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Laser Physics

Vortex States in Fermi-Bose Mixtures

M. Guilleumas, Dora M. Jezek, M. Barranco, R. Mayol, Martí Pi

Published Dec 1, 2005• 0 citations
OpenAlex

Abstract

We consider a vortex state in a confined mixture of bosons and fermions in the quantal degeneracy regime with attractive boson–fermion interactions. Within a mean-field description, we obtain the equilibrium configurations and investigate the phase-stability diagram of the K–Rb mixture assuming that the Bose–Einstein \ncondensate sustains a quantized vortex line.

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We consider a vortex state in a confined mixture of bosons and fermions in the quantal degeneracy regime with attractive boson–fermion interactions. Within a mean-field description, we obtain the equilibrium configurations and investigate the phase-stability diagram of the K–Rb mixture assuming that the Bose–Einstein \ncondensate sustains a quantized vortex line.
We study a confined mixture of bosons and fermions in the quantal degeneracy regime with attractive boson-fermion interaction. We discuss the effect that the presence of vortical states and the displacement of the trapping potentials may have on mixtures near collapse, and investigate the phase stability diagram of the K-Rb mixture in the mean-field approximation supposing in one case that the trapping potentials felt by bosons and fermions are shifted from each other, as it happens in the presence of a gravitational sag, and in another case, assuming that the Bose condensate sustains a vortex state. In both cases, we have obtained an analytical expression for the fermion effective potential when the Bose condensate is in the Thomas-Fermi regime, that can be used to determine the maxima of the Fermionic density. We have numerically checked that the values one obtains for the location of these maxima using the analytical formulas remain valid up to the critical boson and fermion numbers, above which the mixture collapses.
An effective Hamiltonian for the Bose subsystem for the mixture of ultracold atomic clouds of bosons and fermions is obtained by integrating out the fermion degrees of freedom. Using the effective Hamiltonian, a collapse of the trapped boson-fermion mixture due to the boson-fermion attractive interaction without and in the presence of the quantized vortices is studied in the framework of variational Bose wave function and Thomas-Fermi approximation. The properties of the 87Rb^{87}\mathrm{Rb}87Rb and 40K^{40}\mathrm{K}40K mixture are analyzed quantitatively. The critical number of bosons for the collapse transition is estimated without and in the presence of the vortices as a function of the fermion number. It is shown that the critical number of bosons increases in the presence of the vortex. The vortex critical velocities are calculated as functions of the numbers of bosons and fermions.
Using mean field theory, we have studied Bose-Fermi mixtures in a one-dimensional optical lattice in the case of an attractive boson-fermion interaction. We consider that the fermions are in the degenerate regime and that the laser intensities are such that quantum coherence across the condensate is ensured. We discuss the effect of the optical lattice on the critical rotational frequency for vortex line creation in the Bose-Einstein condensate, as well as how it affects the stability of the boson-fermion mixture. A reduction of the critical frequency for nucleating a vortex is observed as the strength of the applied laser is increased. The onset of instability of the mixture occurs for a sizably lower number of fermions in the presence of a deep optical lattice.
We study a single quantized vortex in the fermionic component of a mixture of Fermi superfluid and Bose-Einstein condensate. As the density ratio between the boson and the fermion components is tuned, we identify a transition in the vortex-core structure, across which fermions in the vortex core become completely depleted even in the weak-coupling Bardeen-Cooper-Schrieffer regime. This is accompanied by changes in key properties of the vortex state, as well as by the localization of the Bose-Einstein condensate in the vortex core. The transition in the vortex-core structure can be experimentally probed in Bose-Fermi superfluid mixtures by detecting the size and visibility of the vortices.