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arXiv:cond-mat/0607119 · Physical Review A

Mixing-demixing in a trapped degenerate fermion-fermion mixture

Sadhan K. Adhikari

Published Apr 27, 2006• 25 citations
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Abstract

We use a time-dependent dynamical mean-field-hydrodynamic model to study mixing-demixing in a degenerate fermion-fermion mixture (DFFM). It is demonstrated that with the increase of interspecies repulsion and/or trapping frequencies, a mixed state of a DFFM could turn into a fully demixed state in both three-dimensional spherically symmetric as well as quasi-one-dimensional configurations. Such a demixed state of a DFFM could be experimentally realized by varying an external magnetic field near a fermion-fermion Feshbach resonance, which will result in an increase of interspecies fermion-fermion repulsion, and/or by increasing the external trap frequencies.

DOI
10.1103/physreva.73.043619

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We use a time-dependent dynamical mean-field-hydrodynamic model to study mixing-demixing in a degenerate fermion-fermion mixture (DFFM). It is demonstrated that with the increase of interspecies repulsion and/or trapping frequencies, a mixed state of a DFFM could turn into a fully demixed state in both three-dimensional spherically symmetric as well as quasi-one-dimensional configurations. Such a demixed state of a DFFM could be experimentally realized by varying an external magnetic field near a fermion-fermion Feshbach resonance, which will result in an increase of interspecies fermion-fermion repulsion, and/or by increasing the external trap frequencies.
We investigate the mixing-demixing transition and the collapse in a quasi-two-dimensional degenerate boson-fermion mixture (DBFM) with a bosonic vortex. We solve numerically a quantum-hydrodynamic model based on a new density functional which accurately takes into account the dimensional crossover. It is demonstrated that with the increase of interspecies repulsion, a mixed state of DBFM could turn into a demixed state. The system collapses for interspecies attraction above a critical value which depends on the vortex quantum number. For interspecies attraction just below this critical limit there is almost complete mixing of boson and fermion components. Such mixed and demixed states of a DBFM could be experimentally realized by varying an external magnetic field near a boson-fermion Feshbach resonance, which will result in a continuous variation of interspecies interaction.
We use a time-dependent dynamical hydrodynamic model to study a collapse in a degenerate fermion–fermion mixture (DFFM) of different atoms. Due to a strong Pauli-blocking repulsion among identical spin-polarized fermions at short distances, there cannot be a collapse for repulsive interspecies fermion–fermion interaction. However, there can be a collapse for a sufficiently attractive interspecies fermion–fermion interaction in a DFFM of different atoms. Using a variational analysis and numerical solution of the hydrodynamic model, we study different aspects of collapse in such a DFFM initiated by a jump in the interspecies fermion–fermion interaction (scattering length) to a large negative (attractive) value using a Feshbach resonance. Suggestion for experiments of collapse in a DFFM of distinct atoms is made.
The time evolution of a dilute atomic boson-fermion mixture is studied at zero temperature, when the external magnetic field is brought close to an interspecies Feshbach resonance. On short time scales we find that before a collapse or phase separation of the mixture can occur, oscillations between fermionic atoms and heteronuclear molecules dominate the dynamics. Applying the model presented here to a trapped mixture of ${}^{40}\mathrm{K}{\ensuremath{-}}^{87}\mathrm{Rb}$ atoms, we find that the predicted oscillations can be revealed in degenerate mixtures of these atoms.
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.
We use a semiclassical three-fluid model to evaluate the phenomena of spatial demixing in mesoscopic clouds of fermionic and bosonic atoms at high dilution under harmonic confinement. We assume repulsive boson-boson and boson-fermion interactions and include a bosonic thermal cloud at finite temperature T.T.T. The finite system size allows three different regimes for the equilibrium density profiles at T=0:T=0:T=0: a fully mixed state, a partially mixed state in which the overlap between bosons and fermions is decreasing, and a fully demixed state where the two clouds have zero overlap. We propose simple analytical rules for the two crossovers between the three regimes as functions of the system parameters and support these rules by extensive numerical calculations. A universal ``phase diagram'' is shown to be valid for the transition to the regime of full demixing, where we identify several exotic configurations in addition to simple ones consisting of a core of bosons enveloped by fermions and vice versa. With increasing temperature some exotic configurations are transformed into more symmetric ones, until demixing is ultimately lost. For very high values of the boson-fermion repulsion we also report demixing between the fermions and the thermally excited bosons.
We evaluate in a mean-field model the equilibrium stability conditions of a gaseous mixture of bosonic and spin-polarized fermionic atoms inside a pancake-shaped or a cigar-shaped harmonic trap, under conditions such that the trap thickness approaches the magnitude of the s -wave scattering lengths but the atoms still experience collisions in three dimensions. With decreasing dimensionality, the Fermi pressure plays an increasingly dominant role. Full demixing in the case of repulsive boson-fermion interactions can be induced by squeezing the thickness of the clouds in a pancake-shaped trap or by lowering the number of trapped fermions in a cigar-shaped trap. Collapse under attractive interspecies interaction in quasi-one-dimensional confinement is inhibited within the range of validity of a mean-field model.