaction in the vicinity of a Feshbach resonance magnetic field.The many-body physics of the system is treated at equilibrium using the well-established mean-field and local density approximations. This reduces the physics locally to that of a homogeneous system. We observe a rich local phase structure exhibiting both first and second order phase transitions between the normal and BEC phases. We also consider the global properties of the mixture at a fixed number of particles and investigate how the density profiles and the populations of the various particle species depend on the detuning and trap profile.